A polynomial goal programming approach for intuitionistic fuzzy portfolio optimization using entropy and higher moments

Abstract

Although there are myriad works that deal with fuzzy portfolio optimization, there is a dearth of research that deals with the problem in an intuitionistic fuzzy environment. So, taking the route less travelled, we propose two intuitionistic fuzzy portfolio selection models for optimistic and pessimistic scenarios, respectively. For this purpose, we take into account four objectives, namely return, variance, skewness and entropy, along with some realistic constraints such as a cardinality constraint, a contingent constraint, and complete capital utilization. Also, short selling is prohibited. Another popular constraint, the “floor and ceiling” constraint, is presented and employed in the form of a flexible constraint by considering the confidence interval in the model. The membership and non-membership of the objectives are modelled using the extreme values of the four objectives. The proposed approach provides avenues for the inclusion and minimization of the hesitation degree into the decision making, thereby, resulting in a significantly better portfolio. The proposed model enables the decision makers to obtain a variety of results through the use of several schemes that can be postulated (customized) according to the decision makers’ preferences, and from which, results best suited to their preferences, can be chosen. A numerical illustration with eight different schemes is presented to demonstrate the virtues of the proposed model.