Regret theory-based group decision-making with multidimensional preference and incomplete weight information

In this paper, we study fuzzy multi-attribute group decision-making (FMAGDM) problems with multidimensional preference information in the form of pairwise alternatives and incomplete weight information. We develop a new group decision-making (GDM) method considering regret aversion of the decision-makers (DMs). Firstly, we define a fuzzy regret/rejoice function and a computational formula for the perceived utility of alternative decisions. We propose a perceived utility value-based group consistency index (which reflects the total consistency) and a group inconsistency index (which represents the total inconsistency) for pairwise rankings of alternatives based on regret theory and an a priori multidimensional preference order given by the DMs. Then, under the circumstances of an unknown fuzzy ideal solution, we set up a mathematical programming model to determine the optimal attribute weights and a defuzzified fuzzy ideal solution with the idea of the Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP). We compute the DMs’ optimal comprehensive perceived utility values and obtain the ranking order of alternatives. Finally, we illustrate the application of the developed procedures with an air-fighter selection problem. The rationality and validity of the proposed method is demonstrated by comparing with two other GDM methods, including the fuzzy LINMAP (FLINMAP) method and the prospect theory-based GDM method.