Extraction of fuzzy rules from fuzzy decision trees: An axiomatic fuzzy sets (AFS) approach

  • Authors:

  • Xiaodong Liu;Xinghua Feng;Witold Pedrycz

  • Affiliations:

  • Research Center of Information and Control Dalian University of Technology, Dalian 116024, PR China and Department of Mathematics Dalian Maritime University, Dalian 116026, PR China;Research Center of Information and Control Dalian University of Technology, Dalian 116024, PR China;Department of Electrical and Computer Engineering University of Alberta, Edmonton, Canada T6G 2G7, Department of Electrical and Computer Engineering Faculty of Engineering, King Abdulaziz Universi ...

  • Venue:
  • Data & Knowledge Engineering
  • Year:
  • 2013

Quantified Score

Hi-index 0.00

Visualization

Abstract

In this study, we introduce a new type of coherence membership function to describe fuzzy concepts, which builds upon the theoretical findings of the Axiomatic Fuzzy Set (AFS) theory. This type of membership function embraces both the factor of fuzziness (by capturing subjective imprecision) and randomness (by referring to the objective uncertainty) and treats both of them in a consistent manner. Furthermore we propose a method to construct a fuzzy rule-based classifier using coherence membership functions. Given the theoretical developments presented there, the resulting classification systems are referred to as AFS classifiers. The proposed algorithm consists of three major steps: (a) generating fuzzy decision trees by assuming some level of specificity (detailed view) quantified in terms of threshold; (b) pruning the obtained rule-base; and (c) determining the optimal threshold resulting in a final tree. Compared with other fuzzy classifiers, the AFS classifier exhibits several essential advantages being of practical relevance. In particular, the relevance of classification results is quantified by associated confidence levels. Furthermore the proposed algorithm can be applied to data sets with mixed data type attributes. We have experimented with various data commonly present in the literature and compared the results with that of SVM, KNN, C4.5, Fuzzy Decision Trees (FDTs), Fuzzy SLIQ Decision Tree (FS-DT), FARC-HD and FURIA. It has been shown that the accuracy is higher than that being obtained by other methods. The results of statistical tests supporting comparative analysis show that the proposed algorithm performs significantly better than FDTs, FS-DT, KNN and C4.5.