Duality in fuzzy multi-criteria and multi-constraint level linear programming: a parametric approach

Abstract

This paper presents a parametric approach for duality in fuzzy multi-criteria and multi-constraint level linear programming $\text{(}\text{MC}{}^2$LP) which extends fuzzy linear programming approaches. First, the $\text{MC}{}^2$-simplex method is used to solve the crisp prima–dual $\text{MC}{}^2\text{LP}$ pair and then, through these crisp formulations, separate membership functions are constructed for fuzzy primal and dual program by considering the corresponding primal and dual decisions. For each program, a set of fuzzy potential solutions is determined in terms of the membership function and the related optimal solution with a certain range of decision parameters. Finally, using the primal and dual membership functions, a fuzzy weak duality function is obtained for any pair of primal and dual fuzzy potential solutions.