Evaluation of hospital disaster preparedness by a multi-criteria decision making approach: The case of Turkish hospitals.

Considering the unexpected emergence of natural and man-made disasters over the world and Turkey, the importance of preparedness of hospitals, which are the first reference points for people to get healthcare services, becomes clear. Determining the level of disaster preparedness of hospitals is an important and necessary issue. This is because identifying hospitals with low level of preparedness is crucial for disaster preparedness planning. In this study, a hybrid fuzzy decision making model was proposed to evaluate the disaster preparedness of hospitals. This model was developed using fuzzy analytic hierarchy process (FAHP)-fuzzy decision making trial and evaluation laboratory (FDEMATEL)-technique for order preference by similarity to ideal solutions (TOPSIS) techniques and aimed to determine a ranking for hospital disaster preparedness. FAHP is used to determine weights of six main criteria (including hospital buildings, equipment, communication, transportation, personnel, flexibility) and a total of thirty-six sub-criteria regarding disaster preparedness. At the same time, FDEMATEL is applied to uncover the interdependence between criteria and sub-criteria. Finally, TOPSIS is used to obtain ranking of hospitals. To provide inputs for TOPSIS implementation, some key performance indicators are established and related data is gathered by the aid of experts from the assessed hospitals. A case study considering 4 hospitals from the Turkish healthcare sector was used to demonstrate the proposed approach. The results evidenced that Personnel is the most important factor (global weight = 0.280) when evaluating the hospital preparedness while Flexibility has the greatest prominence (c + r = 23.09).

Introduction

Disaster incidents are one of the most endangering events in human life and emergency solutions are needed because of their sudden occurrence [1]. As such events have devastating effects; they may cause some disruptions in the society to meet their health needs. Man-made and natural disasters can interfere with the activities of some organizations such as healthcare facilities. Sometimes the capacity of these facilities may not be sufficient to combat the physical and financial damage they may cause. Although the ability to be ready for disasters varies by country, it can be said that in the last century, when the frequency and devastating effects of disasters have gradually increased, no country is fully prepared and safe. Turkey, which has experienced many devastating man-made and natural disasters, faces 8 disasters per year (natural and technological) on average. These resulted in 1043 death and 2937 injured annually on average according to the figures in the Emergency Events Database [2]. The disaster trends of Turkey are demonstrated in Fig. 1 . According to these statistics, these disasters have caused serious total damage in terms of financial loss. Turkey has passed a devastating earthquake on 17th August 1999 as can be easily inferred from Fig. 1.

Fig. 1

Disaster trends of Turkey between 1999-2020 (Source: IM-DAT).

Also, in the following years after 1999, earthquakes, mine accidents, floods, transport accidents, storms, epidemics, landslides, and miscellaneous industrial accidents have occurred in Turkey. All of these disasters, especially earthquakes due to their destructive effects on human loss and financial damage, cause various problems in the operation of hospital operations and health services. Nowadays, an overwhelming majority of the world is still fighting against a pandemic. Covid-19, a new type of coronavirus, is an infectious disease that first appeared on December 30, 2019 in Wuhan, China. The World Health Organization (WHO) declared COVID-19 later as an epidemic. In nearly 4 months, the infection, which first expanded with Iran and Italy, is spread all over the world. As of 22 April, 2020, it has caused nearly 2.5 million cases and 169,000 deaths in the world [3]. The world has faced an unusual number of infected people in hospitals. This surge made it mandatory for countries to make their hospitals, field hospitals, or specific pandemic hospitals prepared in a considerable and short time.

Therefore, it is required to prepare the hospitals and all healthcare stakeholders for the disasters. In Hosseini et al. [1]; preparedness is defined as the inclusion of activities set up to build a mechanism for rapid responses to limit the risks and effects. One of the crucial components of improving disaster preparedness is to evaluate the readiness of hospitals and then propose a ranking of them. Hospitals should be prepared for physical infrastructure and resource planning, as they are the only places to provide first care during a disaster. The post-disaster problems encountered by hospitals are stated in the literature as follows [4,5]: A surge in patient arrivals, communication issues, lack of adequate treatment and care area, problems in patient transfer. Keskin and Kalemoğlu [6] pointed out that the most important post-disaster problem faced by hospitals is the excessive patient admission. Similarly, the lack of coordination between disaster area and hospitals [7], lack of telecommunication [8], chaos, and triage difficulty due to patient surge [9] are some of the other problems raised in the current literature. From these studies, it is inferred that disasters directly affect hospital activities. Since the occurrence of disaster events causes mass casualties, public panic and chaos. Most hospitals are unprepared to tackle thousands of patients arrived in case of a major disaster [10]. Therefore, planning of hospital resources (treatment area, equipment and personnel) and determination of disaster preparedness levels of hospitals can be effective in reducing the damage caused by disasters. On the other hand, another issue related to disaster management is the importance of conducting risk analysis and loss assessment studies for urban areas [[11], [12], [13]]. These studies provide insight into the accessibility of hospitals as well as the assessment of losses and thus how they can affect the needs of healthcare services after a disaster.

In this study, a hybrid fuzzy decision making model was proposed to evaluate the disaster preparedness of Turkish hospitals. This model was developed using three well-known multi-criteria decision-making (MCDM) methods named as FAHP, FDEMATEL and TOPSIS. The ultimate target of the study is to determine a ranking among hospitals in terms of disaster preparedness.

FAHP is used to determine weights of six main criteria including hospital buildings, equipment, communication, transportation, personnel, flexibility and thirty-six sub-criteria under these six main criteria. AHP contains some important characteristics such as pair wise comparison, hierarchy, independency and consistency in decision making. Since, FAHP is frequently used as a weighting tool in the literature; we use it in this study with FDEMATEL which has ability to evaluate interdependence between all the sub-criteria of the model. Finally, TOPSIS is used to obtain the ranking of hospitals. To apply the hybrid decision making model, two different questionnaires are created and assessed by five experts related to the field of disaster management of healthcare facilities. To provide inputs for TOPSIS implementation, some key performance indicators are established and related data is gathered by the aid of experts from the assessed hospitals.

The remaining of the study is organized as follows: Section 2 provides a review of the literature covering conceptual and research articles regarding the topic of hospital disaster preparedness evaluation. The third section gives the methodology used for the study. Initially, applied MCDM methods are described then, the proposed hybrid approach is identified. Fourth section concerns with a demonstration of the proposed approach. The evaluation criteria, the decision-making team, implementation of the questionnaires and results of each MCDM method are presented in this section. Final section concludes the study with some future research recommendations and limitations of the current work.

Review of the literature

Various conceptual-based and MCDM-based frameworks are proposed in the literature to assess the preparedness level of hospitals [1,4,[14], [15][69]]. In conceptual-based frameworks, researchers construct their disaster readiness frameworks without using any numerical tools. They directly focus on some dimensions such as structural, non-structural, functional, and human resources. On the other hand, in MCDM-based frameworks, researchers initially determine the main objective, disaster preparedness criteria and sub-criteria, alternative hospitals that will be assessed concerning these criteria/sub-criteria (the decisional hierarchy). Then, a decision matrix is built that includes a weight matrix of criteria/sub-criteria. Using this decision matrix, a final decision is made using an MCDM framework such as TOPSIS.

In the literature, the number of conceptual-based frameworks and cross-sectional survey-based studies are more than MCDM-based frameworks. As an example, Hosseini et al. [1] proposed a TOPSIS-based ranking model for eight selected Iranian hospitals. They ranked these hospitals in terms of disaster preparedness ability. Four crucial criteria of structural preparedness, non-structural preparedness, functional preparedness, and human resources are taken into consideration in their study. The weights of these main criteria are assumed as 40%, 25%, 10%, and 25%, respectively. No MCDM method has been followed to determine weights to these criteria. The results of the study suggest that any of the observed hospitals are not on a well-prepared level. In another study, Ortiz-Barrios et al. [14,15] proposed an analytic decision-making preference model for the disaster preparedness of hospital emergency rooms in Colombia. The MCDM model includes three well-known methods of AHP, TOPSIS and DEMATEL. Gul and Guneri [4] made a conceptual study regarding the preparedness capability of hospital emergency rooms in Istanbul, Turkey. They combined the data of reports, literature, and one-to-one interviews with experts who experienced the recent Istanbul earthquake. The interviews are analysed in terms of some earthquake key statements. The important issues faced during the earthquake from the viewpoint of hospital care are extracted. Akdere et al. [] [69] applied a questionnaire about hospital disaster planning in a total of 430 Turkish hospitals. The focus of the questions is about having any written hospital disaster plan and whether performing an exercise on an annual basis or not. The characteristics of hospital disaster plans are queried concerning the hospital category (public, private, university and all).

Unlike the above-mentioned studies, there exist many papers using a cross-sectional methodology, Delphi, and similar tools [17,18]. For a broad literature review in disaster preparedness of hospitals, scholars refer to the paper of Alruwaili et al. [19]. Tabatabaei and Abbasi [20] performed a semi-quantitative cross-sectional study in some Iranian hospitals to assess risks during disasters based on the hospital safety index. Two different questionnaires were designed for collecting 145 metrics (structural, functional, and nonstructural factors) supporting the evaluation of hospital disaster readiness. Similarly, Naser et al. [21] made a cross-sectional study to assess disaster preparedness of 5 public and 5 private hospitals in South Yemen. The results of the study demonstrated that hospitals are in an unacceptable level of readiness. Samsuddin et al. [22] investigated disaster preparedness attributes and hospital's resilience in Malaysia. A cross-sectional questionnaire has been performed among Malaysian hospitals' staff considering a total 243 preparedness attributes and 23 resilience indicators. The results showed that human resources & training and the ability to adapt promptly were ranked as the most critical attributes. The results can help hospital's stakeholders in Malaysia to improve its preparedness capability. Marzaleh et al. [23] developed a model for hospital emergency room preparedness against radiation and nuclear incidents as well as nuclear terrorism in Iran. By utilizing the Delphi method, 31 criteria are considered under three main classes, namely staff, stuff, and structure (system). In conclusion of the results, staff preparedness and stuff preparedness had the highest and lowest priority levels, respectively. Shabanikiya et al. [24] designed a tool for hospital preparedness for surge capacity during disasters. They used the Delphi method in their developed toolkit as in Marzaleh et al. [23] and assessed 64 components in five categories and 13 sub-categories. The developed tool was used in evaluating hospital preparedness for surge capacity in disasters and planning the future of hospitals against disasters.

