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Indexed by:期刊论文

Date of Publication:2010-08-01

Journal:COMPUTERS & MATHEMATICS WITH APPLICATIONS

Included Journals:SCIE、EI、Scopus

Volume:60

Issue:3

Page Number:610-622

ISSN No.:0898-1221

Key Words:Fuzzy hypergroup; Fuzzy reasoning; Fuzzy relation; Fuzzy set; Category; Topos

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. (C) 2010 Elsevier Ltd. All rights reserved.