A representation theorem for min-transitive fuzzy relations
We provide an abstract representation theorem for an arbitrary min-transitive fuzzy relation mu(R)(x, y) on a set X in terms of a specific 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, satisfies 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. (C) 2000 Elsevier Science B.V. All rights reserved.
representation theorem min-transitivity fuzzy lattice