The current study is differentiated from both studies mentioned under the class of MCDM-based frameworks in some aspects. The first difference concerns the comprehensiveness of the hospital disaster preparedness criteria set. While Hosseini et al. [1] considered four preparedness dimensions as mentioned above, Ortiz-Barrios et al. [14,15] constructed the hierarchy under seven criteria. In Ortiz-Barrios et al. [14,15], the decision-making team identified 7 criteria and 23 sub-criteria to evaluate the readiness of emergency departments for a disaster situation. The criteria set of our study include hospital buildings, equipment, communication, transportation, personnel, and flexibility. These criteria are more inclusive than the two studies and can easily be adapted to potential models that can be developed later. Moreover, Ortiz-Barrios et al. [14,15]'s study is developed for specific emergency departments. A main dimension similar to the one we use in this study and which we called “flexibility” is not mentioned in Hosseini et al. [1]'s study. The second difference stems from methodological sides. In Hosseini et al. [1]; an assumption and full subjectivity are preferred in weighting the main criteria. The assignment of criteria weights is not clear. Any weight assignment is not performed for sub-criteria. Unlike this, we follow a group-decision making procedure via an experienced decision team in weighting both criteria and sub-criteria using FAHP. Besides, none of the studies proposes a fuzzy-based MCDM approach. However, by integrating linguistic expressions and corresponding fuzzy numbers into our approach, we aim to eliminate the insufficiency and preciseness of the crisp pairwise comparison in classical AHP in capturing the right judgments of decision-makers.

As discussed above, many studies have been undertaken for assessing hospital disaster preparedness. Most of the papers contribute to the literature by proposing conceptual-based frameworks that we discussed. On the other hand, cross-sectional questionnaire-based models that suggest new attributes regarding hospital disaster readiness and review papers that provide a comprehensive overview of the topic are also widespread. Also, our brief review in this section shows the importance of hospital disaster preparedness assessment from the MCDM viewpoint throughout the literature. It can be observed that there is a wide range of MCDM methods with application to various areas. So far, however, there have been limited papers regarding the use of FAHP, FDEMATEL, and TOPSIS in hospital disaster preparedness.

By doing the current study, we aim to provide some contributions to the literature. These are as follows:

We developed a model specifically dealing with hospital disaster readiness assessment and ranking. This topic has been also addressed in other studies considering a number of service-quality criteria [25,26]; our model, however, incorporates six disaster readiness criteria (hospital buildings, equipment, communication, transportation, personnel, and flexibility) and thirty-six sub-criteria representing the entire context of hospital disaster management. Most of the criteria are proposed and defined for the first time in the literature.

We developed a three-MCDM-integrated approach that includes FAHP, FDEMATEL, and TOPSIS. FAHP was firstly used for determining the initial weights of hospital disaster preparedness criteria. The FDEMATEL method was then applied for assessing the interrelations among criteria. We have combined these two fuzzy MCDM methods with TOPSIS in this study to rank hospitals in terms of readiness. In view of the characteristics of all these methods either individually and in integrated style, the proposed approach can handle the problem in a systematic and analytical manner. Indeed, the hybrid approaches can tackle the limitations that single methods hold [14,15,27]. For instance, TOPSIS uses criteria weights that are usually defined randomly. FAHP, specialized in prioritizing decision elements [28], has been therefore proposed to address this drawback. On the other hand, FDEMATEL has been incorporated into this approach since FAHP is unable to evaluate interdependence among criteria. Although ANP can be also used to this aim, its application has been proved to be time-consuming and highly complex, especially in models with a significant number of criteria and sub-criteria [29]. On a different tack, TOPSIS was deemed as a suitable method for ranking the hospitals according to their disaster preparedness level. This technique was preferred over AHP since the latter method entails many pairwise comparisons given a large number of hospitals. Although a pilot application including 4 hospitals is presented in this study, it is noteworthy that the proposed approach has been projected to be used at a national level in Turkey where a significant number of alternatives needs to be considered. DEA can be also employed for this particular aim; it, however, assumes that inputs and outputs are known which cannot be fully ensured in all disaster readiness criteria [30].

In Table 1 , we present a comparison with the four aforementioned studies based on some specific aspects. It can be seen from Table 1 that the proposed approach meets all three important aspects (pairwise comparison criteria, fuzziness in determination of criteria weights, and interdependence evaluation between criteria), and is more satisfactory in terms of quantity of criteria and coverage of the criteria. The rest of the approaches only cover two aspects at the most. Based on the previous considerations, the novelty of this study is as follows: a) The inclusion of fuzziness in the calculation of criteria and sub-criteria weights using the FAHP method. This is motivated by the need for dealing with the imprecision and uncertainty of linguistic evaluations which makes the model more realistic and coherent with the real scenario. Besides, this aspect has not been addressed by the previous related studies as evidenced in Table 1 b) The evaluation of fuzzy interdependence between disaster readiness criteria through FDEMATEL for facilitating the design of long-term improvement plans by the government and other stakeholders. Similar to the point a), this aspect has not been dealt in the reported related literature. c) The incorporation of several criteria that have not been considered in other related studies (i.e. flexibility and contingency staff).

Table 1

Comparison of five different approaches.

Different approaches	The aspect considered for comparisons
	Pairwise comparison of the criteria	Fuzziness in determination of criteria weights	Interdependence evaluation between criteria	Number of main criteria	Total number of sub-criteria
Hosseini et al. [1]	×	×	×	4	21
Ortiz-Barrios et al. [14,15]	✓	×	✓	7	23
Marzaleh et al. [23]	✓	×	×	3	31
Tabatabaei and Abbasi [20]	×	×	×	3	145
This study	✓	✓	✓	6	36

Note: ‘✓’ indicates the mentioned approach has enough capability to deal with the specific aspect and ‘×’ indicates the approach cannot deal with the aspect.

Methodology

A six-step procedure (Fig. 2 ) is proposed to evaluate the hospital disaster preparedness and detect the weaknesses that should be tackled by each institution for upgrading their response to disaster incidents:

Fig. 2

The proposed methodology for evaluating hospital disaster preparedness.

Step 1: a decision-making team is chosen considering their expertise (related to disaster management, healthcare management, and MCDM) and experience (at least 10 years in the Turkish healthcare sector). The selected participants (N) will be asked to provide insights on the definition, importance, and influence of assessment decision elements (criteria/sub-criteria) through FAHP and FDEMATEL techniques respectively. In this regard, it is critical to define the number of experts participating in the decision-making process so that criteria weights, interdependence results, and TOPSIS scores can be calculated at a high confidence level (CL = 95% at a minimum) and low error level (e = 5% at a maximum).

Step 2: the assessment criteria and sub-criteria are determined given the related scientific literature, government regulations and experts’ considerations.

Step 3: Fuzzy AHP is implemented to estimate the relative weights of criteria and sub-criteria under vagueness (see sub-section 3.1.1).

Step 4: Fuzzy DEMATEL is applied to pinpoint the dispatchers and receivers per each cluster while estimating the strength of influence among criteria/sub-criteria (see sub-section 3.1.2).

Step 5: FAHP and FDEMATEL are later integrated to calculate the final criteria and sub-criteria weights with basis on interdependence (see sub-section 3.1.3).

Step 6: TOPSIS is finally used for ranking the hospitals on the basis of disaster preparedness. In parallel, weaknesses are identified for propelling the design of focused improvement interventions in each institution (see sub-section 3.1.4).

Applied MCDM methods

In this subsection, we identify the applied MCDM methods either used in fuzzy sets or in crisp environment. Therefore, prior to giving the details of FAHP and FDEMATEL method, an overview on the notations of fuzzy sets may be useful. Zadeh [31] introduced fuzzy sets for better reflecting of the human judgments and assessment in decision making. Also, the usage of fuzzy sets is better for transforming linguistic decision of human judgment and reflecting uncertainty and ambiguity of the real world decision making processes. The inclusion of fuzziness, however, entails more complex calculations compared to the existing related approaches. To tackle this disadvantage, an Excel-based decision support system has been properly designed and adopted to accelerate the disaster preparedness evaluation in relation to: i) weighting and prioritizing disaster readiness criteria and sub-criteria, ii) identifying the dispatchers and receivers within the disaster management scenario, iii) ranking the hospitals according to their preparedness level, and iv) defining focused operational strategies for increasing the response of hospitals against outbreaks.

One representation of fuzzy sets is the use of triangular fuzzy numbers. A triangular fuzzy number comprises lower, medium, and upper numbers of the fuzzy as where l, m and u which is crisp and real numbers ( The membership function of a triangular fuzzy number ( can be defined as follows.

A triangular fuzzy number is presented in Fig. 3 .

Fig. 3

A fuzzy number in triangular style.

and are any two triangular fuzzy numbers, the algebraic operations between two triangular fuzzy numbers are defined as in Table 2 .

Table 2

Algebraic operations between two fuzzy numbers.

Algebraic operator	Equation
Addition operator	A˜_1+A˜_2=(l_1+l_2,m_1+m_2,u_1+u_2)
Subtraction operator	A˜_1−A˜_2=(l_1−u_2,m_1−m_2,u_1−l_2)
Multiplication operator	A˜_1xA˜_2=(l_1xl_2,m_1xm_2,u_1xu_2)
Arithmetic operator	kxA˜_1=(kxl_1,kxm_1,kxu_1),(k>0)A˜_1k=(l_1k,m_1k,u_1k),(k>0)
Defuzzification style: graded mean integration representation (GMIR)	R(A˜_i)=(l_i+4m_i+u_i)6

Fuzzy analytic hierarchy process (FAHP)

FAHP is one of the commonly applied MCDM methods. Crisp AHP cannot mirror the subjectivity broadly. Although Saaty and Tran [32] stated that AHP integration with fuzzy sets cannot be effective, there are many studies in the literature that integrate AHP with these fuzzy sets. Some arguments in these studies are as follows. Kahraman et al. [33] stated that AHP cannot reflect the thinking style of human, therefore, the fuzzy extension of AHP has been developed. Chan et al. [34] stated that with fuzzy cluster and AHP integration, mathematical uncertainty would be better expressed and could be therefore used in solving real-world problems. Also, Wang and Chen [35], expressed that AHP is integrated with fuzzy sets to better reflect uncertainty. Different improved versions of AHP by fuzzy sets are available in the literature [36,37]. In this existing study, Buckley's [36] method is applied to determine hospital disaster preparedness criteria. In some FAHP extensions, for example in Chang's extent analysis, a limitation is released. An irrational zero weight generation problem in criteria weighting [38] is detected in Chang's FAHP.

The steps of Buckley's FAHP method is provided as below (Fig. 4 ) [39,40]:

Fig. 4

Step-by-step procedure of FAHP.

Step 1-Pairwise comparison of each criterion: Linguistic terms are used in determining relative importance of each two criteria based on Eqs. (2), (3)). Although the Saaty natural scale (1: Equal importance; 3: Weak importance; 5: Strong importance; 7: Very strong importance; 9: Absolute importance; reciprocals) was initially proposed to denote the preferences between two elements either criteria or sub-criteria [28], a shorter and fuzzy version of this scale (: Equally important; : More important; : Much more important; : Less important; : Much less important) (Eq. (3)) has been adopted to deal with the imprecision of linguistic evaluations whilst reducing some bias and confusion during the comparison process [14,15,41,42].

Step 2-Fuzzy geometric mean matrix: It is constructed using Eq. (4).

Step 3-Fuzzy weights: For each criterion, the fuzzy weights are obtained by Eq. (5).Here, is the fuzzy weight of criterion i and . Here, represent the lower, middle, and upper value of the fuzzy weight of criterion i.

