Fuzzy logic based solutions for multi criteria decision making problems and its application to portfolio selection

Rapidly changing environmental conditions and increasing complexity of real life problems require decision makers to determine the most appropriate solution method to the problem as soon as possible in order to reach the result. In such cases, Multi-Criteria Decision Making (MCDM) methods are used to make the appropriate choice. The portfolio selection process, which includes more than one purpose, criterion, and alternative, is one of the areas where MCDM methods are used. Modeling the relationship between risk and return is very important in portfolio management. In addition, the immediate impact of social and political changes on financial markets causes uncertainty in the portfolio selection process. In this thesis, a portfolio selection model has been proposed to help savers who will invest in the environment of uncertainty in the financial markets to create their portfolios with maximum profit and minimum risk, and a software developed to enable the operation of this model. In this context, trapezoidal fuzzy numbers were defined for portfolio selection problems instead of triangular fuzzy numbers used in Constrained Fuzzy AHP method. By using the defined fuzzy numbers, the weights of the criteria were obtained as trapezoidal fuzzy numbers. Then, a fuzzy linear programming problem, using the weights of the obtained criteria, was modeled. In this model, the weights obtained from the Constrained Fuzzy AHP method based on trapezoidal fuzzy numbers are used as price variables in the objective function of the linear programming problem, developed for trapezoidal fuzzy numbers. Finally, more than one application was included in the thesis to examine the effectiveness of the proposed hybrid model. In these applications, portfolio distributions were obtained using many different portfolio selection methods, available in the literature, and the results were compared. The proposed algorithm has been converted into a MATLAB code that models and solves the problem by using the decision maker, criterion, and stock information.