Release Time:2019-03-10  Hits:

Indexed by: Journal Article

Date of Publication: 2008-10-01

Journal: COMPUTERS & MATHEMATICS WITH APPLICATIONS

Included Journals: Scopus、EI、SCIE

Volume: 56

Issue: 8

Page Number: 1954-1965

ISSN: 0898-1221

Key Words: Ample field; Possibility; Fuzzy set; Fuzzy variable; Category; Topos

Abstract: 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.