Step 4-Non-fuzzy weights: The non-fuzzy weights are computed using GMIR. Finally, the consistency ratio (CR) is calculated via applying Eqs. (6), (7)). Here, CI denotes the consistency index while RI represents the random index. If CR < 10%, the matrix is concluded to be consistent and the derived weights are therefore valid for supporting the decision-making process.

Fuzzy decision making trial and evaluation laboratory (FDEMATEL)

The FDEMATEL method is an improved version of classical DEMATEL method initially proposed by Gabus and Fontela [43]. Classical DEMATEL considers the relationship between the evaluation criteria in an MCDM problem and classified them into cause-and-effect criteria [44,45]. The common plus of FDEMATEL is to consider the fuzziness and to provide flexibility in a fuzzy MCDM environment [44,46].

The implementation steps of FDEMATEL method are explained briefly in the following (Fig. 5 ) [44,45,47]:

Fig. 5

Step-by-step procedure of FDEMATEL.

Step 1-Set up of the expert team.

Step 2-Determination of evaluation criteria A five-point linguistic scale is used (no influence, very low influence, low influence, high influence, and very high influence) considering linguistic terms and corresponding triangular fuzzy numbers as given in Table 3 .

Table 3

The five-point linguistic scale with triangular fuzzy numbers.

Linguistic terms	Triangular fuzzy numbers
No influence (No)	(0, 0, 0.25)
Very low influence (VL)	(0, 0.25, 0.5)
Low influence (L)	(0.25, 0.5, 0.75)
High influence (H)	(0.5, 0.75, 1)
Very high influence (VH)	(0.75, 1, 1)

Step 3-Initial direct-relation fuzzy matrix: The pairwise comparisons of experts are performed considering linguistics variables, as stated in Step 2. As a result, initial direct-relation fuzzy matrix () of experts is constructed (Eqs. (8), (9))).

Step 4-Normalized direct-relation fuzzy matrix: In this step, benefiting from the initial direct-relation matrix, the normalized direct-relation fuzzy matrix is constructed (Eq. (10), (11), (12))). Where

Step 5-Total relation fuzzy matrix: Hereafter the matrix , a total-relation fuzzy matrix is calculated as follows (Eq. (13), (14), (15), (16))).where

Step 6: After the computation of matrix , and are computed. Here, and show the sum of the rows and columns of matrix . Whilst shows the importance of criterion , shows the net effect of criterion .

Step 7: Defuzzification is the conversion of a fuzzy quantity to a precise quantity [48]. In this case, and are defuzzified by using center of area defuzzification style with Eq. (17).

Step 8: In the last step, the cause and effect relation diagram are drawn by the aid of and .

In FDEMATEL, we have used fuzzy arithmetic till Step-7. In step-7, finally, we have applied defuzzification. Although some authors from literature have used initially defuzzification then followed crisp DEMATEL, we have done vice versa [49]. Since the nature of our problem is under a situation where the output of the fuzzy process needs to be a single scalar quantity as opposed to a fuzzy set. As we will use crisp TOPSIS in determining hospital rankings in terms of disaster preparedness, we need defuzzified values of weights from FAHP and FDEMATEL. Therefore, we have applied defuzzification. As stated by Oussalah [50]; in many engineering applications, the need for a numerical value has been usually provided by a defuzzification process.

The combination of FAHP and FDEMATEL

In this study, we use FAHP to obtain the relative weights of criteria i (i = 1, 2, …, k) and sub-criteria j (j = 1, 2, …, n). Nevertheless, FAHP does not analyse the dynamic interrelations inherent to the healthcare scenario [51,52]. We therefore propose the integration of FAHP and FDEMATEL methods to address this limitation. While FAHP provides enough support for conducting short-term interventions, FDEMATEL underpins the definition of improvement actions at a long-term horizon which is consistent with the timetables of the disaster management plans established by governments. The result of this combined approach is a set of weights on the basis of interdependence that are later incorporated in TOPSIS method (Fig. 6 ).

Fig. 6

Step-by-step procedure of the integrated FAHP-FDEMATEL approach.

The resulting global criterion importance GCW (i = 1, 2, …, k), local sub-criterion importance (j = 1, 2, …, n), and global sub-criterion weight GSW (j = 1, 2, …, n) derived from the hybrid approach can be estimated by implementing Eq. (18), Eq. (19), and Eq. (20) respectively. In these formulas, k denotes the total number of criteria whilst n represents the total number of sub-criteria deemed in the MCDM model. On the other hand, and are the prominence and relation parameters of criterion i (i = 1, 2, …, k) whereas and represent the prominence and relation of sub-criterion j (j = 1, 2, …, n) respectively. Eq. (18), (19)) combine the weights derived from FAHP and F-DEMATEL to calculate the criteria and sub-criteria importance on the basis of interdependence. Specifically, F-DEMATEL weights are estimated through the vector length method as follows: . These weights are further combined with FAHP weights by incorporating the vector E (Eq. (11)). Lately, the terms and in Eq. (18), (19)) are introduced for normalizing the weights.

Technique for order preference by similarity to ideal solution (TOPSIS)

TOPSIS initially suggested by Hwang and Yoon [53] aims at determining the best alternative based on the closeness to the ideal solution. TOPSIS procedural steps are provided in the following (Fig. 7 ) [39]:

Fig. 7

Step-by-step procedure of TOPSIS.

Step 1: The first step concerns with determination of criteria and alternative set. Here, shows the set of alternatives, represents the criteria set where denotes the set of performance ratings and demonstrates the criteria weights.

Step 2: The second step is related to the normalization. It is formulated by Eq. (21).

Step 3: The third step presents a weighted normalized matrix which is determined by Eq. (22).

Step 4: The positive ideal point (PIS) and the negative ideal point (NIS) are obtained by Eqs. (23), (24). Where J1 and J2 are the benefit and the cost criteria, respectively.

Step 5: The fifth step is on calculation of the separation from the PIS and the NIS. The separation from PIS and NIS values can also be computed using the Euclidean distance formulae as in Eqs. (25), (26):

Step 6: Then, the final TOPSIS score is calculated by Eq. (27).

By calculating the score in Eq. (27), the ranking orders are determined via a value in descending order.

Demonstration of the proposed approach: the case of Turkish hospitals

The decision-making team

The proper selection of a decision-making team is critical for determining the importance of criteria considered in the assessment of hospital disaster preparedness. Likewise, it will provide significant support for identifying the presence of interdependence and feedback within the MCDM model. In this case, seven experts were finally chosen to participate in the decision-making process: academicians (5), IT technician (1), and disaster manager (1). It is noteworthy that the academicians are also consultants and researchers who have conducted several projects in the hospital sector. The number of experts (n = 7) participating in this application was defined considering CL = 95%, p = 50%, e = 5%, N = 7 (experts fulfilling the inclusion criteria described in Step 1 – “3.Methodology”); and is hence sufficient for obtaining reliable weights. A description of the experts’ profile can be found in Table 4 :

Table 4

Description of experts participating in the decision-making team.

Expert	Job title	Experience (in years)	Expertise area
Expert 1	Disaster manager	~10	Image processing; MCDM; forensic informatics; healthcare management
Expert 2	IT technician	~10	MCDM; data mining; artificial intelligence; healthcare management
Expert 3	Academician	~15	Healthcare management; MCDM; risk assessment; fuzzy sets
Expert 4	Academician	~10	Artificial neural networks; heuristic methods; neuro-fuzzy; site selection; experimental design; MCDM; simulation; healthcare management
Expert 5	Academician	~15	Disaster management; MCDM; fuzzy sets; humanitarian logistics
Expert 6	Academician	~10	Logistics; optimization; line balancing; healthcare management; MCDM; fuzzy sets
Expert 7	Academician	~15	Healthcare management; MCDM; risk assessment; fuzzy sets

In particular, these experts were selected considering their job title, expertise area (≥10 years), and experience (related to MCDM and healthcare). Apart from these participants, three researchers with vast experience (≥10 years) in disaster management and healthcare logistics acted as facilitators of the decision-making process. Specifically, they built the multi-criteria model for evaluating the hospital preparedness when facing disaster situations. In this activity, the decision-making team provided meaningful insights on the criteria to be considered within the model. On a different note, the facilitators also designed the data-collection instruments and indicated experts how to conduct the paired judgments inherent to FDEMATEL and FAHP techniques. Moreover, they established the indicators underpinning the TOPSIS implementation. It is worth highlighting that this project was initially discussed with the participating experts to facilitate the comprehension on the study goals and obtain feedback before implementation.

Design of the disaster preparedness assessment model

Turkish healthcare regulations, the pertinent scientific literature and experts’ opinion served as a basis for defining the criteria and sub-criteria to be included within the disaster preparedness assessment model. A brief explanation of each decision element was incorporated in the FAHP and FDEMATEL surveys for ensuring proper understanding on the model. The final version of the multi-criteria structure is depicted in Fig. 8 . In particular, 6 criteria and 36 sub-criteria were deemed to rank four hospitals (H1, H2, H3, and H4) and detect their weaknesses as a support for focused improvement. An explanation of each decision element can be consulted in Table 5 .

Fig. 8

Multi-criteria model for assessing the hospital preparedness when facing disaster situations.

Table 5

Description of criteria.

Criterion	Sub-criteria	Criterion description
Hospital buildings (C1)	Physical infrastructure (SC1.1)Location (SC1.2)Number of floors (SC1.3)Capacity (SC1.4)Disaster gathering area (SC1.5)Insulation (SC1.6)Ventilation (SC1.7)	It is defined as the structural preparedness of hospitals when facing disaster events. It covers installed capacity, location, and infrastructure quality criteria.
Equipment (C2)	Medicine (SC2.1)Potential hazardous substance (SC2.2)Material safety management (SC2.3)Medical equipment for ES (SC2.4)Power generator (SC2.5)Drinking water (SC2.6)Tent (SC2.7)Food (SC2.8)Bed (SC2.9)Triage tag (SC2.10)Finance (SC2.11)Supply source (SC2.12)	It is about non-structural preparedness. This criterion focuses on the availability of quality and quantity of the equipment.
Communication (C3)	Emergency network (SC3.1)Communication tools/device (SC3.2)Information quality (SC3.3)	It concerns the information technology ability of the hospital under disaster.
Transportation (C4)	Number of vehicles (SC4.1)Helipad space (SC4.2)Safety (SC4.3)Accessibility (SC4.4)	This criterion specifies the transportation resources of the hospital and the status of the roads to the hospital in case of disaster.
Personnel (C5)	Education (SC5.1)Disaster drill (SC5.2)Emergency response team (SC5.3)Coordination (SC5.4)Number of personnel (SC5.5)Working hours (SC5.6)	This criterion shows the capability of the hospital regarding the qualification and quantity of personnel.
Flexibility (C6)	Flexibility in the use of facilities (SC6.1)Contingency staff (SC6.2)Blood bank (SC6.3)Supply chain of medicines and supplies (SC6.4)	This criterion considers the ability of hospitals for expanding their capacity aiming at admitting the greatest possible number of patients.

