A Piecewise Linear Approximation Method to Solve Fuzzy Separable Quadratic Programming Problem

This paper presents a piecewise linear approximation method for solving separable quadratic programming problems by using linear fuzzy goal programming ( F GP) metho do logy. In the proposed approach, the objectives are first described fuzzily by introducing imprecise aspiration level to each of them. The fuzzy goals are then characterized by their associated membership functions for representation of goal achievement in terms of membership values of fuzzy goals. In the model formulation of the problem, the defined membership functions are first transformed into membership goals by assigning the highest membership value (unity) and introducing under - and over - deviational variable s to each of them. The n, the membership goals in quadratic form are transformed into linear goals by using piecewise linear approximation method. In the solution process, minimization of under - deviational variables in the goal achievement function under t he minsum F GP solution approach is considered. To illustrate the proposed approach a numerical example is solved. The model solution is also compared with the solution achieved by using Taylor series approximation method