Solvability and Stability of Fuzzy Relation Equations
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(n3) algorithm. Analogous results are presented for the stability and periodicity problem of a fuzzy relation equation. The matrix period of a given square matrix is characterized by periods of non-trivial strongly connected components of associated threshold digraphs. The result enables to compute the matrix period in O(n3) time.
KeywordsUnique Solvability Fuzzy Relation Maximum Solution Discrete Dynamic System Matrix Period
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