In “Hospital buildings” (C1) domain, seven sub-criteria were considered: “Physical infrastructure” (SC1.1), “Location” (SC1.2), “Number of floors” (SC1.3), “Capacity” (SC1.4), “Disaster gathering area” (SC1.5), “Insulation” (SC1.6), and “Ventilation” (SC1.7). “Physical infrastructure” (SC1.1) evaluates whether the buildings are resistant to disaster such as earthquakes, fire, radiation, nuclear, and terror incidents. “Location” (SC1.2) is defined as finding the right place for construction of hospitals in terms of the degree and severity of earthquake occurrence. On a different tack, “Number of floors” (SC1.3) refers to the number of floors that the hospital has. “Capacity” (SC1.4) measures the total capacity capability that the hospital has in terms of human, medical equipment and treatment areas. On the other hand, “Disaster gathering area” (SC1.5) assesses the availability of any disaster gathering area of the hospital. “Insulation” (SC1.6) identifies the capability and/or availability of the insulation capability of the hospital. Finally, “Ventilation” (SC1.7) evaluates the ventilation capability of the hospital.

Regarding “Equipment” (C2) category, 12 decision elements were defined: “Medicine” (SC2.1), “Potential hazardous substance” (SC2.2), “Material safety management” (SC2.3), “Medical equipment for ES” (SC2.4), “Power generator” (SC2.5), “Drinking water” (SC2.6), “Tent” (SC2.7), “Food” (SC2.8), “Bed” (SC2.9), “Triage tag” (SC2.10), “Finance” (SC2.11), and “Supply source” (SC2.12). “Medicine” (SC2.1) refers to the medicine stocks and medicine capability in emergency situations for hospital facilities whereas “Potential hazardous substance” (SC2.2) concerns the management of the potential hazardous substance during emergency events. “Material safety management” (SC2.3) specifies the Material Safety Data Sheets (MSDS) standards while “Medical equipment for ES” (SC2.4) shows the quantity and quality of the medical equipment for emergency services (ES). “Power generator” (SC2.5) evidences the availability of any power generator for the hospital whilst “Drinking water” (SC2.6) evaluates the availability and management of the drinking water for the hospital. On the other hand, “Tent” (SC2.7) assesses the availability and quantity of required tents for the hospital whereas “Food” (SC2.8) represents the availability and sufficiency of food for the hospital under disaster conditions. On a different note, “Bed” (SC2.9) denotes the availability and adequacy of beds for the hospital under disaster incidents while “Triage tag” (SC2.10) shows the availability and quantity of required triage tags for the hospital. Lately, financing and supplying sources of the equipment are evaluated through SC2.11 and SC2.12.

Concerning “Communication” (C3) area, three sub-criteria were deemed: “Emergency network” (SC3.1), “Communication tools/device” (SC3.2), and “Information quality” (SC3.3). The first sub-criterion (SC3.1) checks the communication ability of hospitals with the institutions having a say in disaster response. The second aspect (SC3.2) verifies the type and quantity of communication tools/devices a hospital has. Finally, “Information quality” (SC3.3) evaluates how reliable and effective the communication flows are within a hospital and with their partners during a disaster event.

In “Transportation” (C4) domain, four pillar aspects were included: “Number of vehicles” (SC4.1), “Helipad space” (SC4.2), “Safety” (SC4.3), and “Accessibility (roads)” (SC4.4). In this respect, “Number of vehicles” (SC4.1) considers the quantity of the vehicles that the hospital has for their usage during disaster situations. “Helipad space” (SC4.2) verifies whether the hospital has an available helipad space for admitting patients transported by helicopter. Another element of consideration is “Safety” (SC4.3) which encompasses the general safety standards of the hospital under disaster situations. Finally, “Accessibility” (roads)” (SC4.4) evaluates the presence and deterioration of roads providing access to hospital in case of disaster.

On a different tack, “Personnel” (C5) criterion was characterized through six decision elements: “Education” (SC5.1), “Disaster drill” (SC5.2), “Emergency response team” (SC5.3), “Coordination” (SC5.4), “Number of personnel” (SC5.5), and “Working hours” (SC5.6). “Education” (SC5.1) evidences the education level of hospital staff in terms of disaster preparedness and behaviour in case of disaster. “Disaster drill” (SC5.2) verifies the implementation of disaster drills for hospital staff and patients. Another aspect of consideration in this domain is “Emergency response team” (SC5.3). In particular, this sub-criterion determines the availability/implementation of education/training for emergency medical services. Also, “Coordination” (SC5.4) was considered to examine the coordination level of staff in terms of disaster preparedness and behaviour in case of disaster. Other sub-criteria to be studied within this factor are: “Number of personnel” (SC5.5), and “Working hours” (SC5.6). The first one involves evaluating the quantity of trained staff that the hospital has for facing devastating situations; whereas the second sub-factor represents the number of working hours that the hospital trained staff have in relation to disaster events.

The last criterion included in the MCDM model is “Flexibility” (C6). For its assessment, four sub-factors were specified: “Flexibility in the use of facilities” (SC6.1), “Contingency staff” (SC6.2), “Blood bank” (SC6.3), and “Supply chain of medicines and medical supplies” (SC6.4). The first sub-factor (SC6.1) considers the administrative areas that can be allocated for taking care of affected people. Such areas can be primarily used for providing emergency care to people with minor affectations. On the other hand, “Contingency staff” (SC6.2) denotes the staff who do not work directly with the hospital but can be further linked for facing the disaster (i.e. professionals who are not located in the disaster occurrence city). Another decision element considered in this assessment domain is “Blood bank” (SC6.3) which verifies the availability of a blood bank for effectively underpinning healthcare during a disaster. Ultimately, “Supply chain of medicines and medical supplies” (SC6.4) has been included into the model considering that hospitals should count on supply chains providing medicines and supplies in the shortest possible time.

Linear dependency: the FAHP application

In this intervention, a survey format was designed for collecting the paired judgments resulting from the FAHP application. The format layout proposed in this study (Fig. 4) was found to be comprehensible and easy to complete by the participant experts. In various studies, the appropriate design of the data-gathering tools has been concluded to be effective for decreasing the risk of inconsistency in related decision-making applications [54,55]. As depicted in Fig. 9 , the following question was asked: “¿How important is each element on the left column over the element on the right?” The selected experts responded this survey by employing the 3-point scale [14,15] presented in Eq. (3) [14,15,41,42].

Fig. 9

Survey used for collecting FAHP comparisons: the case of “Communication” cluster.

An illustration of a fuzzy geometric mean matrix is shown in Table 6 , where the collected judgments were aggregated and organized in accordance with Eqs. (2), (3), (4)). After this, the fuzzy weights were computed using Eq. (5). The derived global and local priorities are presented in Table 7 .

Table 6

Fuzzy geometric mean matrix for “Flexibility” sub-criteria.

	SC6.1	SC6.2	SC6.3	SC6.4
SC6.1	[1,1,1]	[1.00,1.31,1.68]	[0.25,0.33,0.50]	[0.59,0.76,1.00]
SC6.2	[0.59,0.76,1.00]	[1,1,1]	[0.50,0.57,0.71]	[0.71,0.76,0.84]
SC6.3	[2.00,3.00,4.00]	[1.41,1.73,2.00]	[1,1,1]	[1.19,1.49,1.86]
SC6.4	[1.00,1.31,1.68]	[1.19,1.32,1.41]	[0.53,0.67,0.84]	[1,1,1]

Table 7

Local and global weights of criteria and sub-criteria using FAHP.

	FAHP
	LW	GW
Hospital buildings (C1)		0.128
Physical infrastructure (SC1.1)	0.323	0.041
Location (SC1.2)	0.202	0.026
Number of floors (SC1.3)	0.066	0.008
Capacity (SC1.4)	0.174	0.022
Disaster gathering area (SC1.5)	0.084	0.011
Insulation (SC1.6)	0.072	0.009
Ventilation (SC1.7)	0.080	0.010
Equipment (C2)		0.263
Medicine (SC2.1)	0.151	0.040
Potential hazardous substance (SC2.2)	0.036	0.009
Material safety management (SC2.3)	0.091	0.024
Medical equipment for ES (SC2.4)	0.167	0.044
Power generator (SC2.5)	0.050	0.013
Drinking water (SC2.6)	0.128	0.034
Tent (SC2.7)	0.053	0.014
Food (SC2.8)	0.105	0.028
Bed (SC2.9)	0.060	0.016
Triage tag (SC2.10)	0.058	0.015
Finance (SC2.11)	0.049	0.013
Supply source (SC2.12)	0.053	0.014
Communication (C3)		0.110
Emergency network (SC3.1)	0.628	0.069
Communication tools/device (SC3.2)	0.163	0.018
Information quality (SC3.3)	0.209	0.023
Transportation (C4)		0.086
Number of vehicles (SC4.1)	0.153	0.013
Helipad space (SC4.2)	0.207	0.018
Safety (SC4.3)	0.284	0.024
Accessibility (roads) (SC4.4)	0.356	0.031
Personnel (C5)		0.272
Education (SC5.1)	0.339	0.092
Disaster drill (SC5.2)	0.168	0.046
Emergency response team (SC5.3)	0.168	0.046
Coordination (SC5.4)	0.176	0.048
Number of personnel (SC5.5)	0.085	0.023
Working hours (SC5.6)	0.064	0.018
Flexibility (C6)		0.140
Flexibility in the use of facilities (SC6.1)	0.163	0.023
Contingency staff (SC6.2)	0.158	0.022
Blood bank (SC6.3)	0.444	0.062
Supply chain of medicines and medical supplies (SC6.4)	0.235	0.033

We later proceeded with the estimation of consistency ratios (CR) to check the reliability of resulting weights (Table 8 ). Considering that CR values are not over the threshold (0.01), the calculated priorities are concluded to be appropriate for their use in the assessment model. It is noteworthy that the biggest matrix (Equipment) was found to present very low inconsistency (CR = 0.0324). Such findings evidence the effectiveness of the assessment process based on: i) the careful design of the questionnaire, ii) the reduced comparison scale and iii) the high expertise of decision-makers.

Table 8

CR for fuzzy geometric mean matrixes.

	Consistency Ratio (CR)
Criteria	0.0325
Hospital buildings	0.0928
Equipment	0.0324
Communication	0.0337
Transportation	0.0719
Personnel	0.0131
Flexibility	0.0529

Interdependence: the FDEMATEL application

A questionnaire was also created to collect the paired judgments outlining the interdependence and feedback relationships among criteria/sub-criteria considered in the model (Fig. 10 ). In this case, it was asked: “According to your expertise, how much influence each criterion on the left exerts over each criterion on the right?” In difference to FAHP, the experts performed the comparisons by employing the five-point linguistic scale (with triangular fuzzy numbers) illustrated in Table 2. The judgment procedure was then iterated until finishing all the combinations “criterion i vs. criterion i” and “sub-criterion j vs. sub-criterion j”.

Fig. 10

Data-gathering instrument used for collecting FDEMATEL judgments.

Following this, the fuzzy paired comparisons were arranged in an initial direct-relation fuzzy matrix () using Eqs. (6), (7)). An illustration of matrix is presented in Table 9 . Then, the normalized direct-relation fuzzy matrix was achieved by applying Eqs. (8), (9), (10)) (Table 10 ). Ultimately, the total relation fuzzy matrix was estimated by implementing Eq. (11), (12), (13), (14)) (Table 11 ).

