Similarity relations, fuzzy linear orders, and fuzzy partial orders

✍ Scribed by Sukhamay Kundu

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 230 KB
• Volume: 109
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(97)00370-9

✦ Synopsis

We show that for a fuzzy partial order R on a ÿnite universe , there is a ÿnite family of fuzzy linear orders {Li: 16i6k} such that R(x; y) = min{ L i (x; y): 16i6k} for all x and y. This generalizes a well-known result on crisp partial orders, which states that each partial order on a ÿnite set is a ÿnite intersection of linear orders. As a special case, a similarity relation S, where S (x; y)¡1 for x = y, is shown to be the intersection R(x; y) ∧ R(y; x) for a fuzzy linear ordering R.