YOUNG DIAGRAMS OF EQUIVALENT FUZZY SUBSETS

Abstract

We consider in this paper a natural equivalence relation on the set of all fuzzy subsets of a finite set with degree of membership values being taken from the unit interval. This equivalence is a generalization of equality of crisp sets. Maximal chains are called flags and finite chains of real numbers in the unit interval are called keychains. Maximal chains together with keychains twinned in an appropriate manner are called pinned-flags. First we prove that there is a one-to-one correspondence between equivalence classes of fuzzy subsets and the class of pinned-flags. We then represent equivalent classes of fuzzy subsets, using the one-toone correspondence with pinned-flags, as Young diagrams or as other diagrams arising from Young diagrams.