Effective allocation of resources in water pollution treatment alternatives: a multi-stage gray group decision-making method based on hesitant fuzzy linguistic term sets.

With the significant economic shift, water pollution treatment has gradually become a key problem which needs to be deeply investigated for the sustainable development of China. In the face of specific water pollution incidents, multiple alternatives are often required to work together in order to achieve better results. However, due to the limitation of resources, alternatives must be ranked to realize the effective allocation of resources, which means the more highly ranked ones should possess more disposable resources. Furthermore, the water pollution treatment process is a multi-stage and multi-objective process. In each stage, decision-makers may have different emphasis and thus have different preferences for the treatment alternatives. How to effectively aggregate decision-makers' preferences in different stages into an overall preference so as to form a ranking of treatment alternatives under global constraints has turned into a problem worthy of discussion. Under such background, this paper proposes a multi-stage gray group decision-making method, where decision-makers use Group-G1 to rank and weight the criteria, and in this way, the weights of decision-makers and criteria in each stage could be determined. Considering the difference and deficiency of the cognitive level of decision-makers, this paper adopts the form of hesitant fuzzy linguistic term sets (HFITS) to express the evaluation information of decision-makers. And then, gray incidence analysis is selected to rank the alternatives. After ranking the alternatives in each stage, the multi-stage rankings will be aggregated into an overall ranking and the resource allocation is made according to the priorities of the alternatives. Finally, an example of water pollution treatment alternatives ranking based on a cyanobacterial bloom in Taihu Lake, China, is given to illustrate the proposed approach.