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论文类型：期刊论文

发表时间：2010-08-01

发表刊物：COMPUTERS & MATHEMATICS WITH APPLICATIONS

收录刊物：SCIE、EI、Scopus

卷号：60

期号：3

页面范围：610-622

ISSN号：0898-1221

关键字：Fuzzy hypergroup; Fuzzy reasoning; Fuzzy relation; Fuzzy set; Category; Topos

摘要：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.