Optimal Solution of Fuzzy Optimization using Pentagonal Fuzzy Numbers

The fundamental goal of portfolio optimization is to optimally allocate funds between different investment alternatives. The mean-variance (MV) methodology has become the most important quantitative tool used which considers the trade-off between risk and return. However the classical Markowitz's MV method does not match the real world in numerous circumstances, thus researchers done are to improve and modify the MV model to represent the practicality. This paper discusses on a portfolio selection model that extends the classical Markowitz's mean-variance model where the returns is represented by pentagonal fuzzy numbers. The concept of alpha level set is used to define the expected return and variance of fuzzy number. The proposed model gives better performance as compared to classical mean-variance model. Numerical examples are also presented to illustrate the usability of the model