Compatibility and traces of bipolar fuzzy relations: Characterizations and extensions

In this paper, we introduce Bělohl’avek’s concept of compatibility within the context of bipolar fuzzy relations. We provide a comprehensive characterization of both left and right compatibility for these relations. Additionally, we explore several properties of traces in relation to bipolar fuzzy relations and offer novel characterizations of compatibility in terms of left and right traces. Building upon the work of De Baets et al., who studied the compatibility of fuzzy tolerance relations (and fuzzy equivalence relations in particular) with a given (strict) order relation, we extend their analysis by examining the left and right compatibility of bipolar fuzzy tolerance (or equivalence) relations with bipolar characteristic functions of (strict) order relations.

کلیدواژه ها:

Left compatibility ، right compatibility ، Traces ، order relation ، bipolar fuzzy relation ، bipolar fuzzy tolerance relation