On Solving Multiobjective Quadratic Programming Problems in a Probabilistic Fuzzy Environment

Abstract

In this paper, a fuzzy goal programming (FGP) approach for solving fuzzy multiobjective quadratic chance-constrained programming (CCP) problem involving exponentially distributed fuzzy random variables (FRVs) is developed. In the proposed methodology, the problem is first converted into interval-valued quadratic programming problem using CCP technique and $\alpha$-cut of fuzzy numbers. Then, using fuzzy partial order relations, the problem is converted into its equivalent deterministic form. The individual optimal value of each objective is found in isolation to construct the quadratic fuzzy membership goals of each of the objective. The quadratic membership goals are transferred into linear goals by applying piecewise linear approximation technique. A minsum goal programming (GP) method is then applied to both the linearized and quadratic model to achieve the highest membership degree of each of the membership goals in the decision-making context. Finally, a comparison is made on the two different approaches with the help of distance function. An illustrative numerical example is provided to demonstrate the applicability of the proposed methodology.