Fuzzy Lattice Order Group Decision for Preference Ranking in Conflict Analysis

Abstract

Methods of fuzzy multi-objective lattice order decision making (F-MOLODM) for analyses of the fuzzy and intransitive preferences of decision makers involved in a conflict analysis are devised for the preference ranking of the states in a conflict, which defines the trapezoidal fuzzy number of the preference and constructs a multi-objective group decision-making fuzzy preference matrix. An algorithm for F-LOGDM is proposed to capture uncertainty and intransitive decision problems, and the relationship among lattice elements of the preference structure under fuzzy environments is defined. The application of these decision technologies to the square dance conflict illustrate how the method proposed in this paper can be utilized in practice. The performance of the lattice order preference ranking method applied to the conflict is compared with that of traditional methods. Research shows that either lattice order preference ranking, or traditional methods acquires Nash stability. However, the stable state under traditional methods will be reached only if all players pay a certain price.