The set-valued mapping based on ample fields

Authors:
Xue-Hai Yuan;Hong-Xing Li;Cheng Zhang
Affiliations:
School of Electronic and Information Engineering, Dalian University of Technology, Dalian 116024, PR China;School of Electronic and Information Engineering, Dalian University of Technology, Dalian 116024, PR China;School of Information Engineering, Dalian University, Dalian 116622, PR China
Venue:
Computers & Mathematics with Applications
Year:
2008

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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 @X(@W,A) of possibilistic sets are built up respectively. It is proved that the category @X(@W,A) is a topos.