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Compatibility of Fuzzy Relations
Author(s) -
Kheniche A.,
Baets B.,
Zedam L.
Publication year - 2016
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.21783
Subject(s) - extensionality , compatibility (geochemistry) , mathematics , fuzzy logic , pure mathematics , algebra over a field , discrete mathematics , computer science , artificial intelligence , engineering , chemical engineering
The notion of extensionality, introduced by Höhle and Blanchard, and the notion of compatibility, as coined by Bělohlávek, of a fuzzy relation with respect to a fuzzy equality are trivially equivalent. Here, this compatibility property is dissected into left and right compatibility, mimicking the original twofold definition of extensionality, and studied in detail in the context of arbitrary fuzzy relations. Relying on the notions of left and right traces of a fuzzy relation, it is shown that compatibility can be characterized in terms of inclusions, shedding another light on the matter.