Table 9

Initial direct-relation fuzzy matrix for “Flexibility” cluster.

	SC6.1	SC6.2	SC6.3	SC6.4	∑j=1nlij(k)	∑j=1nmij(k)	∑j=1nuij(k)	r^(k)
SC6.1	[0.00,0.00,0.25]	[0.25,0.50,0.75]	[0.20,0.35,0.60]	[0.20,0.40,0.65]	0.65	1.25	2.25	2.45
SC6.2	[0.25,0.50,0.75]	[0.00,0.00,0.25]	[0.20,0.45,0.70]	[0.30,0.55,0.75]	0.75	1.5	2.45
SC6.3	[0.20,0.40,0.65]	[0.20,0.35,0.55]	[0.00,0.00,0.25]	[0.25,0.50,0.75]	0.65	1.25	2.2
SC6.4	[0.20,0.45,0.70]	[0.20,0.35,0.55]	[0.25,0.50,0.75]	[0.00,0.00,0.25]	0.65	1.3	2.25

Table 10

Normalized direct-relation fuzzy matrix for “Flexibility” cluster.

	SC6.1	SC6.2	SC6.3	SC6.4
SC6.1	[0.00,0.00,0.10]	[0.10,0.20,0.31]	[0.08,0.14,0.24]	[0.08,0.16,0.27]
SC6.2	[0.10,0.20,0.31]	[0.00,0.00,0.10]	[0.08,0.18,0.29]	[0.12,0.22,0.31]
SC6.3	[0.08,0.16,0.27]	[0.08,0.14,0.22]	[0.00,0.00,0.10]	[0.10,0.20,0.31]
SC6.4	[0.08,0.18,0.29]	[0.08,0.14,0.22]	[0.10,0.20,0.31]	[0.00,0.00,0.10]

Table 11

Total relation fuzzy matrix for “Flexibility” cluster.

	SC6.1	SC6.2	SC6.3	SC6.4	rˇ
SC6.1	[0.03,0.17,3.37]	[0.12,0.33,3.24]	[0.11,0.29,3.44]	[0.11,0.33,3.57]	[0.37,1.12,13.63]
SC6.2	[0.13,0.37,3.78]	[0.03,0.18,3.29]	[0.11,0.35,3.70]	[0.15,0.40,3.84]	[0.42,1.30,14.61]
SC6.3	[0.11,0.31,3.43]	[0.11,0.28,3.11]	[0.03,0.17,3.24]	[0.13,0.35,3.52]	[0.37,1.11,13.30]
SC6.4	[0.11,0.33,3.51]	[0.11,0.29,3.16]	[0.12,0.34,3.47]	[0.03,0.19,3.41]	[0.37,1.15,13.55]
cˇ	[0.37,1.19,14.09]	[0.37,1.08,12.81]	[0.37,1.16,13.85]	[0.42,1.27,14.34]

The prominence and relation values are calculated considering the results presented in Table 11. Such measures were defuzzified using the center of area defuzzification style (Eq. (15)) and further consolidated in Table 12 . Receivers and dispatchers were also identified in this table. The results revealed that Flexibility (C6) has the greatest prominence (23.09) and is therefore deemed as the main influencer when evaluating the hospital disaster preparedness. Hence, Flexibility (C6) should be targeted for continuous intervention within the disaster management plans. This was also pointed out by Zhong et al. [56] who concluded that disaster resilience arrangement of hospitals highly depends of flexibility in terms of resources, an aspect increasing the pre-disaster strength of each institution and propelling fast response and recovery. On a different note, significant correlations are observed among criteria (c + r > 10) which are consistent with the interactive nature often found in healthcare scenarios [57].

Table 12

Prominence and relation values derived from FDEMATEL.

	c + r	c - r	Dispatcher	Receiver
Hospital buildings (C1)	21.15	1.58	x
Physical infrastructure (SC1.1)	7.33	−0.18		x
Location (SC1.2)	6.72	−0.23		x
Number of floors (SC1.3)	6.53	−0.22		x
Capacity (SC1.4)	6.50	−0.29		x
Disaster gathering area (SC1.5)	5.91	0.68	x
Insulation (SC1.6)	5.98	0.67	x
Ventilation (SC1.7)	5.86	0.76	x
Equipment (C2)	22.38	2.80	x
Medicine (SC2.1)	5.84	−0.12		x
Potential hazardous substance (SC2.2)	3.76	−0.18		x
Material safety management (SC2.3)	5.51	−0.23		x
Medical equipment for ES (SC2.4)	5.78	0.64	x
Power generator (SC2.5)	4.29	1.00	x
Drinking water (SC2.6)	4.53	−0.51		x
Tent (SC2.7)	4.02	−0.29		x
Food (SC2.8)	4.39	−0.13		x
Bed (SC2.9)	3.97	0.83	x
Triage tag (SC2.10)	3.73	3.49	x
Finance (SC2.11)	5.48	−0.21		X
Supply source (SC2.12)	4.73	−5.48		X
Communication (C3)	22.43	0.56	x
Emergency network (SC3.1)	17.18	6.29	x
Communication tools/device (SC3.2)	17.57	1.77	x
Information quality (SC3.3)	16.67	0.95	x
Transportation (C4)	20.82	0.30	x
Number of vehicles (SC4.1)	6.55	0.72	x
Helipad space (SC4.2)	6.77	0.61	x
Safety (SC4.3)	6.53	−1.16		x
Accessibility (roads) (SC4.4)	7.84	1.33	x
Personnel (C5)	23.05	1.02	x
Education (SC5.1)	9.03	−1.75		x
Disaster drill (SC5.2)	8.98	0.61	x
Emergency response team (SC5.3)	9.08	−2.55		x
Coordination (SC5.4)	9.25	0.52	x
Number of personnel (SC5.5)	8.92	0.54	x
Working hours (SC5.6)	8.14	0.83	x
Flexibility (C6)	23.09	1.25	x
Flexibility in the use of facilities (SC6.1)	11.54	0.60	x
Contingency staff (SC6.2)	11.51	2.49	x
Blood bank (SC6.3)	11.30	0.57	x
Supply chain of medicines and medical supplies (SC6.4)	11.70	0.66	x

The interrelations within each sub-criteria cluster were assessed through impact digraph maps (Fig. 11, Fig. 12, Fig. 13 ). The influence diagram for criteria is presented in Fig. 11a. In this cluster, the adopted threshold (p) was established as after defuzzifying the respective total relation fuzzy matrix . From the graph, it can be discriminated that all the criteria are dispatchers. Moreover, several interrelations are observed among these decision elements; some of them are of feedback nature (C2-C3; C2-C5, C3-C5; C3-C6). In light of the above-mentioned considerations, multidimensional emergency operation plans should be designed, disseminated, simulated, and deployed by disaster managers to upgrade the performance of hospitals upon facing disaster events. Simulation of such plans will provide further analysis on each criterion so that hospital weaknesses can be properly detected and tackled before the occurrence of a disastrous situation.

Fig. 11

Impact-Diagram map for a) criteria and b) hospital buildings clusters.

Fig. 12

Impact-Diagram map for a) communication and b) transportation clusters.

Fig. 13

Ranking of hospitals based on closeness coefficient.

Likewise, the (D + R, D-R) data set was graphed for Hospital buildings (C1), Communication (C3), and Transportation (C4) (Fig. 11, Fig. 12b) as examples of how interdependence was assessed in each cluster of sub-criteria. For example, the accepted threshold value for “Hospital buildings” (C1) was defined as . In this cluster (Fig. 11a), Disaster gathering area (SC1.5), Insulation (SC1.6), and Ventilation (SC1.7) were found to be dispatchers while Physical infrastructure (SC1.1), Location (SC1.2), Number of floors (SC1.3), and Capacity (SC1.4) were classified as receivers. Similar to the “criteria” group, C1 elements are of interactive nature including one-direction influences and feedback (SC1.1-SC1.2; SC1.1-SC1.3; SC1.1-SC1.4; SC1.1-SC1.5; SC1.1-SC1.6; SC1.1-SC1.7). The influence of SC1.5, SC1.6, and SC1.7 on the rest of elements is based on the fact that these sub-criteria greatly restrict building, design, and location conditions of hospital infrastructure; aspects often considered by administrators when expanding, relocating, and adapting their facilities to the potential requirements derived from devastations.

The influence diagram for “Communication” (C3) sub-factors is depicted in Fig. 12a. In this configuration, the reference value was stated as . In this domain, a feedback interrelation was detected between SC3.2 and SC3.1. The need for constant communication support is critical for effectively underpinning the operation flows within ECNs. In the opposite direction, the ECN configuration affects the quantity and deployment of communication devices in each hospital. As also found in the previous clusters, interactions are present in each paired relation which entails high degree of complexity for managers when including these aspects in the emergency operation programmes.

Finally, an influence map (Fig. 12b) was drawn to analize the interdependence among “Transportation” (C4) sub-criteria. The limit value considered in this cluster was set as . Based on the diagram, the decision elements strongly interact with each other even in a double-direction form as presented in SC4.1-SC4.4, SC4.2-SC4.4, and SC4.3-SC4.4. Also, “Number of vehicles” (SC4.1), “Helipad space” (SC4.2), and “Accessibility (roads)” (SC4.4) were concluded to be deliverers whilst “Safety” (SC4.3) was classified as receiver. It is noteworthy that all transportation modes used in the healthcare system are insights required for the correct deployment of safety measures seeking for protecting victims in the wake of a disaster. Understanding the relationship between transportation conditions and patient safety will help disaster managers reduce potential adverse events during catastrophic events and establish guidelines for appropriate risk management.

Integrating the FAHP and FDEMATEL methods

The global priorities of criteria ( and sub-criteria on the basis of interdependence were estimated by implementing Eq. (16) and Eq. (18) correspondingly. Likewise, local interdependence weights of sub-criteria were calculated using Eq. (17). The results derived from these equations have been compiled in Table 13 . Based on FAHP-FDEMATEL outcomes, Personnel (C5) was found to be the most important factor () when assessing the hospital preparedness when facing devastating situations. Little difference (0.015) was also detected between this criterion and Equipment (C2). Such results invite disaster management planners to fully consider these categories to effectively respond to the shock of disasters and return to stability. Indeed, effective management of Personnel (C5) and Equipment (C2) is critical for upgrading the performance of emergency care networks when facing catastrophic events. For instance, the availability of medical teams, administrative staff, and resources play a key role for ensuring successful onsite-rescue and within-hospital medical care. Moreover, sharing medical staff and other resources is one the main activities specified in the Memorandums of Understanding (MoUs) signed by hospitals. In particular, the presence of suitable and sufficient personnel and equipment supports hospital response, especially in the aftermath of a disaster. Considerable efforts should be then made on C2 and C5 to establish appropriate supplier agreements and train medical staff in disaster management so that Flexibility (C6) can be effectively pursued as highlighted in the previous section.

Table 13

Local and global interdependence weights of criteria and sub-criteria using FAHP-FDEMATEL.

