Eigen fuzzy sets and fuzzy relations |
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Authors: | Elie Sanchez |
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Institution: | Laboratoire de Biomathématiques, Statistiques, et Informatique Médicale Faculté de Médecine, 13385 Marseille Cedex 4, France |
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Abstract: | When 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 , 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. |
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