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ABSTRACT
In this paper, a crisp equivalent of a pair of fuzzy primal-dual linear programming problems (LPP) is proposed by using the concept of goal programming (GP) in which goal and system constraints are related to each other by weights. For these crisp equivalent LPP, the duality results are calculated. Using the concept of duality gap, this examines that duality gap can be changed by varying the weights of membership functions of objective function and system constraints of fuzzy primal-dual problems. This examination investigates that how selecting the weights which reflects the importance of goal and system constraints of primal-dual pair effects the gap.
Acknowledgements
The author wishes to express his deep gratitude to the editor, associate editor and the anonymous referees for their useful suggestions and remarks for improving the original paper.
Disclosure statement
No potential conflict of interest was reported by the author.
Additional information
Notes on contributors
Sandeep Kumar
Sandeep Kumar is an assistant professor with the Department of Mathematics, Ch. Charan Singh University Campus, Meerut, Uttar Pradesh (India). His research interests include fuzzy group decision making, fuzzy game theory and deterministic, stochastic and fuzzy control theory. He has published more than ten research papers in reputed journals and proceedings of international conferences.