A clone-based representation of the fuzzy tolerance or equivalence relations a strict order relation is compatible with

作者：De Baets Bernard^*; Zedam Lemnaouar; Kheniche Azzedine

来源：Fuzzy Sets and Systems, 2016, 296: 35-50.

DOI：10.1016/j.fss.2015.09.015

• Clone relation
• Compatibility
• Equivalence relation
• Fuzzy relation
• Order relation
• Tolerance relation

We show that although there exists no non-trivial (fuzzy) tolerance relation a partial order relation is compatible with (in the sense of Bclohlavck), the situation is quite different when considering its strict part. More specifically, we provide a representation of all fuzzy tolerance (and, in particular, all fuzzy equivalence) relations a strict order relation is compatible with. To that end, we introduce the notion of clone relation associated with a partially ordered set and discuss its basic properties. The mentioned representation is intimately connected with this clone relation.

• 出版日期2016-8-1