Eigen fuzzy sets and fuzzy relations
Copyright policy )Eigen fuzzy sets and fuzzy relations
AbstractWhen R is a fuzzy relation between the elements of a finite set X, the fuzzy sets A of X such that R ∘ A = A (MAX-MIN composition) are called eigen fuzzy sets. The main result of this paper is the determination of the greatest eigen fuzzy set associated with a given fuzzy relation and we give three methods illustrated by an example. We then state that the greatest eigen fuzzy set associated with R̂, the transitive closure of R, is exactly the one associated with R. Finally we describe how to obtain all fuzzy relations keeping invariant a given fuzzy set.
Applied Mathematics, Other classical set theory (including functions, relations, and set algebra), transitive closure of fuzzy relations, Theory of fuzzy sets, etc., Analysis
Applied Mathematics, Other classical set theory (including functions, relations, and set algebra), transitive closure of fuzzy relations, Theory of fuzzy sets, etc., Analysis
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