Atanassov’s Intuitionistic Fuzzy Sets in Classification of Imbalanced and Overlapping Classes

2008 ◽  
pp. 455-471 ◽  
Author(s):  
Eulalia Szmidt ◽  
Marta Kukier
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
Overlapping Classes ◽  
Atanassov’S Intuitionistic Fuzzy Sets

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

2009 ◽  
pp. 85-101 ◽  
Author(s):  
Eulalia Szmidt ◽  
Marta Kukier
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Classifier ◽  
Frequency Distributions ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Classifiers ◽  
Imbalanced Classes ◽  
Confusion Matrices ◽  
Atanassov’S Intuitionistic Fuzzy Sets

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.

Correlation in Interval-Valued Atanassov’s Intuitionistic Fuzzy Sets — Conjugate and Negation Operators

2017 ◽  
Vol 25 (05) ◽  
pp. 787-819 ◽  
Author(s):  
Renata Hax Sander Reiser ◽  
Benjamin Bedregal
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Sets ◽  
Correlation Coefficient ◽  
Intuitionistic Fuzzy Sets ◽  
Conjugate Functions ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Index ◽  
Intuitionistic Fuzzy Logic ◽  
Interval Valued ◽  
Atanassov’S Intuitionistic Fuzzy Sets

This paper studies the conjugate functions related to main connectives of the Intervalvalued Atanassov’s Intuitionistic Fuzzy Logic. The relationships among automorphism classes are formalized by the ϕ-representability theorem, passing from automorphisms to interval-valued intuitionistic automorphisms, also visiting other two ones, intuitionistic automorphisms and interval-valued automorphisms. Additionally, the ϕ-conjugate of an interval-valued Atanassov’s intuitionistic fuzzy negation can be obtained either from an interval-valued fuzzy negation or from an Atanassov’s intuitionistic fuzzy negation, including a discussion presenting such reverse constructions. The ϕ-conjugate of an interval-valued Atanassov’s intuitionistic fuzzy negation not only preserves the main properties of its corresponding fuzzy negation but also of two other ones, the intuitionistic fuzzy negation and interval-valued fuzzy negation. Moreover, an extension of the intuitionistic fuzzy index as well as the correlation coefficient is discussed in terms of fuzzy negations, by considering the Atanassov’s Intuitionistic Fuzzy Logic.

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