Analysing skewness of credibilistic coherent trapezoidal fuzzy numbers: Implications for portfolio selection

Abstract

The outset of this manuscript involves introducing an analytical formula for the credibility of coherent trapezoidal fuzzy numbers, which represent an extended version of the traditional trapezoidal fuzzy numbers. With this formula, we present a precise counterpart to compute the credibilistic mean, semivariance, and skewness of coherent trapezoidal fuzzy numbers. Leveraging these analytical formulations, we construct a novel tri-objective portfolio selection problem, integrating credibilistic mean, semivariance, and skewness as objectives, along with some practical constraints. When used with the returns of the portfolio as a whole, the derived analytical expressions help to overcome the otherwise computationally expensive approach involving the simulation of results using individual assets' returns. The proposed model is solved by adapting an efficient multiobjective genetic algorithm. The algorithm has been specifically designed to solve portfolio selection models of this type. The efficiency of the proposed model is then demonstrated by taking a real-world scenario of financial stock market datasets from the NSE India. Based on the results of this study, it appears that the proposed novel tri-objective portfolio selection model produces promising results compared to the baseline model and the NIFTY 50 Index considered as a benchmark.