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What is Intuitionistic Fuzzy Set

Chapter 12
Handbook of Research on Advances and Applications of Fuzzy Sets and Logic
Intuitionistic fuzzy sets are sets whose elements have membership grades and non-membership grades. The intuitionistic fuzzy set generalizes fuzzy set, since the indicator function of fuzzy set is a special case of the membership function and non-membership function of intuitionistic fuzzy set.
Published in Chapter:
Tanimoto Similarity Coefficients Measuring Bipolar q-Rung Picture Fuzzy Information and Their Applications
Hüseyin Kamacı (Yozgat Bozok University, Turkey) and Subramanian Petchimuthu (University College of Engineering, Nagercoil, India)
Copyright: © 2022 |Pages: 30
DOI: 10.4018/978-1-7998-7979-4.ch012
Abstract
In this chapter, the concepts of bipolar q-rung picture fuzzy set and bipolar q-rung picture fuzzy number are introduced. Moreover, the fundamentals of bipolar q-rung picture fuzzy sets and bipolar q-rung picture fuzzy numbers are studied. Relatedly, some basic operations, aggregation operators, and relations on the bipolar q-rung picture fuzzy sets/numbers are derived. The intuitive definition of Tanimoto's similarity coefficient is proposed to measure the similarity between two bipolar q-rung picture fuzzy sets. Finally, it is shown that the proposed Tanimoto similarity measures can be used to deal with the problems of medical diagnosis and pattern recognition under the bipolar q-rung picture fuzzy environment.
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Chapter 143
Intuitionistic Fuzzy Image Processing
An extension of the fuzzy set. It is defined using two characteristic functions, the membership and the non-membership that do not necessarily sum up to unity. They attribute to each individual of the universe corresponding degrees of belongingness and non-belongingness with respect to the set under consideration.
Published in Chapter: Intuitionistic Fuzzy Image Processing; From: Encyclopedia of Artificial Intelligence
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Chapter 1
On Theory of Multisets and Applications
It is an uncertainty based model proposed by K.T.Attanasov in 1986, which extends the notion of fuzzy sets by relaxing the constraint in fuzzy sets that the non-membership value is one’s complement of the membership value of every element.
Published in Chapter: On Theory of Multisets and Applications; From: Handbook of Research on Generalized and Hybrid Set Structures and Applications for Soft Computing
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Chapter 5
Soft Sets and Its Applications
An (IFS) A over E, is characterised by two functions µ A and ? A called the membership and non-membership function of A respectively such that µ A :U ? [0, 1] and ? A :U ? [0, 1]. For any x ? U , we have 0 = µ A ( x ) + ? A ( x ) = 1. The hesitation function of A is denoted by p A and for any x ? U , is given by p A ( x ) = 1 – µ A ( x ) – ? A ( x ). It is the indeterministic part of x.
Published in Chapter: Soft Sets and Its Applications; From: Handbook of Research on Generalized and Hybrid Set Structures and Applications for Soft Computing
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Chapter 16
Evaluation of the Global Competitiveness Index (GCI) by Multi-Criteria Decision-Making Methods Based on Intuitionistic Fuzzy Sets: Comparative Analysis
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