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A representation theorem for min-transitive fuzzy relations

✍ Scribed by Sukhamay Kundu

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
112 KB
Volume
109
Category
Article
ISSN
0165-0114

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✦ Synopsis

We provide an abstract representation theorem for an arbitrary min-transitive fuzzy relation R(x; y) on a set X in terms of a speciΓΏc min-transitive relation on the interval [0, 1]. The technique used here gives us a fuzzy lattice structure on F(X ) = the set of all fuzzy subsets of X . The underlying partial ordering on F(X ), which can be regarded as a fuzzy subset-hood relation, satisΓΏes the min-transitivity and is superior to Kosko's notion of subset-hood in the sense that the latter does not satisfy the min-transitivity.

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