On a representation of posets by fuzzy sets

✍ Scribed by Branimir Šešelja; Andreja Tepavčević

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 368 KB
• Volume: 98
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(96)00385-5

✦ Synopsis

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, ~< ).