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Linear optimization problem constrained by fuzzy max-min relation equations. (English) Zbl 1284.90103
Summary: 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.

MSC:
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
90C08 Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.)
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