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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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