A Linear Approximation Approach to Chance Constrained Multiobjective Decision Making Problems

This article presents a linear approximation approach to the fuzzy goal programming (FGP) formulation of solving multiobjective decision making (MODM) problems with chance constraints. In the proposed approach, first the chance constraints are converted into their deterministic equivalent in the decision making environment. Then, the individual best and worst solutions of each of the objectives are determined for fuzzy description of them in the context of making decision. In the model formulation of the problem, the concept of tolerance membership functions are defined for measuring the degree of satisfaction of the decision maker (DM) with the solution for achievement of the fuzzily described objectives of the problem. In the executable FGP model, minimization of under-deviational variables of the membership goals defined for the membership functions for achievement of the highest membership value (unity) of each of them to the extent possible on the basis of their weights of importance is taken into consideration. In the solution process, the quadratic in form of the defined deterministic constraints are transformed into the linear form by using the Taylor series approximation method to solve the problem by employing the linear FGP methodology and thereby to reach a satisfactory decision. To illustrate the proposed approach, a numerical example is solved. The model solution is compared with the additive FGP approach studied previously.