Optimization of fuzzy relational equations with max-av composition.

*(English)*Zbl 1140.90523Summary: 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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##### References:

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