Comparison of different T-norm operators in classification problems

TL;DR

This paper compares nine different T-norm operators in fuzzy rule-based classification systems, demonstrating that the choice of T-norm significantly impacts classification accuracy across various datasets.

Contribution

It introduces the use of multiple T-norms for calculating confidence and support in fuzzy classification, showing their effect on system performance.

Findings

Aczel-Alsina T-norm yields the highest accuracy

Dubois-Prade T-norm performs second best

Dombi T-norm is third in effectiveness

Abstract

Fuzzy rule based classification systems are one of the most popular fuzzy modeling systems used in pattern classification problems. This paper investigates the effect of applying nine different T-norms in fuzzy rule based classification systems. In the recent researches, fuzzy versions of confidence and support merits from the field of data mining have been widely used for both rules selecting and weighting in the construction of fuzzy rule based classification systems. For calculating these merits the product has been usually used as a T-norm. In this paper different T-norms have been used for calculating the confidence and support measures. Therefore, the calculations in rule selection and rule weighting steps (in the process of constructing the fuzzy rule based classification systems) are modified by employing these T-norms. Consequently, these changes in calculation results in altering the overall accuracy of rule based classification systems. Experimental results obtained on some well-known data sets show that the best performance is produced by employing the Aczel-Alsina operator in terms of the classification accuracy, the second best operator is Dubois-Prade and the third best operator is Dombi. In experiments, we have used 12 data sets with numerical attributes from the University of California, Irvine machine learning repository (UCI).