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Journal of Applied Mathematics
Volume 2012, Article ID 796028, 20 pages
http://dx.doi.org/10.1155/2012/796028
Research Article

Two Weighted Fuzzy Goal Programming Methods to Solve Multiobjective Goal Programming Problem

Department of Mathematics, National Institute of Technology Agartala, Tripura, Jirania 799055, India

Received 4 March 2012; Revised 2 June 2012; Accepted 4 June 2012

Academic Editor: Hak-Keung Lam

Copyright © 2012 Mousumi Gupta and Debasish Bhattacharjee. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We propose two new methods to find the solution of fuzzy goal programming (FGP) problem by weighting method. Here, the relative weights represent the relative importance of the objective functions. The proposed methods involve one additional goal constraint by introducing only underdeviation variables to the fuzzy operator λ (resp., 1-λ), which is more efficient than some well-known existing methods such as those proposed by Zimmermann, Hannan, Tiwari, and Mohamed. Mohamed proposed that every fuzzy linear program has an equivalent weighted linear goal program where the weights are restricted as the reciprocals of the admissible violation constants. But the above proposition of Mohamed is not always true. Furthermore, the proposed methods are easy to apply in real-life situations which give better solution in the sense that the objective values are sufficiently closer to their aspiration levels. Finally, for illustration, two real examples are used to demonstrate the correctness and usefulness of the proposed methods.