Three-way decision oriented rational behavior multi-attribute decision-making

Abstract

Three-way decision is a methodology that utilizes human cognitive thinking to handle multi-attribute decision-making with deferral decision-making. The key to achieving this goal is to reasonably fuse evaluation values from multiple attributes of alternatives to extract rules for classifying and ranking alternatives. There have been already lots of literature addressing this issue by considering the regret psychology of decision-makers. However, the regret theory oriented multi-attribute decision-making may lead to irrational or incomplete decision strategies. To tackle such a challenge, this paper introduces the idea of game theory into behavior three-way decision based multi-attribute decision-making (GBMADM) to weighted fuse regret and rejoice values of each alternative across all attributes to extract game rules for classifying and ranking alternatives. Firstly, a decision state set is fuzzified with the idea of TOPSIS and the weight of each attribute is determined based on the self-information of approximate accuracy from generalized fuzzy rough set theory. Secondly, a pair of utility functions is introduced to act as players to play in game. Two pairs of weighted regret functions and weighted rejoice functions are achieved by fusing the regret values and rejoice values of each alternative across all attributes, respectively. A payoff matrix for each alternative is then constructed by fusing the weighted regret value and weighted rejoice value. All decision rules for classification and ranking are thereafter extracted from the payoff matrix through optimal Nash equilibrium solutions. Finally, a practical example and simulation experiments on two benchmark datasets demonstrate the superiority of the proposed method compared to representative methods.