Cutting-plane Algorithm for Solving Linear Semi-infinite Programming in Fuzzy Case

Volume 5, Issue 3, pp 212 - 218 http://dx.doi.org/10.22436/jmcs.05.03.09

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Authors

Alireza Fakharzadeh - Department of Mathematics, Shiraz University of Technology. Somayeh Khosravi - Department of Mathematics, Shiraz University of Technology. Hamidreza Maleki - Department of Mathematics, Shiraz University of Technology.

Abstract

This paper introduces a cutting-plane algorithm for solving semi-infinite linear programming problems in fuzzy case; the problem contains a crisp objective linear function and the infinite number of fuzzy linear constraints. In the first step; the designed algorithm solves a LP problem, which was created by the ranking function method based on a fuzzy sub-problem of the original one. In each iteration of the proposed algorithm, a cutting is created by adding a fuzzy constraint of the original problem to the fuzzy sub-problem. The convergence of the algorithm is proved and some numerical examples are given.

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Keywords

• Semi-infinite linear programming
• Cutting-plane
• Fuzzy linear programming.

MSC

•  90C34
•  90C57
•  03B52

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