Triangular intuitionistic fuzzy random decision making based on combination of parametric estimation, score functions, and prospect theory

Abstract

This study investigates and improves the operational laws of triangular intuitionistic fuzzy numbers. The triangular intuitionistic fuzzy random variable (TIFRV) is introduced on the basis of the concepts of the triangular intuitionistic fuzzy number and triangular fuzzy random variable. Related properties of a TIFRV are also proposed and verified. To solve the problem of multi-criteria decision making on aspiration levels—a situation in which criterion weights are unknown and criterion values are given in terms of TIFRVs—this study proposes a triangular intuitionistic fuzzy random decision- making method based on a combination of parametric estimation, score functions, and prospect theory. In this method, the decision maker evaluates alternatives with triangular intuitionistic fuzzy numbers in different periods of decision making and thus enables the estimation of the parameters of the triangular intuitionistic fuzzy population and the creation of an intuitionistic triangular fuzzy random matrix. An expectation-variance intuitionistic fuzzy matrix is constructed on the basis of mean-variance analysis, and a fuzzy random score function is then defined to transform a normalized expectation-variance intuitionistic fuzzy matrix into a score function matrix. Prospect theory is used to calculate the values of prospect score functions, and the information entropy method is used to determine criterion weights. This procedure generates comprehensive prospect score function values that determine the final ranking of alternatives. A practical example is presented to show the feasibility and effectiveness of the proposed approach.