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Optimization of fuzzy relational equations with max-av composition. (English) Zbl 1140.90523
Summary: Max-min and max-product compositions are commonly utilized to optimize a linear objective function subject to fuzzy relational equations. Both are members in the class of max-$$t$$-norm composition. In this study, the max-av composition is considered for the same optimization model, which does not belong to the max-$$t$$-norm composition. However, max-av composition generates some properties of the solution set that are similar to the max-product composition. Thanks to these properties, a simple value matrix with rules can be applied to reduce problem size. Thus, this study proposes an efficient procedure for obtaining optimal solutions without decomposing the problem into two sub-problems or finding all the potential minimal solutions.

##### MSC:
 90C70 Fuzzy and other nonstochastic uncertainty mathematical programming 03E72 Theory of fuzzy sets, etc.
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