	FAHP-FDEMATEL
	LW	GW
Hospital buildings (C1)		0.121
Physical infrastructure (SC1.1)	0.354	0.043
Location (SC1.2)	0.203	0.025
Number of floors (SC1.3)	0.064	0.008
Capacity (SC1.4)	0.169	0.020
Disaster gathering area (SC1.5)	0.075	0.009
Insulation (SC1.6)	0.065	0.008
Ventilation (SC1.7)	0.071	0.009
Equipment (C2)		0.265
Medicine (SC2.1)	0.171	0.045
Potential hazardous substance (SC2.2)	0.026	0.007
Material safety management (SC2.3)	0.097	0.026
Medical equipment for ES (SC2.4)	0.188	0.050
Power generator (SC2.5)	0.043	0.011
Drinking water (SC2.6)	0.113	0.030
Tent (SC2.7)	0.041	0.011
Food (SC2.8)	0.089	0.024
Bed (SC2.9)	0.047	0.012
Triage tag (SC2.10)	0.057	0.015
Finance (SC2.11)	0.052	0.014
Supply source (SC2.12)	0.074	0.020
Communication (C3)		0.110
Emergency network (SC3.1)	0.643	0.071
Communication tools/device (SC3.2)	0.161	0.018
Information quality (SC3.3)	0.195	0.022
Transportation (C4)		0.080
Number of vehicles (SC4.1)	0.141	0.011
Helipad space (SC4.2)	0.197	0.016
Safety (SC4.3)	0.264	0.021
Accessibility (roads) (SC4.4)	0.397	0.032
Personnel (C5)		0.280
Education (SC5.1)	0.341	0.096
Disaster drill (SC5.2)	0.166	0.046
Emergency response team (SC5.3)	0.174	0.049
Coordination (SC5.4)	0.179	0.050
Number of personnel (SC5.5)	0.083	0.023
Working hours (SC5.6)	0.057	0.016
Flexibility (C6)		0.144
Flexibility in the use of facilities (SC6.1)	0.163	0.024
Contingency staff (SC6.2)	0.161	0.023
Blood bank (SC6.3)	0.436	0.063
Supply chain of medicines and medical supplies (SC6.4)	0.239	0.035

Following this, we have stratified our analysis to look into the importance of each sub-criterion in each cluster. For instance, in Hospital buildings (C1) category, the most important decision element was Physical infrastructure (SC1.1) () whereas the second sub-criterion in the ranking was Location (SC1.2) (). Such aspects represent more than a half of importance (0.557) in C1 criterion and they should be therefore urgently focused for continuous monitoring and improvement in hospitals. In particular, disaster managers should analyse the current state of the division of internal hospital spaces, the external envelope, structure, services, and contents to grant the safety of medical staff and victims after the catastrophic event. Unfortunately, most hospitals fail to include built environment issues in their disaster management plans [58,59]. In this regard, it is recommended to: i) check and modify (if needed) the hospital layout to facilitate flow throughout the hospital during a disaster, ii) perform maintenance activities to minimize infrastructure vulnerabilities, and iii) review past disaster experiences and their effects on physical hospital infrastructure. In relation to Location (SC1.2), it is necessary to lessen the average travel distance for strikes’ victims over a range of potential disaster scenarios. Hospital location models [60,61] should be then used for supporting this decision so that timely medical care can be provided to patients.

In Equipment (C2) criterion, Medical equipment for ES (SC2.4) and Medicine (SC2.1) were concluded to be the most relevant sub-factors with local weights of 0.188 and 0.171 respectively. Such results call for clearly determining the supplies and medical equipment needed for handling disasters effectively. In this regard, it is vital to partner with supply chains capable of providing the sufficient and appropriate resources during disasters without stockpiling within the hospitals’ facilities. Prior to this, disaster managers should identify, plan, and coordinate the timely supply of medical equipment and supplies so that hospitals can deliver the appropriate medical care before and after the strike. Some other significant recommendations to properly manage these aspects can be found at de Jong and Benton [62].

Looking into the results within the Communication (C3) domain, it was concluded that the most critical aspect is Emergency network (SC3.1) (). It is noteworthy that failure of hospitals during catastrophic events can highly affect public morale and increase needless deaths. In this sense, Emergency care networks (ECNs) may alleviate the burden faced by hospitals individually by co-ordinately sharing medical staff, emergency drugs, and other critical resources. Thereby, the service level for disaster resources can be meaningfully improved which consequently ensures timely disaster response. Notwithstanding the tremendous efforts made by governments in this particular aim, ECNs are still at the earlier stages. In this sense, inefficiency factors such as the lack of coordination among hospitals and the presence of non-value added activities should be properly tackled by disaster managers to grant their adequate performance when facing devastating community events.

With regards to Transportation (C4) category, Accessibility (roads) (SC4.4) was identified as the most important sub-criterion with a local priority of 0.397. Road accessibility to hospital facilities is critical for granting rapid medical care to disaster victims. In this respect, ground failure, imploding buildings to road edges, and bridges collapse may occur and limit the patient flows during catastrophic situations. As accessibility changes after disastrous events [63], it is suggested to: i) evaluate road closure probabilities during the different types of disaster, ii) elaborate a disaster management plan in which hospitals can be pre-allocated to improve accessibility, and iii) implement accessibility models for helping emergency managers to better define emergency routes for evacuation and medical care.

In relation to Personnel (C5) area, the most critical aspect to be considered during disastrous situations is Education (SC5.1) whose local weight was calculated to be 0.341. In the presence of unanticipated strikes, disaster management preparedness is recognized as crucial for medical staff and nurses so that effective care can be provided to the multiple victims arriving to the hospitals. Indeed, continuing disaster management courses have become an important strategy for avoiding errors that may hinder the response of hospitals before and after devastating events [64]; hence SC5.1 has been also considered as the sub-criterion with the major interdependence weight in the hospital preparedness evaluation (. Some recommendations for effectively managing the disaster preparedness of staff include: i) continuously evaluate the core competencies, skills, and knowledge of physicians, nurses, and other support staff regarding the management of disastrous situations, ii) the inclusion of disaster preparedness in national curricula of medical staff so that worsening of events in mass causalty disasters can be effectively prevented, and iii) the implementation of disaster facility drills given the strong interrelationship found between this element and education.

Ultimately, Blood bank (SC6.3) was found to be the most crucial aspect in the Flexibility (C6) domain with a local interdependence weight of 0.436. Undoubtedly, the use of blood products is vital for effectively addressing the diverse kinds of injuries emanating from disasters (either man-made or natural). In the wake in the past disaster experiences, it is then imperative to optimize the blood supply chain so that the healthcare system can navigate through events deviating from the normal day-to-day demands. In light of these considerations, it is recommended to i) determine the need for blood products depending on the potential disaster coverage, ii) ensure a seven-day supply of blood [65], and iii) model and simulate transfusion services throughout the long and short run of a disaster.

Ranking of hospitals: the TOPSIS implementation

This chapter details the application of TOPSIS method whose main objective was to rank the hospitals based on their disaster preparedness whereas pinpointing the weaknesses that should be tackled by each institution so that better response can be expected when facing devastating events. Moreover, the sub-criteria most contributing to the PIS and NIS of each hospital can be discriminated so that focused enhancement strategies can be effectively deployed in the practical disaster scenario. Initially, a performance indicator (Table 14 ) was established per each sub-criterion. Following this, initial TOPSIS decision matrix X (Table 15 ) was arranged considering the hospital alternatives (), performance indicators, and sub-criteria. In particular, the performance indicators values were computed considering the mathematical formula depicted in Table 14. Regarding the hospitals’ profile, H (217 available beds) is a hospital specialized in the education and research of cardiovascular diseases in the north-east of the country. The hospital serves with Cardiology, Cardiovascular Surgery, Chest Diseases, Thoracic Surgery, Anesthesia and Reanimation, Infection, Dental, Internal Medicine, Biochemistry, Microbiology, Radiology and Intensive Care Units. H (620 available beds) is a training and research Hospital status has been gained by giving the authority to train specialists. In addition, the hospital operates as a Health Research and Application Center. The hospital has 41 medical units. It is one of the largest hospitals in the region. Substance abuse treatment center oncology and genetic diseases diagnosis center are one of the unique units of the hospital. H (215 available beds) is one of the oldest hospitals established in the region. It serves in an area where the population is quite crowded. Finally, H (200 available beds) is one of the leading hospitals in the region specialized in bone and rehabilitation. It is distinguished from other hospitals in the region with its robotic rehabilitation unit.

Table 14

Performance indicators supporting TOPSIS application.

Sub-criterion	Performance indicator	Formula
Physical infrastructure (SC1.1)	% of rooms in good infrastructure condition	NRGICTNR*100Where:NRGIC: Number of rooms in good infrastructure condition.TNR: Total number of rooms
Location (SC1.2)	Average distance from target community	∑i=1cd_icWhere: di: Distance from hospital to target community ic: Number of target communities
Number of floors (SC1.3)	Number of floors	Number of floors that the hospital has
Capacity (SC1.4)	Total medical staff	N+D+MSSWhere:N: Total number of nursesD: Total number of doctorsMSS: Number of medical support staff
Disaster gathering area (SC1.5)	Availability of disaster gathering area	If available (2), otherwise (1)
Insulation (SC1.6)	% of correctly insulated ED rooms	NCIEDRTNR−ED*100Where:NCIEDR: Number of correctly insulated ED rooms.TNR-ED: Total number of rooms in ED
Ventilation (SC1.7)	% of rooms with appropriate ventilation	NRAVTNR*100Where:NRAV: Number of rooms with appropriate ventilation.TNR: Total number of rooms
Medicine (SC2.1)	Average fill rate of medicines	∑k=1mFR_kmWhere:FRk: Fill rate of medicine k m: Number of medicines
Potential hazardous substance (SC2.2)	Availability of protocols for the management of potential hazardous substance	If available (2), otherwise (1)
Material safety management (SC2.3)	Implementation of MSDS standards	If implemented (2), otherwise (1)
Medical equipment for ES (SC2.4)	Availability of medical equipment	NAMDTNMD*100Where:NAMD: Number of available medical devices.TNMD: Total number of medical devices.
Power generator (SC2.5)	Availability of power generator	If available (2), otherwise (1)
Drinking water (SC2.6)	Availability of drinking water	If available (2), otherwise (1)
Tent (SC2.7)	Tent availability	If available (2), otherwise (1)
Food (SC2.8)	Availability of Food Services Department	If available (2), otherwise (1)
Bed (SC2.9)	Bed capacity in ED	Number of available beds in ED
Triage tag (SC2.10)	Usage of triage tags	If used (2), otherwise (1)
Finance (SC2.11)	Availability of budget for disaster events	If available (2), otherwise (1)
Supply source (SC2.12)	Availability of equipment supplying sources	If available (2), otherwise (1)
Emergency network (SC3.1)	Connection with Emergency Care Network (ECN)	If connected (2), otherwise (1)
Communication tools/device (SC3.2)	Availability of ECN communication platform	If available (2), otherwise (1)
Information quality (SC3.3)	Information quality level	Linguistic term (1-Very Low, 2-Low, 3-Medium, 4-High, 5-Very High)
Number of vehicles (SC4.1)	Total number of ambulances	Total number of ambulances that the hospital has
Helipad space (SC4.2)	Availability of helipad space	If available (2), otherwise (1)
Safety (SC4.3)	Total number of security guards	Number of security guards that the hospital usually employs
Accessibility (roads) (SC4.4)	Road accessibility	Linguistic term (1-Very Low, 2-Low, 3-Medium, 4-High, 5-Very High)
Education (SC5.1)	Disaster management training	Number of disaster management programs organized by the hospital
Disaster drill (SC5.2)	Number of disaster drills	Number of disaster drill that the hospital has performed
Emergency response team (SC5.3)	Emergency response degree	Linguistic term (1-Very Low, 2-Low, 3-Medium, 4-High, 5-Very High)
Coordination (SC5.4)	Coordination level	Linguistic term (1-Very Low, 2-Low, 3-Medium, 4-High, 5-Very High)
Number of personnel (SC5.5)	Trained staff	Number of staff trained in disaster management
Working hours (SC5.6)	Disaster management experience	∑n=1zWH_nWhere:WHn: Number of working hours of employee n in disaster situations z: Total number of staff trained in disaster management.
Flexibility in the use of facilities (SC6.1)	Extra capacity	Number of administrative areas that can be adapted for emergency care in case of disaster
Contingency staff (SC6.2)	Availability of contingency staff	If available (2), otherwise (1)
Blood bank (SC6.3)	Availability of blood bank	If available (2), otherwise (1)
Supply chain of medicines and medical supplies (SC6.4)	Supply chain size	Number of allied suppliers providing medicines and medical supplies

