Group decision-making model with incomplete fuzzy preference relations based on additive consistency.

In decision-making problems there may be cases in which experts do not have an in-depth knowledge of the problem to be solved. In such cases, experts may not put their opinion forward about certain aspects of the problem, and as a result they may present incomplete preferences, i.e., some preference values may not be given or may be missing. In this paper, we present a new model for group decision making in which experts' preferences can be expressed as incomplete fuzzy preference relations. As part of this decision model, we propose an iterative procedure to estimate the missing information in an expert's incomplete fuzzy preference relation. This procedure is guided by the additive-consistency (AC) property and only uses the preference values the expert provides. The AC property is also used to measure the level of consistency of the information provided by the experts and also to propose a new induced ordered weighted averaging (IOWA) operator, the AC-IOWA operator, which permits the aggregation of the experts' preferences in such a way that more importance is given to the most consistent ones. Finally, the selection of the solution set of alternatives according to the fuzzy majority of the experts is based on two quantifier-guided choice degrees: the dominance and the nondominance degree.