A New Approach to Classification of Imbalanced Classes via Atanassov's Intuitionistic Fuzzy Sets

Abstract

We present a new method of classification of imbalanced classes. The crucial point of the method lies in applying Atanassov’s intuitionistic fuzzy sets (which are a generalization of fuzzy sets) while representing the classes during the first training phase. The Atanassov’s intuitionistic fuzzy sets are generated according to an automatic and mathematically justified procedure from the relative frequency distributions representing the data. Next, we use the information about so-called hesitation margins (which besides membership and non-membership values characterize Atanassov’s intuitionistic fuzzy sets) making it possible to improve the results of data classification. The results obtained in the testing phase were examined not only in the sense of general error/accuracy but also by using confusion matrices, that is, exploring a detailed behavior of the intuitionistic fuzzy classifiers. Detailed analysis of the errors for the examined examples has shown that applying Atanassov’s intuitionistic fuzzy sets gives better results than the counterpart approach via fuzzy sets. Better performance of the intuitionistic fuzzy classifier concerns mainly the recognition power of a smaller class. The method was tested using a benchmark problem from UCI machine learning repository.

The Spearman and Kendall rank correlation coefficients between intuitionistic fuzzy sets

“…Such a generalization of fuzzy sets gives us an additional possibility to represent imperfect knowledge which may lead to describing many real problems in a more adequate way. This is confirmed by successful applications of A-IFSs to group decision making, negotiations, voting and other situations are presented in Szmidt and Kacprzyk [15], [17], [19], [21], [22], [23], [24], [26], [31], Szmidt and Kukier [34], [35].…”

An extended numerical analysis of an intuitionistic fuzzy classifier for imbalanced classes

“…Bustince et al [12], [11]) and classification of imbalanced and overlapping classes (cf. Szmidt and Kukier [37], [38], [39]), group decision making, negotiations, voting and other situations (cf. Szmidt and Kacprzyk papers).…”

“…Szmidt and Kukier [37], [38], [39]) on the classification of imbalanced and overlapping classes via employing intuitionistic fuzzy sets (Atanassov [1], [3], [4]). We consider a twoclass classification problem ( -relatively small class, and -a bigger class).…”

Geometric similarity measures for the intuitionistic fuzzy sets

“…Bustince et al [7], [6]) and classification of imbalanced and overlapping classes (cf. Szmidt and Kukier [27], [28], [29]), group decision making, negotiations, voting and other situations (cf. Szmidt and Kacprzyk papers).…”