Elsevier

Fuzzy Sets and Systems

Volume 98, Issue 1, 16 August 1998, Pages 127-132
Fuzzy Sets and Systems

On a representation of posets by fuzzy sets

https://doi.org/10.1016/S0165-0114(96)00385-5Get rights and content

Abstract

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, ⩽) can be represented by the poset of levels of a particular fuzzy set, defined on the collection of meet-irreducible elements of (P, ⩽).

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