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Solvability and unique solvability of max-min fuzzy equations. (English) Zbl 0994.03047
Summary: The problem of solvability and the problem of unique solvability of a fuzzy relation equation in an arbitrary max-min algebra are considered and corresponding necessary and sufficient conditions are presented. The results allow to solve both problems by an $$O(mnp)$$ algorithm, where $$m$$, $$n$$, $$p$$ are the dimensions of the corresponding relations in the equation. The existence of the greatest and of the least solution is also considered.

##### MSC:
 03E72 Theory of fuzzy sets, etc. 15B33 Matrices over special rings (quaternions, finite fields, etc.) 08A72 Fuzzy algebraic structures 15A06 Linear equations (linear algebraic aspects)
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