A fuzzy goal programming method for solving chance constrained programming with fuzzy parameters

Abstract

This paper develops a fuzzy goal programming methodology for solving chance constrained programming problem involving fuzzy numbers and fuzzy random variables which follow standard normal distribution. In the model formulation process, the problem is converted into an equivalent fuzzy programming problem by applying chance constrained programming technique. Then the problem is divided into equivalent sub problems by considering the tolerance limit of the fuzzy numbers relating to the system constraint having different forms of membership functions in the decision making context. Afterwards the objective and the constraints resulting from chance constraints are converted into fuzzy goals by assigning some imprecise aspiration levels. In the decision process, a fuzzy goal programming methodology is introduced to find the most satisfactory solution in the decision making environment. To demonstrate the potentiality of the proposed approach, an illustrative example, studied previously, is solved and is compared with the existing methodologies. © 2011 Springer-Verlag Berlin Heidelberg.