Approaches to the representations and logic operations of fuzzy concepts in the framework of axiomatic fuzzy set theory I

Authors:
Xiaodong Liu;Tianyou Chai;Wei Wang;Wanquan Liu
Affiliations:
Research Center of Information and Control, Dalian University of Technology, Dalian 116024, PR China and Research Center of Automation, Northeastern University, Shenyang 110004, PR China and Depar ...;Research Center of Automation, Northeastern University, Shenyang 110004, PR China;Department of Computing, Curtin University of Technology, Bentley, WA 6102, Australia;Department of Computing, Curtin University of Technology, Bentley, WA 6102, Australia
Venue:
Information Sciences: an International Journal
Year:
2007

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Abstract

In this paper, the representations of fuzzy concepts based on raw data have been investigated within the framework of AFS (Axiomatic Fuzzy Set) theory. First, a brief review of AFS theory is presented and a completely distributive lattice, the E^#I algebra, is proposed. Secondly, two kinds of E^#I algebra representations of fuzzy concepts are derived in detail. In order to represent the membership functions of fuzzy concepts in the interval [0,1], the norm of AFS algebra is defined and studied. Finally, the relationships of various representations with their advantages and drawbacks are analyzed.