Fuzzy hypergroups based on fuzzy relations

Authors:
Kaibiao Sun;Xuehai Yuan;Hongxing Li
Affiliations:
School of Control Science and Engineering, Dalian University of Technology, Dalian, Liaoning 116024, China;School of Control Science and Engineering, Dalian University of Technology, Dalian, Liaoning 116024, China;School of Control Science and Engineering, Dalian University of Technology, Dalian, Liaoning 116024, China
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

Based on fuzzy reasoning in fuzzy logic, this paper studies a fuzzy hyperoperation and a fuzzy hypergroupoid associated with a fuzzy relation. A sufficient and necessary condition for such a fuzzy hypergroupoid being a fuzzy hypergroup is given, and the properties of the fuzzy hypergroups associated with fuzzy relations are investigated. Furthermore, the definition of normal fuzzy hypergroups is put forward and it is shown that the category NFHG of normal fuzzy hypergroups satisfies all the axioms of topos except for the subobject classifier axiom.