Research On Competitive Multi-attribute Group Decision Making Based On Game Theory

Multi-attribute group decision making mainly focuses on the evaluation and ranking of alternatives by group experts according to attribute indexes.However,the existing research on multi-attribute group decision does not consider the influence of external environment on the decision result.That is,the multi-attribute group decision making process may be in a highly competitive environment.In view of the above competitive multi-attribute group decision problem,the experts involved in the decision often give subjective evaluation of the alternative,and among the numerous subjective evaluation information,2-dimension 2-tuple linguistic variables and2-dimension uncertain linguistic variables can describe the subjective preference of experts more directly and accurately.Therefore,it is an urgent problem to determine the Nash equilibrium of the competitive multi-attribute group decision making problem with2-dimension 2-tuple linguistic variables and 2-dimension uncertain linguistic variables.In this thesis,based on the improved evidence combination theory and the 3? principles of gaussian distribution,2-dimension 2-tuple linguistic variables and 2-dimension uncertain linguistic variables are assembled respectively.First of all,this thesis improves the theory of evidence combination from two aspects of evidence source and evidence combination rule,and proposes a new operator for aggregation of 2-dimension 2-tuple linguistic variables,and proves the feasibility and advantages of the operator through an example analysis.Second,for 2-dimension uncertain linguistic variables,this thesis analyzes the existing two-dimensional uncertain linguistic variable scoring function and distance formula and based on 3 ? principles of gaussian distribution defines the new scoring function and distance formula,and then based on the new distance formula weight model of 2-dimension uncertain linguistic variable is established and based on the weighted average operator assembled2-dimension uncertain linguistic variables,the comprehensive evaluation value of the alternative is determined based on the new score function value.Finally,based on the non-cooperative game theory,a simultaneous optimization model is established to determine the Nash equilibrium of competitive multi-attribute group decision problems with two linguistic variables.