Table 15

Initial TOPSIS decision matrix X for evaluating the hospital disaster preparedness.

	H1	H2	H3	H4	A+	A-	W	Norm
SC1.1	0.900	0.800	0.300	0.250	1	0	0.043	1.266
SC1.2	2	3	1	3	1	3	0.025	4.796
SC1.3	10	7	5	5	10	5	0.008	14.107
SC1.4	400	750	550	458	750	400	0.020	1111.199
SC1.5	2	2	2	2	2	1	0.009	4.000
SC1.6	0.800	0.800	0.350	0.300	1	0	0.008	1.222
SC1.7	0.850	0.900	0.400	0.300	1	0	0.009	1.335
SC2.1	0.750	0.800	0.850	0.850	1	0	0.045	1.627
SC2.2	2	2	2	2	2	1	0.007	4.000
SC2.3	2	2	2	2	2	1	0.026	4.000
SC2.4	0.015	0.213	0.167	0.106	1	0	0.050	0.291
SC2.5	2	2	2	2	2	1	0.011	4.000
SC2.6	2	2	2	2	2	1	0.030	4.000
SC2.7	1	2	1	1	2	1	0.011	2.646
SC2.8	2	2	2	2	2	1	0.024	4.000
SC2.9	217	620	215	200	620	200	0.012	719.523
SC2.10	2	2	2	2	2	1	0.015	4.000
SC2.11	2	2	2	2	2	1	0.014	4.000
SC2.12	2	2	2	2	2	1	0.020	4.000
SC3.1	2	2	2	2	2	1	0.071	4.000
SC3.2	2	2	2	2	2	1	0.018	4.000
SC3.3	4	5	5	5	5	1	0.022	9.539
SC4.1	2	10	2	1	10	1	0.011	10.440
SC4.2	1	1	1	1	2	1	0.016	2.000
SC4.3	31	62	56	18	62	18	0.021	90.912
SC4.4	4	5	3	3	5	1	0.032	7.681
SC5.1	2	3	2	2	3	2	0.096	4.583
SC5.2	5	5	5	5	5	0	0.046	10.000
SC5.3	4	4	4	4	5	1	0.049	8.000
SC5.4	3	3	3	4	5	1	0.050	6.557
SC5.5	30	480	300	430	480	30	0.023	711.477
SC5.6	9	9	9	9	9	0	0.016	18.000
SC6.1	2	4	3	1	4	1	0.024	5.477
SC6.2	1	1	1	1	2	1	0.023	2.000
SC6.3	2	2	2	2	2	1	0.063	4.000
SC6.4	20	46	30	15	46	15	0.035	60.341

PIS and NIS were also specified in Table 15 by employing Eq. (21) and Eq. (22) correspondingly. The normalized ratings are later calculated using Eq. (19) (Table 16 ) whereas the weighted normalized ratings were estimated by applying Eq. (20) (Table 17 ). The interdependence weights of sub-criteria were calculated through the integrated FAHP-FDEMATEL approach illustrated in the previous section. On the other hand, the Euclidean distance of each hospital ( from the PIS () was calculated using Eq. (23) (Table 18 ). In a similar vein, the separation of each hospital from the NIS () was estimated by applying Eq. (24) (Table 19 ).

Table 16

The normalized TOPSIS decision matrix for evaluating the hospital disaster preparedness.

	H1	H2	H3	H4	A+	A-	W
SC1.1	0.711	0.632	0.237	0.197	0.790	0	0.043
SC1.2	0.417	0.626	0.209	0.626	0.209	0.626	0.025
SC1.3	0.709	0.496	0.354	0.354	0.709	0.354	0.008
SC1.4	0.360	0.675	0.495	0.412	0.675	0.360	0.020
SC1.5	0.500	0.500	0.500	0.500	0.500	0.250	0.009
SC1.6	0.655	0.655	0.286	0.246	0.819	0	0.008
SC1.7	0.637	0.674	0.300	0.225	0.749	0	0.009
SC2.1	0.461	0.492	0.522	0.522	0.615	0	0.045
SC2.2	0.500	0.500	0.500	0.500	0.500	0.250	0.007
SC2.3	0.500	0.500	0.500	0.500	0.500	0.250	0.026
SC2.4	0.051	0.733	0.573	0.364	3.436	0	0.050
SC2.5	0.500	0.500	0.500	0.500	0.500	0.250	0.011
SC2.6	0.500	0.500	0.500	0.500	0.500	0.250	0.030
SC2.7	0.378	0.756	0.378	0.378	0.756	0.378	0.011
SC2.8	0.500	0.500	0.500	0.500	0.500	0.250	0.024
SC2.9	0.302	0.862	0.299	0.278	0.862	0.278	0.012
SC2.10	0.500	0.500	0.500	0.500	0.500	0.250	0.015
SC2.11	0.500	0.500	0.500	0.500	0.500	0.250	0.014
SC2.12	0.500	0.500	0.500	0.500	0.500	0.250	0.020
SC3.1	0.500	0.500	0.500	0.500	0.500	0.071	0.071
SC3.2	0.500	0.500	0.500	0.500	0.500	0.018	0.018
SC3.3	0.419	0.524	0.524	0.524	0.524	0.022	0.022
SC4.1	0.192	0.958	0.192	0.096	0.958	0.011	0.011
SC4.2	0.500	0.500	0.500	0.500	1	0.016	0.016
SC4.3	0.341	0.682	0.616	0.198	0.682	0.021	0.021
SC4.4	0.521	0.651	0.391	0.391	0.651	0.032	0.032
SC5.1	0.436	0.655	0.436	0.436	0.655	0.096	0.096
SC5.2	0.500	0.500	0.500	0.500	0.500	0.046	0.046
SC5.3	0.500	0.500	0.500	0.500	0.625	0.049	0.049
SC5.4	0.457	0.457	0.457	0.610	0.762	0.050	0.050
SC5.5	0.042	0.675	0.422	0.604	0.675	0.023	0.023
SC5.6	0.500	0.500	0.500	0.500	0.500	0.016	0.016
SC6.1	0.365	0.730	0.548	0.183	0.730	0.024	0.024
SC6.2	0.500	0.500	0.500	0.500	1	0.023	0.023
SC6.3	0.500	0.500	0.500	0.500	0.500	0.063	0.063
SC6.4	0.331	0.762	0.497	0.249	0.762	0.035	0.035

Table 17

The weighted normalized TOPSIS decision matrix for evaluating the hospital disaster preparedness.

	H1	H2	H3	H4	A+	A-
SC1.1	0.03	0.027	0.01	0.008	0.034	0
SC1.2	0.01	0.015	0.005	0.015	0.005	0.015
SC1.3	0.006	0.004	0.003	0.003	0.006	0.003
SC1.4	0.007	0.014	0.01	0.008	0.014	0.007
SC1.5	0.005	0.005	0.005	0.005	0.005	0.002
SC1.6	0.005	0.005	0.002	0.002	0.006	0
SC1.7	0.005	0.006	0.003	0.002	0.006	0
SC2.1	0.021	0.022	0.024	0.024	0.028	0
SC2.2	0.003	0.003	0.003	0.003	0.003	0.002
SC2.3	0.013	0.013	0.013	0.013	0.013	0.006
SC2.4	0.003	0.037	0.029	0.018	0.171	0
SC2.5	0.006	0.006	0.006	0.006	0.006	0.003
SC2.6	0.015	0.015	0.015	0.015	0.015	0.007
SC2.7	0.004	0.008	0.004	0.004	0.008	0.004
SC2.8	0.012	0.012	0.012	0.012	0.012	0.006
SC2.9	0.004	0.011	0.004	0.003	0.011	0.003
SC2.10	0.008	0.008	0.008	0.008	0.008	0.004
SC2.11	0.007	0.007	0.007	0.007	0.007	0.003
SC2.12	0.01	0.01	0.01	0.01	0.01	0.005
SC3.1	0.035	0.035	0.035	0.035	0.035	0.018
SC3.2	0.009	0.009	0.009	0.009	0.009	0.004
SC3.3	0.009	0.011	0.011	0.011	0.011	0.002
SC4.1	0.002	0.011	0.002	0.001	0	0.001
SC4.2	0.008	0.008	0.008	0.008	0.016	0.008
SC4.3	0.007	0.014	0.013	0.004	0.014	0.004
SC4.4	0.017	0.021	0.012	0.012	0.021	0.004
SC5.1	0.042	0.063	0.042	0.042	0.063	0.042
SC5.2	0.023	0.023	0.023	0.023	0.023	0
SC5.3	0.024	0.024	0.024	0.024	0.03	0.006
SC5.4	0.023	0.023	0.023	0.03	0.038	0.008
SC5.5	0.001	0.016	0.01	0.014	0.016	0.001
SC5.6	0.008	0.008	0.008	0.008	0.008	0
SC6.1	0.009	0.017	0.013	0.004	0.017	0.004
SC6.2	0.012	0.012	0.012	0.012	0.023	0.012
SC6.3	0.031	0.031	0.031	0.031	0.031	0.016
SC6.4	0.011	0.026	0.017	0.009	0.026	0.009

Table 18

The Euclidean distances from PIS.

