Fuzzy Multi-criteria Decision Making Method Based On Fuzzy Owa Operator And Prospect Theory

Multi-criteria decision-making problems(MCDM) are generally to rank and optimize finite alternatives according to certain ways by utilizing known decision information.As many decision making problems have their fuzziness,there exist a great many of fuzzy multi-criteria decision-making(FMCDM) problems which have some uncertain parameters such as criteria of alternative,weights and preferences of decision makers.Hence,it is of great theoretical significance as well as practical value for the systematic studies on the fuzzy multi-criteria ranking problems.And decision makers viewed as rational decision makers in current decision making problems but not considered to be non-rational,so it is also significant to introduce non-rational factor into FMCDM problems.On the basis of researches on relative theories,this paper investigates fuzzy OWA operator,prospect theory and their applications in MCDM,presents a corresponding decision model and solves problems with the optimization theories and algorithms.And the details are as follows:(1) Fuzzy ordered weighted averaging(FOWA) operator,weighted fuzzy ordered weighted averaging(WF-OWA) operator,ordered weighted fuzzy ordered weighted averaging(OWF-OWA) operator and combined F-OWA(COWF-OWA) operator are defined firstly.And some properties of these operators are investigated.Then,two FMCDM approaches,which are based on WF-OWA operator and OWF-OWA operator respectively,are developed and an approach for solving multi-criteria fuzzy group decision-making(FMCGDM) problems based on COWF-OWA operator is proposed.(2) The prospect value function of trapezoidal fuzzy number,the prospect function of trapezoidal fuzzy number and extended preference function based on prospect value function are defined.With regard to uncertain MCDM problems,in which the criteria weights are incompletely certain and the criteria value of alternatives are in the form of trapezoidal fuzzy numbers,a nonlinear programming model which maximizes prospect value of alternative are constructed based on prospect theory.After that,the genetic algorithm is used to solve the model to attain the criteria weights,and the order of alternatives can be listed consequently.And for MCDM problems,in which the criteria values of alternatives are in the form of trapezoidal fuzzy numbers and the criteria weights are completely known,an improved PROMETHEEⅡmethod based on prospect theory is proposed,which combines PROMETHEEⅡmethod with prospect theory and better reflects the preference of decision makers.Then for the FMCGDM problem,in which the criteria values of alternatives are in the form of trapezoidal fuzzy numbers and the criteria weights are completely known,a similar matrix of two decision makers' preferences on each alternative can be obtained by using grey incidence coefficient,and the group decision matrix of alternatives can be attained by conditional prospect function, then the ranking of alternatives is attained by aggregating group decision matrix.(3) Based on previous research,fuzzy OWA operator and prospect theory are considered into FMCDM simultaneously.Cumulative prospect theory based on fuzzy OWA operator and three aggregate operators of n dimensional trapezoidal fuzzy number are defined.For the MCDM problems,in which the criteria weights are incompletely certain and the criteria value of alternatives are in the form of trapezoidal fuzzy numbers, the minimum deviation method,which has subjective preference on alternatives,is proposed.And for the FMCDM problem,in which the criteria values of alternatives are in the form of trapezoidal fuzzy numbers and the criteria weights are completely known,a FMCDM method based on fuzzy OWA operator and cumulative prospect theory is presented.Then for the FMCGDM problem,in which the criteria values of alternatives are in the form of trapezoidal fuzzy numbers and the criteria weights are completely known,a FMCGDM method based on fuzzy preference relation is developed.