Modeling Mean-Semivariance Portfolio Selection Problems Using Coherent Trapezoidal Fuzzy Numbers

In this study, the portfolio selection problem is tackled using coherent trapezoidal fuzzy numbers, which is an extension of traditional trapezoidal fuzzy numbers. The work outlined in this paper commences by presenting analytical expressions for the credibilistic mean and credibilistic semivariance of coherent trapezoidal fuzzy numbers. These expressions are then utilized to formulate a pioneering bi-objective Mean-Semivariance (MSv) portfolio selection model, incorporating various practical constraints. The proposed bi-objective MSv Model is solved using a modified Multi-Objective Evolutionary Algorithm (MOEA) with an integrated repair mechanism. To demonstrate the model's performance stability, an empirical analysis is conducted using monthly stock return data from 18 distinct stocks selected from the Bombay Stock Exchange (BSE), India. The obtained results are juxtaposed with the benchmark BSE Sensex for comparison.