Solving Fuzzy Linear Programming Problems with Fuzzy Decision Variables

Hsien-Chung Wu
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Hsien-Chung Wu: Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 802, Taiwan

Mathematics, 2019, vol. 7, issue 7, 1-105

Abstract: The numerical method for solving the fuzzy linear programming problems with fuzzy decision variables is proposed in this paper. The difficulty for solving this kind of problem is that the decision variables are assumed to be nonnegative fuzzy numbers instead of nonnegative real numbers. In other words, the decision variables are assumed to be membership functions. One of the purposes of this paper is to derive the analytic formula of error estimation regarding the approximate optimal solution. On the other hand, the existence of optimal solutions is also studied in this paper. Finally we present two numerical examples to demonstrate the usefulness of the numerical method.

Keywords: discretized linear programming problems; fuzzy numbers; nondominated solutions; strong duality theorem; weak duality theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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