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论文类型：期刊论文

发表时间：2008-10-01

发表刊物：COMPUTERS & MATHEMATICS WITH APPLICATIONS

收录刊物：SCIE、EI、Scopus

卷号：56

期号：8

页面范围：1954-1965

ISSN号：0898-1221

关键字：Ample field; Possibility; Fuzzy set; Fuzzy variable; Category; Topos

摘要：Ample fields play an important role in possibility theory. Based on the ample fields in possibility theory, two new concepts such as possibilistic set and possibility mapping are presented. A theoretical approach to define operations and implication operations of fuzzy sets based on the theory of falling shadows of possibilistic sets is established, and the category PosM of ample spaces and possibility mappings and the category Xi(Omega, A) of possibilistic sets are built up respectively. It is proved that the category Xi(Omega, A) is a topos. (c) 2008 Elsevier Ltd. All rights reserved.