The clone relation of a binary relation

详细信息    查看全文

• 作者：Hassane Bouremel ; ^a ; ^{bouremel73@gmail.com} ; Raú ; l Pé ; rez-Ferná ; ndez^b ; Lemnaouar Zedam^a ; Bernard De Baets^b
• 关键词：Binary relation ; Clone relation ; Tolerance relation ; Equivalence relation ; Disjoint union
• 刊名：Information Sciences
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：382-383
• 期：Complete
• 页码：308-325
• 全文大小：775 K
• 卷排序：382

文摘

In a recent paper, De Baets et al. introduced the clone relation of a strict order relation. Two elements of a poset are said to be a pair of clones (or to be clones) if every other element that is greater (resp. smaller) than one of them is also greater (resp. smaller) than the other one. This clone relation played a key role in the characterization of the L-fuzzy tolerance relations and the L-fuzzy equivalence relations that a strict order relation is compatible with. In this paper, we extend the notion of clone relation to any binary relation. Although the definition of such extension is trivial, the corresponding properties significantly differ from those of the clone relation of a strict order relation. We analyse the most important ones among these properties, paying particular attention to a partition of the clone relation in terms of three different types of pairs of clones.