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

This paper presents a parametric approach for duality in fuzzy multi-criteria and multi-constraint level linear programming ((MCLP)-L-2) which extends fuzzy linear programming approaches. First, the MC2-simplex method is used to solve the crisp prima-dual (MCLP)-L-2 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. (C) 2002 Elsevier Science B.V. All rights reserved.