Linear optimization problem constrained by fuzzy max-min relation equations

Authors:
Cheung-Wen Chang;Bih-Sheue Shieh
Affiliations:
Dept. of Information Management, Chia Nan University of Pharmacy and Science, Taiwan, ROC;Dept. of Applied Mathematics, National University of Tainan 33, Sec. 2, Shu-Lin St., Tainan 700, Taiwan, ROC
Venue:
Information Sciences: an International Journal
Year:
2013

Citing 9
Cited 1

Solving fuzzy relation equations with a linear objective function

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Optimization of fuzzy relation equations with max-product composition

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Fuzzy Relation Equations (II): The Branch-point-solutions and the Categorized Minimal Solutions

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Solutions of fuzzy relation equations based on continuous t-norms

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On the minimal solutions of max--min fuzzy relational equations

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Minimization of linear objective functions under the constraints expressed by a system of fuzzy relation equations

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Minimizing a linear objective function under a max-t-norm fuzzy relational equation constraint

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Minimizing a linear objective function under a fuzzy max-t norm relation equation constraint

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An accelerated approach for solving fuzzy relation equations with a linear objective function

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Solution to the covering problem

Information Sciences: an International Journal

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Abstract

Fang and Li introduced the optimization model with a linear objective function and constrained by fuzzy max-min relation equations. They converted this problem into a 0-1 integer programming problem and solved it using the jump-tracking branch-and-bound method. Subsequently, Wu et al. improved this method by providing an upper bound on the optimal objective value and presented three rules for simplifying the computation of an optimal solution. This work presents new theoretical results concerning this optimization problem. They include an improved upper bound on the optimal objective value, improved rules for simplifying the problem and a rule for reducing the solution tree. Accordingly, an accelerated approach for finding the optimal objective value is presented, and represents an improvement on earlier approaches. Its potential applications are discussed.