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

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

Eulalia Szmidt (Polish Academy of Sciences, Poland) and Marta Kukier (Polish Academy of Sciences, Poland)
DOI: 10.4018/978-1-59904-982-3.ch005
OnDemand PDF Download:


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.
Chapter Preview


Imbalanced and overlapping classes are a real challenge for the standard classifiers. The problem is not only theoretical but it concerns many different types of real tasks. Examples are given by Kubat, Holte, and Matwin (1998); Fawcett and Provost (1997); Japkowicz (2003); Lewis and Catlett (1994); and Mladenic and Grobelnik (1999). The problem of imbalanced classes occurs when the training set for a classifier contains far more examples from one class (majority illegal class) than the other (minority legal class).

To deal with the imbalance problems, up-sampling and down-sampling usually are used. Alas, both methods interfere in the structure of the data, and in a case of overlapping classes even the artificially obtained balance does not solve the problem (some data points may appear as valid examples in both classes). As the problem is still open, the new methods are investigated and trying to be improved (Chawla, Hall, & Kegelmeyer, 2002; Maloof, 2003; Visa & Ralescu, 2004; Zhang & Mani, 2003).

In this chapter we propose a new approach to the problem of classification of imbalanced and overlapping classes. The method proposed uses Atanassov’s intuitionistic fuzzy sets (A-IFSs for short) (Atanassov, 1983, 1986, 1999). We consider a two-class classification problem (legal and illegal class).

Atanassov’s theory of intuitionistic fuzzy sets (Atanassov, 1983, 1986, 1999) is one among many extensions of fuzzy sets (Zadeh, 1965) which has gained popularity in recent. Basically, it introduces, for each element of a universe of discourse, a degree of membership and a degree of non-membership, both from interval [0,1], but which do not sum up to 1 as in the conventional fuzzy sets. Such an extended definition can help more adequately represent situations when, for instance, decision makers abstain from expressing their testimonies, some assessments can not be classified but also can not be discarded, and so on. Therefore, A-IFSs provide a richer apparatus to grasp the inherent imprecision of information than the conventional fuzzy sets by assigning to each element of the universe besides membership and non-membership functions also the corresponding lack of knowledge called hesitation margin, or intuitionistic fuzzy index (Atanassov, 1999).

The classification method which will be presented here (using A-IFSs) has its roots in the fuzzy set approach given in (Baldwin, Lawry, & Martin 1998). In that approach the classes are represented by fuzzy sets. The fuzzy sets are generated from the relative frequency distributions representing the data points used as examples of the classes (Baldwin et al., 1998). In the process of generating fuzzy sets a mass assignment based approach is adopted (Baldwin, Martin, & Pilsworth, 1995), (Baldwin et al., 1998). For the obtained model (fuzzy sets describing the classes), using a chosen classification rule, a testing phase is performed to assess the performance of the proposed method.

The approach proposed in this paper is similar to the above one in the sense of the same steps are performed. The main difference lies in using A-IFSs for the representation of classes, and next - in exploiting the structure of A-IFSs to obtain a classifier better recognizing the smaller classes.

The crucial point of the method is in representing the classes by A-IFSs (first, training phase). The A-IFSs are generated from the relative frequency distributions representing the data points used as examples of the classes. A-IFSs are obtained according to the automatic, and mathematically justified procedure given in (Szmidt, & Baldwin, 2005, 2006).

