Multicriteria Portfolio Selection with Intuitionistic Fuzzy Goals as a Pseudoconvex Vector Optimization

Abstract

Portfolio selection involves optimizing simultaneously financial goals such as risk, return and Sharpe ratio. This problem holds considerable importance in economics. However, little has been studied related to the nonconvexity of the objectives. This paper proposes a novel generalized approach to solve the challenging Portfolio Selection problem in an intuitionistic fuzzy environment where the objectives are soft pseudoconvex functions, and the constraint set is convex. Specifically, we utilize intuitionistic fuzzy theory and flexible optimization to transform the fuzzy pseudoconvex multicriteria vector into a pseudoconvex programming problem that can be solved by recent gradient descent methods. We demonstrate that our method can be applied broadly without special forms on membership and nonmembership functions as in previous works. Computational experiments on real-world scenarios are reported to show the effectiveness of our method.