A novel portfolio selection with prospect value constraint and distance measure of IFSs based on the improved entropy-weighted method

Abstract

The purpose of this paper is to solve the portfolio selection problem when historical data are unavailable. In this paper, the problem is viewed as a multi-criteria decision making (MCDM) problem under intuitionistic fuzzy circumstances, and the prospect theory is utilized to reflect decision makers’ psychological state, which is always bounded rational. Therefore, a new approach to solve MCDM problems is presented based on the following improvements. (a) The entropy-weighted method with extreme data resistance is proposed instead of weight function to deal with the weight of criteria, because weight stands for the decision maker’s preference of criteria rather than objective probability and should not be distorted. (b) A new entropy-weighted method with confidence degree is presented, which can not only describe the uncertainty of information each criterion provides but also reflect the decision maker’s confidence in the information. (c) To reduce the interference from extreme data, the median is selected as reference point instead of mean or extreme value. (d) Based on the distance measure, the intuitionistic fuzzy prospect value function is presented to capture decision makers’ psychological state. Finally, a novel model with prospect value constraint and risk preference is constructed to allocate investment ratios. For our proposed method and model, two numerical applications are given to verify their validity and the sensitivity analysis is carried out to illustrate their practical significance.