Method for Fuzzy-stochastic Multi-criteria Decision-making Based on Prospect Theory and Improved TOPSIS with its Application

Abstract

This paper investigates the grey-probability multi-criteria decision-making problem in which the criteria value is interval grey-intuitionistic fuzzy number and the weighted coefficients are partially known. A decisionmaking approach based on improved TOPSIS and Prospect theory is proposed. This approach is composed of two steps: the first one is defining prospect value function and probability weighting function of grey intuitionistic fuzzy numbers and constructing prospects decision matrix via prospect theory,and the second one is ordering the corresponding alternatives by applying the complex closeness degree of the improved TOPSIS method. As for the TOPSIS we improve it in two aspects: On the one hand,we first define the concept of the difference between alternatives,and consequently construct a maximum average difference program model by using the idea of maximizing deviations,and then,a calculating weight method which satisfies the manager subjective information with the algorithm of maximum deviation is proposed. On the other hand,we use the degree of grey relational instead of applying the distance of positive-negative ideal solution to measure the closeness degree of distance between alternatives and positive-negative ideal solution. Finally,an example is provided to examine the effectiveness of our method.