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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 726296, 10 pages
http://dx.doi.org/10.1155/2013/726296
Research Article

Solving a Fully Fuzzy Linear Programming Problem through Compromise Programming

1School of Management, Huazhong University of Science and Technology, Wuhan 430074, China
2College of Economics and Management, Zhejiang University of Technology, Hangzhou 310023, China

Received 22 February 2013; Accepted 9 May 2013

Academic Editor: Reinaldo Martinez Palhares

Copyright © 2013 Haifang Cheng et al. 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

In the current literatures, there are several models of fully fuzzy linear programming (FFLP) problems where all the parameters and variables were fuzzy numbers but the constraints were crisp equality or inequality. In this paper, an FFLP problem with fuzzy equality constraints is discussed, and a method for solving this FFLP problem is also proposed. We first transform the fuzzy equality constraints into the crisp inequality ones using the measure of the similarity, which is interpreted as the feasibility degree of constrains, and then transform the fuzzy objective into two crisp objectives by considering expected value and uncertainty of fuzzy objective. Since the feasibility degree of constrains is in conflict with the optimal value of objective function, we finally construct an auxiliary three-objective linear programming problem, which is solved through a compromise programming approach, to solve the initial FFLP problem. To illustrate the proposed method, two numerical examples are solved.