	H1	H2	H3	H4
SC1.1	0.000	0.000	0.001	0.001
SC1.2	0.000	0.000	0.000	0.000
SC1.3	0.000	0.000	0.000	0.000
SC1.4	0.000	0.000	0.000	0.000
SC1.5	0.000	0.000	0.000	0.000
SC1.6	0.000	0.000	0.000	0.000
SC1.7	0.000	0.000	0.000	0.000
SC2.1	0.000	0.000	0.000	0.000
SC2.2	0.000	0.000	0.000	0.000
SC2.3	0.000	0.000	0.000	0.000
SC2.4	0.028	0.018	0.020	0.023
SC2.5	0.000	0.000	0.000	0.000
SC2.6	0.000	0.000	0.000	0.000
SC2.7	0.000	0.000	0.000	0.000
SC2.8	0.000	0.000	0.000	0.000
SC2.9	0.000	0.000	0.000	0.000
SC2.10	0.000	0.000	0.000	0.000
SC2.11	0.000	0.000	0.000	0.000
SC2.12	0.000	0.000	0.000	0.000
SC3.1	0.000	0.000	0.000	0.000
SC3.2	0.000	0.000	0.000	0.000
SC3.3	0.000	0.000	0.000	0.000
SC4.1	0.000	0.000	0.000	0.000
SC4.2	0.000	0.000	0.000	0.000
SC4.3	0.000	0.000	0.000	0.000
SC4.4	0.000	0.000	0.000	0.000
SC5.1	0.000	0.000	0.000	0.000
SC5.2	0.000	0.000	0.000	0.000
SC5.3	0.000	0.000	0.000	0.000
SC5.4	0.000	0.000	0.000	0.000
SC5.5	0.000	0.000	0.000	0.000
SC5.6	0.000	0.000	0.000	0.000
SC6.1	0.000	0.000	0.000	0.000
SC6.2	0.000	0.000	0.000	0.000
SC6.3	0.000	0.000	0.000	0.000
SC6.4	0.000	0.000	0.000	0.000
Si+	0.174	0.137	0.149	0.161

Table 19

The Euclidean distances from NIS.

	H1	H2	H3	H4
SC1.1	0.001	0.001	0.000	0.000
SC1.2	0.000	0.000	0.000	0.000
SC1.3	0.000	0.000	0.000	0.000
SC1.4	0.000	0.000	0.000	0.000
SC1.5	0.000	0.000	0.000	0.000
SC1.6	0.000	0.000	0.000	0.000
SC1.7	0.000	0.000	0.000	0.000
SC2.1	0.000	0.000	0.001	0.001
SC2.2	0.000	0.000	0.000	0.000
SC2.3	0.000	0.000	0.000	0.000
SC2.4	0.000	0.001	0.001	0.000
SC2.5	0.000	0.000	0.000	0.000
SC2.6	0.000	0.000	0.000	0.000
SC2.7	0.000	0.000	0.000	0.000
SC2.8	0.000	0.000	0.000	0.000
SC2.9	0.000	0.000	0.000	0.000
SC2.10	0.000	0.000	0.000	0.000
SC2.11	0.000	0.000	0.000	0.000
SC2.12	0.000	0.000	0.000	0.000
SC3.1	0.000	0.000	0.000	0.000
SC3.2	0.000	0.000	0.000	0.000
SC3.3	0.000	0.000	0.000	0.000
SC4.1	0.000	0.000	0.000	0.000
SC4.2	0.000	0.000	0.000	0.000
SC4.3	0.000	0.000	0.000	0.000
SC4.4	0.000	0.000	0.000	0.000
SC5.1	0.000	0.000	0.000	0.000
SC5.2	0.001	0.001	0.001	0.001
SC5.3	0.000	0.000	0.000	0.000
SC5.4	0.000	0.000	0.000	0.001
SC5.5	0.000	0.000	0.000	0.000
SC5.6	0.000	0.000	0.000	0.000
SC6.1	0.000	0.000	0.000	0.000
SC6.2	0.000	0.000	0.000	0.000
SC6.3	0.000	0.000	0.000	0.000
SC6.4	0.000	0.000	0.000	0.000
Si−	0.060	0.080	0.063	0.059

The ranking of hospitals and closeness coefficients are shown in Fig. 13. Such coefficients were computed using Eq. (25). The results revealed that the hospitals performed between 0.632 (H2) and 0.742 (H1); there is therefore much room for improvement and interventions from the stakeholders. It is then necessary to estimate the distances from PIS and NIS to identify the weaknesses of each hospital (sub-criteria whose Euclidean separation from PIS is over zero || Euclidean separation from NIS is equal to 0). In particular, it was found that H2 evidences low availability of medical equipment – SC2.4 (21.3%; separation from PIS = 0.01813) which may cause delays in medical care provided during disaster and consequently increase the risk of mortality. Moreover, H2 is the hospital with the farthest distance from the target community – SC1.2 (3 km; separation from NIS = 0), an aspect that may limit the timely medical care also considering the potential collapse of roads and adjacent buildings. Another weakness is the non-availability of a helipad space – SC4.2 - which highly restricts the patient transferring process from the disaster zone to hospital facilities (separation from NIS = 0). Additionally, there are no contingency staff – SC6.2 - for facing the disaster situation (separation from NIS = 0). Such disadvantage may compromise the hospital response mainly in large-scale catastrophic situations.

On a different tack, similar to H2, H3 concerns about the low availability of medical equipment – SC2.4 (16.7%; separation from PIS = 0.02034) and non-availability of helipad space – SC4.2 (separation from NIS = 0) and contingency staff – SC6.2 (separation from NIS = 0). Also, it has the lowest number of floors – SC1.3 (5 floors, separation from NIS = 0) and ambulances – SC4.1 (2 vehicles, separation from NIS = 0), an aspect limiting the capacity for addressing the peaks of demand that may arise from the disaster. Moreover, H3 does not evidence the use of tents – SC2.7 (separation from NIS = 0) which also restricts its disaster preparedness. The major disadvantage is the number of disaster management programs organized by the hospital – SC5.1 (2 training programs; separation from NIS = 0), a fact that may trigger errors during on-site rescue, patient transportation, and medical care.

Regarding H4, more investment and maintenance intervention is needed for increasing the availability of medical devices – SC2.4 (10.6%; separation from PIS = 0.02342). In addition, H4 also has the farthest separation from the target community – SC1.2 (3 km; separation from NIS = 0) and the lowest number of floors – SC1.3 (5 floors, separation from NIS = 0). Apart from these findings, it is observed that H4 presents the shortest % of correctly insulated ED rooms – SC1.6 (30.0%; separation from NIS = 0) and % of rooms with appropriate ventilation – SC1.7 (30.0%; separation from NIS = 0). Both conditions may hinder the correct deployment of disaster management plans in the wild; especially during medical intervention Similar to H3, H4 does not either denote tent usage – SC2.7 (separation from NIS = 0). Also, the number of beds – SC2.9 - is limited compared to the rest of hospitals (200 beds; separation from NIS = 0). Shortage of beds has become a significant barrier for addressing large-scale outbreaks as those expected in the future. Moreover, H4 only has one ambulance – SC4.1 (separation from NIS = 0) which may not be enough for facing the potential upcoming events (i.e. coronavirus [66]). On the other hand, as all the hospitals participating in this study, no helipad space is available – SC4.2 (separation from NIS = 0). Moreover, H4 has the lowest number of security guards – SC4.3 (18 guards; separation from NIS = 0) which may not facilitate the patient flow and medical staff protection during a disaster. The number of training programms in disaster management is also low – SC5.1 (2 programs; separation from NIS = 0) and new courses should be therefore implemented for increasing the competences, knowledge, and skills of H4 workers. Lately, this hospital was not found to be flexible as revealed through poor outcomes in the associated sub-criteria.

Finally, in relation to the leading hospital, the TOPSIS results evidenced the need for intervention in the next sub-criteria: SC1.4 (400; separation from NIS = 0), SC2.4 (1.5%; separation from PIS = 0.02842), SC2.7 (separation from NIS = 0), SC4.2 (separation from NIS = 0), SC5.1 (2 training programs; separation from NIS = 0), SC5.5 (30 trained employees; separation from NIS = 0), and SC6.2 (separation from NIS = 0).

Conclusions

Recently, due to the increase in natural and man-made disasters occurring over the world and Turkey, the importance of the level of preparedness for hospitals becomes clearer once again. Determining the level of disaster preparedness of hospitals is an important and necessary issue. This is because identifying hospitals with a low level of preparedness is very essential for disaster preparedness planning. Given the results of the Covid-19 pandemic, where the healthcare sector is currently in a great struggle, it is clear that the making the hospitals, field hospitals or pandemic hospitals prepared and ready for such disasters should be made quickly and reliably. This reinforces the conclusion that a possible rapid demand situation scenario which has not mentioned sufficiently in the literature will play a very important role in the disaster management decisions. In this study, an iterative decision making model under fuzzy sets is proposed to evaluate hospital disaster preparedness. Existed model has been developed including FAHP, FDEMATEL, and TOPSIS methods. It is aimed to determine ranking orders of four observed and analysed hospitals in Turkey regarding disaster preparedness. FAHP is used to determine weights of six main criteria of hospital buildings, equipment, communication, transportation, personnel, flexibility and a total of thirty-six sub-criteria. FDEMATEL is hereafter applied to uncover the interdependence between criteria and sub-criteria. As a ranking tool, TOPSIS is used to determine a ranking of hospitals. In application phase of the existed decision making model, two different questionnaires are created and assessed by seven experts related to the field of disaster management of healthcare facilities and academicians who are experienced for the disaster management topics.

The numerical results demonstrated that “Personnel” is the most important factor (with a global weight value of 0.280) when evaluating the hospital preparedness while “Flexibility” has the greatest prominence (with a c + r value of 23.09). In the light of the numerical results obtained from this study, it is crucial that the observed and analysed hospitals design a better disaster preparedness plan in order to be more prepared against disasters. In relation to the scenario under study, the results revealed that the hospitals performed between 0.632 (H2) and 0.742 (H1); there is hence much room (Gap to target: 0.258–0.368) for interventions increasing the current disaster readiness level. These interventions must address the main weaknesses detected in the cited set of hospitals: i) low availability of medical equipment, ii) lack of helipad spaces, iii) low availability of contingency staff, iv) lack of tents, and v) low number of disaster management training programs. Thereby, these hospitals will be better prepared for facing future outbreaks in terms of timeliness, quality, and efficiency.

This approach is useful for the related research field considering that methods measuring the hospital disaster preparedness levels are lacking [56,67]. However, it has some limitations from both methodological and application viewpoints. We consider triangular fuzzy sets in both AHP and DEMATEL stages. Considering there exist various new versions of fuzzy set theory that reflect uncertainty and ambiguity of decision making process better, the current approach may be extended to integrate AHP and DEMATEL with some new versions of fuzzy set such as intuitionistic fuzzy sets, interval type-2 fuzzy sets, hesitant fuzzy sets, Pythagorean fuzzy sets and spherical fuzzy sets. From application viewpoint, we limit the current study with four Turkish hospitals. The proposed approach can be offered to health policy makers of Turkey as a model on a national scale. In this context, the authors intend to further improve the approach by means such as considering some new hospital disaster preparedness criteria that will be suggested by these policy makers. Also, as a second attempt, the authors contemplate adapt the approach to Colombian hospital emergency department disaster preparedness assessment.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.