Title: Fuzzy efficient and Pareto-optimal solution for multi-objective linear fractional programming problems

Authors: Pitam Singh; Shiv Datt Kumar; R.K. Singh

Addresses: Department of Mathematics, Motilal Nehru National Institute of Technology, Allahabad – 211004, India ' Department of Mathematics, Motilal Nehru National Institute of Technology, Allahabad – 211004, India ' Department of Electrical Engineering, Motilal Nehru National Institute of Technology, Allahabad – 211004, India

Abstract: Many practical optimisation problems usually have several conflicting objectives. In these multi-objective optimisation problems, solution optimising all the objective functions simultaneously does not exist, in general. Instead, Pareto-optimal solutions, which are efficient in terms of all objective functions, are introduced. Nevertheless, many optimal solutions exist. A final solution among Pareto-optimal solutions is to be selected based on the balance among objective functions. In this paper, we find fuzzy efficient and Pareto-optimal solution to the multi-objective linear fractional programming problem (MOLFP). It has shown that when any fuzzy goal is fully achieved, the fuzzy efficient solution may or may not be Pareto-optimal. Therefore, a procedure is proposed to obtain fuzzy efficient solution which is also Pareto-optimal. The efficiency of proposed method is verified by numerical examples and a practical application in production planning.

Keywords: multi-objective programming; linear fractional programming; Pareto optimal solutions; fuzzy goal programming; multi-objective optimisation; production planning.

DOI: 10.1504/IJMOR.2014.060854

International Journal of Mathematics in Operational Research, 2014 Vol.6 No.3, pp.357 - 376

Published online: 28 Jun 2014 *

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