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July  2008, 4(3): 581-609. doi: 10.3934/jimo.2008.4.581

The framework of axiomatics fuzzy sets based fuzzy classifiers

Xiaodong Liu 1, and  Wanquan Liu 2,

1. 

Research Center of Information and Control, Dalian University of Technology, Dalian, 116024, China
2. 

Dept. of Computing, Curtin University of Technology, Bentley, WA, 6102, Australia

Received  November 2006 Revised  March 2008 Published  July 2008

In this paper we will propose a new classifier design based on the AFS fuzzy theory. First, we will briefly review the current researches in data classification based on fuzzy and rough set theories and then present the AFS framework. Second, we will present new membership functions for fuzzy sets with their logic operations in the AFS framework and then tackle some theoretical and computational problems related to classifier design. Third, we will develop a new approach for fuzzy classifier design based on the proposed membership functions and their logic operations. Finally, a well-known example is used to illustrate its effectiveness. The advantage of this classifier is in two-folds. One is that it can mimic the human reasoning comprehensively and offers a far more flexible and effective way for the study of large-scale intelligent systems. The other is its simplicity in methodology and mathematical beauty in fuzzy theory.
Keywords: Fuzzy classification., Sub-preference relation, Molecular lattice, AFS algebra, AFS structure.
Mathematics Subject Classification: Primary: 03E72, 06D72; Secondary: 93A3.
Citation: Xiaodong Liu, Wanquan Liu. The framework of axiomatics fuzzy sets based fuzzy classifiers. Journal of Industrial and Management Optimization, 2008, 4 (3) : 581-609. doi: 10.3934/jimo.2008.4.581
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