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

Authors:
Yihua Zhong;Yong Shi
Affiliations:
Department of Computer Science, Southwest Petroleum Institute 637001, Nanchong, Sichuan, People's Republic of China;College of Information Science and Technology, University of Nebraska at Omaha, 6001 Dodge Street, Omaha, NE
Venue:
Fuzzy Sets and Systems
Year:
2002

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Abstract

This paper presents a parametric approach for duality in fuzzy multi-criteria and multi-constraint level linear programming (MC2LP) which extends fuzzy linear programming approaches. First, the MC2-simplex method is used to solve the crisp prima-dual MC2LP 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.