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Fuzzy \(H_V\)-substructures in a two dimensional Euclidean vector space. (English) Zbl 1211.20069

The aim of this paper is to establish a connection between fuzzy substructures and \(H_v\)-structures. To this aim, the authors combine geometrical hyperoperations obtained in the two dimensional Euclidian vector space with fuzzy sets. Several hyperstructures of group-like or ring-like type are considered. These hyperstructures are further connected with theta-operations [see T. Vougiouklis, in Structure elements of hyper-structures. Proceedings of the meeting, Alexandroupolis, Greece, 2005. Xanthi: Spanidis. 53-64 (2005; Zbl 1080.20066)] to obtain more strict hyperstructures, as \(H_v\)-groups or \(H_v\)-rings (the dual ones).

MSC:

20N20 Hypergroups
20N25 Fuzzy groups
16Y99 Generalizations
51A25 Algebraization in linear incidence geometry

Citations:

Zbl 1080.20066
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