Recent zbMATH articles in MSC 20N25https://www.zbmath.org/atom/cc/20N252021-04-16T16:22:00+00:00WerkzeugIntuitionistic fuzzy relations compatible with the group \(Z_n\).https://www.zbmath.org/1456.030792021-04-16T16:22:00+00:00"Emam, E. G."https://www.zbmath.org/authors/?q=ai:emam.e-gIn the paper the concept of compatibility of fuzzy relations with some multiplicative semi-group is extended to the case of intuitionistic fuzzy relations. The mentioned compatibility of intuitionistic fuzzy relations is studied in the case of the well-known abelian group \(Z_n\) with the sum modulo \(n\) (which is isomorphic to some multiplicative abelian group). As a result the concept of \(Z_n\)-compatiblity of intuitionistic fuzzy relations is considered and several related properties are provided. Namely, a characterization of \(Z_n\)-compatible intuitionistic fuzzy relation is presented, the number of elements in \(Z_n\)-compatible intuitionistic fuzzy relation is determined, preservation of \(Z_n\)-compatiblity by basic operations on intuitionistic fuzzy relations (sum, intersection, converse relation, the complement) as well as some other operations are considered. Moreover, the symmetry of the composition of two \(Z_n\)-compatible intuitionistic fuzzy relations is proved. Finally, two relations related to any intuitionistic fuzzy relation are distinguished and their properties in the context of \(Z_n\)-compatiblity are delivered.
Reviewer: Urszula Bentkowska (Rzeszów)