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Optimization of fuzzy relation equations with max-product composition. (English) Zbl 1044.90533
Summary: An optimization problem with a linear objective function subject to a system of fuzzy relation equations using max-product composition is considered. Since the feasible domain is non-convex, traditional linear programming methods cannot be applied. We study this problem and capture some special characteristics of its feasible domain and the optimal solutions. Some procedures for reducing the original problem are presented. The problem is transformed into a 0-1 integer program which is then solved by the branch-and-bound method. For illustration purpose, an example of the procedures is provided.

##### MSC:
 90C70 Fuzzy and other nonstochastic uncertainty mathematical programming 90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
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