Extension principle-based solution approach to full fuzzy multi-objective linear fractional programming

Abstract

In this paper, we propose a solution approach to solving full fuzzy multiple objective linear fractional problems based on Zadeh’s extension principle. We adopt the idea of using triangular fuzzy numbers for the coefficients of the original problem and derive the shapes of the fuzzy variables with respect to the extension principle. The solution concept built in the novel approach strictly follows the basic arithmetic of fuzzy numbers, and the developed methodology contributes to correcting some inconsistencies in an existing approach from the recent literature. The solution we propose to the original problem is constructed out of the non-dominated points of crisp multiple objective linear fractional problems formed with feasible values of the fuzzy coefficients. The membership degree of each identified non-dominated point is computed with respect to the membership degrees of the coefficients involved. Our empirical results confirm and clearly illustrate the theoretical foundations