Research On Group Decision-making Based On Fuzzy Evolutionary Game

With the continuous development of modern society,it is difficult for human groups to make correct decisions when faced with risks and challenges in the face of massive amounts of informational data.In recent years,many scholars have applied evolutionary game theory to group risk decision-making,which has solved many important problems in theory and practice.However,the evolution of groups over time is often full of uncertainty,so the numerical simulation is very complicated,and even the results cannot be calculated.Fuzzy mathematical theory is a mathematical tool for solving various uncertain problems.If fuzzy mathematics is integrated into evolutionary game theory,it is possible to better simulate the complex and changeable phenomena in reality.However,under the framework of relevant fuzzy theory,whether the steady-state distribution of evolutionary games can be analyzed by numerical experiments,and whether the obtained results are consistent with classical theory,these are the problems that need to be answered.Therefore,this paper is devoted to introducing the triangular fuzzy numbers in fuzzy mathematics into the classical evolutionary game theory,and constructs several types of fuzzy evolutionary game models.This verifies the plausibility of the models.The main research content of this paper is as follows:1.For the fuzzy set theory,the definition and properties of triangular fuzzy numbers are given in the form of cut sets,and then the relevant algorithms are defined,and finally the relevant calculation examples are given.2.Aiming at the limitation of the classical evolutionary game model to the simulation of group decision-making,by introducing triangular fuzzy numbers,the relevant parameters in the finite group model are fuzzified,and the corresponding fuzzy evolution is given under the penalty conditions,incentive conditions and sampling conditions respectively.game model.Then,using pairwise comparison rules and random process theory,by describing its fuzzy probability transition state matrix and further calculating the fuzzy eigenvectors of the matrix,the steady-state distribution of the system evolution is obtained,and then the fuzzy transition probability matrix with penalty model is calculated using an example.Numerical results show that the change of fuzzy transition probability matrix is more sensitive to high risk value,which is consistent with the results of classical game theory,so the fuzzy evolutionary game model is reasonable.3.To solve the eigenvector problem of fuzzy transition probability matrix in fuzzy evolutionary game,the solution of fuzzy homogeneous linear equations is studied.In this paper,by taking the 1-cut set on both sides of the characteristic equation,it is transformed into a classical linear equation system to solve.At the same time,the upper and lower bounds of the fuzzy eigenvalues are specified by using the upper and lower price difference,and the triangular fuzzy number is brought in for further calculation.In addition,when discussing the value of fuzzy eigenvectors,different cut sets such as the maximum and minimum values,triangle median and membership function median are taken for relevant parameters according to the situation,and they are transformed into linear problems to solve.Further,the theory is integrated into the evolutionary game model,and the steady-state distribution of the system is calculated.Numerical results show that groups will ultimately tend to choose betray at low risk,and ultimately tend to make cooperative decisions at high risk.Therefore,this conclusion is consistent with the group decisionmaking behavior in the classical model,which proves that the fuzzy evolutionary game model has certain application value.