Solvability and unique solvability of max-min fuzzy equations

Abstract 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.

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