IJPTT

On Fuzzy Multi-Objective Multi-Item Solid Transportation Problems

	International Journal of Computer & Organization Trends  (IJCOT)
	© 2015 by IJCOT Journal
	Volume - 5 Issue - 1
	Year of Publication : 2015
	Authors : E. E. Ammar , H. A. Khalifa
	DOI : 10.14445/22492593/IJCOT-V17P301

Citation

E. E. Ammar , H. A. Khalifa "On Fuzzy Multi-Objective Multi-Item Solid Transportation Problems", International Journal of Computer & organization Trends (IJCOT), V5(1):32-50 Jan - Feb 2015, ISSN:2249-2593, www.ijcotjournal.org. Published by Seventh Sense Research Group.

Abstract

In general. There is no single optimal solution in multi-objective problems, but rather a set of non inferior (pareto optimal) solutions from which the decision maker (DM) must select the most preferred or best compromise solution as the one to implement. In this paper, a multi-objective multi-item solid transportation problem by incorporating fuzzy numbers into the coefficients of the objective functions and / or supply quantities and / or demand quantities and / or conveyance capacities . The concept of -fuzzy efficient solution is introduced in which the ordinary efficient solution is extended based on the -levels of fuzzy numbers. A necessary and sufficient condition for such a solution is established. The existing results concerning the qualitative analysis of the notions (solvability set and stability set of the first kind under the concept of -parametric optimality are studied. A solution procedure for determining the stability set of the first kind corresponding to one of -pareto optimal solution is proposed. An illustrative numerical example is given to clarify the obtained results.

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Keywords
Multi-objective multi-item solid transportation; fuzzy numbers; ?-fuzzy efficient; ?-optimality; parametric analysis.