Additive Generators Based on Generalized Arithmetic Operators in Interval-Valued Fuzzy and Atanassov’s Intuitionistic Fuzzy Set Theory

2015 ◽  
pp. 137-157
Author(s):  
Glad Deschrijver ◽  
Etienne E. Kerre
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy ◽  
Interval Valued ◽  
Generalized Arithmetic

SMETS-MAGREZ AXIOMS FOR R-IMPLICATORS IN INTERVAL-VALUED AND INTUITIONISTIC FUZZY SET THEORY

2005 ◽  
Vol 13 (04) ◽  
pp. 453-464 ◽  
Author(s):  
GLAD DESCHRIJVER ◽  
ETIENNE E. KERRE
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Intuitionistic Fuzzy Set ◽  
Membership Degree ◽  
Triangular Norms ◽  
Intuitionistic Fuzzy ◽  
Special Lattice ◽  
Interval Valued

Interval-valued fuzzy sets constitute an extension of fuzzy sets which give an interval approximating the "real" (but unknown) membership degree. Interval-valued fuzzy sets are equivalent to intuitionistic fuzzy sets in the sense of Atanassov which give both a membership degree and a non-membership degree, whose sum must be smaller than or equal to 1. Both are equivalent to L-fuzzy sets w.r.t. a special lattice L*. In fuzzy set theory, an important class of triangular norms is the class of those that satisfy the residuation principle. In a previous paper5 we gave a construction for t-norms on L* satisfying the residuation principle which are not t-representable. In this paper we investigate the Smets-Magrez axioms and some other properties for the residual implicator generated by such t-norms.

scholarly journals An Improved Correlation Coefficient of Intuitionistic Fuzzy Sets

2019 ◽  
Vol 28 (2) ◽  
pp. 231-243 ◽  
Author(s):  
Han-Liang Huang ◽  
Yuting Guo
Keyword(s):  
Fuzzy Sets ◽  
Correlation Coefficient ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

Abstract The intuitionistic fuzzy set is a useful tool to deal with vagueness and uncertainty. Correlation coefficient of the intuitionistic fuzzy sets is an important measure in intuitionistic fuzzy set theory and has great practical potential in a variety of areas, such as decision making, medical diagnosis, pattern recognition, etc. In this paper, an improved correlation coefficient of the intuitionistic fuzzy sets is defined, and it can overcome some drawbacks of the existing ones. The properties of this correlation coefficient are discussed. Then, the generalization of the coefficient of interval-valued intuitionistic fuzzy sets is also introduced. Finally, two examples about the application of the proposed correlation coefficient of the intuitionistic fuzzy sets in medical diagnosis and clustering are shown to illustrate the advantages over the existing methods.

Atanassov’s interval-valued intuitionistic fuzzy set theory applied in KU-subalgebras

2019 ◽  
Vol 11 (02) ◽  
pp. 1950023 ◽  
Author(s):  
Tapan Senapati ◽  
K. P. Shum
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Cartesian Product ◽  
Intuitionistic Fuzzy Set ◽  
Inverse Image ◽  
Fundamental Properties ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

In this paper, the notion of interval-valued intuitionistic fuzzy (IVIF) [Formula: see text]-subalgebras of [Formula: see text]-algebras are introduced and some fundamental properties are discussed. The image and the inverse image of IVIF [Formula: see text]-subalgebras are defined and how the image and the inverse image of IVIF [Formula: see text]-subalgebras in [Formula: see text]-algebras become IVIF [Formula: see text]-subalgebras are studied. Moreover, the cartesian product of IVIF [Formula: see text]-subalgebras are given.

A Hesitant Intuitionistic Fuzzy Set Approach to Study Ideals of Semirings

2021 ◽  
Vol 10 (3) ◽  
pp. 1-17
Author(s):  
Debabrata Mandal
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Cartesian Product ◽  
Intuitionistic Fuzzy Set ◽  
Ideal Theory ◽  
Hesitant Fuzzy Set ◽  
Neutrosophic Set ◽  
Intuitionistic Fuzzy ◽  
Interval Valued ◽  
The Ideal

The classical set theory was extended by the theory of fuzzy set and its several generalizations, for example, intuitionistic fuzzy set, interval valued fuzzy set, cubic set, hesitant fuzzy set, soft set, neutrosophic set, etc. In this paper, the author has combined the concepts of intuitionistic fuzzy set and hesitant fuzzy set to study the ideal theory of semirings. After the introduction and the priliminary of the paper, in Section 3, the author has defined hesitant intuitionistic fuzzy ideals and studied several properities of it using the basic operations intersection, homomorphism and cartesian product. In Section 4, the author has also defined hesitant intuitionistic fuzzy bi-ideals and hesitant intuitionistic fuzzy quasi-ideals of a semiring and used these to find some characterizations of regular semiring. In that section, the author also has discussed some inter-relations between hesitant intuitionistic fuzzy ideals, hesitant intuitionistic fuzzy bi-ideals and hesitant intuitionistic fuzzy quasi-ideals, and obtained some of their related properties.

Segmentation Of Blood Clot MRI Images Using Intuitionistic Fuzzy Set Theory

2018 ◽  
Author(s):  
Nur Lyana Shahfiqa Binti Albashah ◽  
Sarat Chandra Dass ◽  
Vijanth Sagayan Asirvadam ◽  
Fabrice Meriaudeau
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Blood Clot ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy
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