On a representation of posets by fuzzy sets

The aim of the paper is to present an application of fuzzy sets in mathematics, namely, in the theory of ordered sets. An algorithm for the construction of P-fuzzy sets with distinct levels is given. In connection with this, every finite poset can be mapped, by an anti-isotone bijection, onto the poset of levels of a suitable fuzzy set. Moreover, it is proved that every finite partially ordered set (P, less than or equal to) can be represented by the poset of levels of a particular fuzzy set, defined on the collection of meet-irreducible elements of (P, less than or equal to). (C) 1998 Elsevier Science B.V. All rights reserved.