Complete Chapter List

Search this Book:
Editorial Advisory Board
Table of Contents
Hsiao-Fan Wang
Hsiao-Fan Wang
Chapter 1
Martin Spott, Detlef Nauck
This chapter introduces a new way of using soft constraints for selecting data analysis methods that match certain user requirements. It presents a... Sample PDF
Automatic Intelligent Data Analysis
Chapter 2
Hung T. Nguyen, Vladik Kreinovich, Gang Xiang
It is well known that in decision making under uncertainty, while we are guided by a general (and abstract) theory of probability and of statistical... Sample PDF
Random Fuzzy Sets: Theory & Applications
Chapter 3
Gráinne Kerr, Heather Ruskin, Martin Crane
Microarray technology1 provides an opportunity to monitor mRNA levels of expression of thousands of genes simultaneously in a single experiment. The... Sample PDF
Pattern Discovery in Gene Expression Data
Chapter 4
Erica Craig, Falk Huettmann
The use of machine-learning algorithms capable of rapidly completing intensive computations may be an answer to processing the sheer volumes of... Sample PDF
Using "Blackbox" Algorithms Such AS TreeNET and Random Forests for Data-Ming and for Finding Meaningful Patterns, Relationships and Outliers in Complex Ecological Data: An Overview, an Example Using G
Chapter 5
Eulalia Szmidt, Marta Kukier
We present a new method of classification of imbalanced classes. The crucial point of the method lies in applying Atanassov’s intuitionistic fuzzy... Sample PDF
A New Approach to Classification of Imbalanced Classes via Atanassov's Intuitionistic Fuzzy Sets
Chapter 6
Arun Kulkarni, Sara McCaslin
This chapter introduces fuzzy neural network models as means for knowledge discovery from databases. It describes architectures and learning... Sample PDF
Fuzzy Neural Network Models for Knowledge Discovery
Chapter 7
Ivan Bruha
This chapter discusses the incorporation of genetic algorithms into machine learning. It does not present the principles of genetic algorithms... Sample PDF
Genetic Learning: Initialization and Representation Issues
Chapter 8
Evolutionary Computing  (pages 131-142)
Thomas E. Potok, Xiaohui Cui, Yu Jiao
The rate at which information overwhelms humans is significantly more than the rate at which humans have learned to process, analyze, and leverage... Sample PDF
Evolutionary Computing
Chapter 9
M. C. Bartholomew-Biggs, Z. Ulanowski, S. Zakovic
We discuss some experience of solving an inverse light scattering problem for single, spherical, homogeneous particles using least squares global... Sample PDF
Particle Identification Using Light Scattering: A Global Optimization Problem
Chapter 10
Dominic Savio Lee
This chapter describes algorithms that use Markov chains for generating exact sample values from complex distributions, and discusses their use in... Sample PDF
Exact Markov Chain Monte Carlo Algorithms and Their Applications in Probabilistic Data Analysis and Inference
Chapter 11
J. P. Ganjigatti, Dilip Kumar Pratihar
In this chapter, an attempt has been made to design suitable knowledge bases (KBs) for carrying out forward and reverse mappings of a Tungsten inert... Sample PDF
Design and Development of Knowledge Bases for Forward and Reverse Mappings of TIG Welding Process
Chapter 12
Malcolm J. Beynon
This chapter considers the role of fuzzy decision trees as a tool for intelligent data analysis in domestic travel research. It demonstrates the... Sample PDF
A Fuzzy Decision Tree Analysis of Traffic Fatalities in the US
Chapter 13
Dymitr Ruta, Christoph Adl, Detlef Nauck
In the telecom industry, high installation and marketing costs make it six to 10 times more expensive to acquire a new customer than it is to retain... Sample PDF
New Churn Prediction Strategies in the Telecom Industry
Chapter 14
Malcolm J. Beynon
This chapter demonstrates intelligent data analysis, within the environment of uncertain reasoning, using the recently introduced CaRBS technique... Sample PDF
Intelligent Classification and Ranking Analyses Using CARBS: Bank Rating Applications
Chapter 15
Fei-Chen Hsu, Hsiao-Fan Wang
In this chapter, we used Cumulative Prospect Theory to propose an individual risk management process (IRM) including a risk analysis stage and a... Sample PDF
Analysis of Individual Risk Attitude for Risk Management Based on Cumulative Prospect Theory
Chapter 16
Francesco Giordano, Michele La Rocca, Cira Perna
This chapter introduces the use of the bootstrap in a nonlinear, nonparametric regression framework with dependent errors. The aim is to construct... Sample PDF
Neural Networks and Bootstrap Methods for Regression Models with Dependent Errors
Chapter 17
Lean Yu, Shouyang Wang, Kin Keung Lai
Financial crisis is a kind of typical rare event, but it is harmful to economic sustainable development if occurs. In this chapter, a... Sample PDF
Financial Crisis Modeling and Prediction with a Hilbert-EMD-Based SVM Approachs
Chapter 18
Chun-Jung Huang, Hsiao-Fan Wang, Shouyang Wang
One of the key problems in supervised learning is due to the insufficient size of the training data set. The natural way for an intelligent learning... Sample PDF
Virtual Sampling with Data Construction Analysis
About the Contributors