On multi-level quadratic fractional programming problem with modified fuzzy goal programming approach

Abstract

The present paper addresses an extended algorithm for the solution of multi-level quadratic fractional programming problem(ML-QFPP) based on fuzzy goal programming (FGP) approach. In this algorithm, suitable linear and nonlinear membership functions for the fuzzily described numerator and denominator of the quadratic objective functions of all levels as well as the control vectors of higher levels are respectively defined using individual optimal solutions. Then usual fuzzy goal programming approach is applied for the achievement of highest degree of each of the membership goal by minimising the negative deviational variables. The proposed algorithm is an extension of modified FGP approach for ML-QFPPs and a simple algorithm to obtain compromise optimal solution of ML-QFPPs with all major types of nonlinear membership functions. Comparative analysis over the variation in the types of membership functions is also carried out with numerical example to show suitability of different membership functions in the proposed algorithm.