Cartesian product over intuitionistic fuzzy multiset of second type

2022 ◽  
Author(s):  
R. Srinivasan ◽  
K. Mariyam Jameela ◽  
S. Sheik Dhavudh
Keyword(s):  
Cartesian Product ◽  
Intuitionistic Fuzzy

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.

Fα,β over Cartesian product of antagonistic- intuitionistic fuzzy H-ideals in division BG-algebras

2019 ◽  
Author(s):  
S. Jeyanthi ◽  
C. Ragavan ◽  
B. Lena
Keyword(s):  
Cartesian Product ◽  
Intuitionistic Fuzzy

scholarly journals Dominating Energy of Operations on Intuitionistic Fuzzy Graphs

2018 ◽  
Vol 7 (4.10) ◽  
pp. 328 ◽  
Author(s):  
A. Kalimulla ◽  
R. Vijayaragavan ◽  
S. Sharief Basha
Keyword(s):  
Cartesian Product ◽  
Fuzzy Graph ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Graphs ◽  
Intuitionistic Fuzzy Graphs

The concept of energy of an Intuitionistic Fuzzy Graph is extended to dominating Energy in operations on Intuitionistic Fuzzy Graph. In this paper, We have obtained the value of dominating Energy in different operations such as complement, Union, Join, Cartesian product and composition between two intuitionistic Fuzzy graphs. Also we study the relation between the dominating Energy in the operations on two Intuitionistic Fuzzy Graphs.  

scholarly journals Multivariate Extension Principle and Algebraic Operations of Intuitionistic Fuzzy Sets

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Yonghong Shen ◽  
Wei Chen
Keyword(s):  
Fuzzy Sets ◽  
General Framework ◽  
Cartesian Product ◽  
Intuitionistic Fuzzy Sets ◽  
Extension Principle ◽  
Algebraic Operation ◽  
Multivariate Extension ◽  
Intuitionistic Fuzzy ◽  
Algebraic Operations

This paper mainly focuses on multivariate extension of the extension principle of IFSs. Based on the Cartesian product over IFSs, the multivariate extension principle of IFSs is established. Furthermore, three kinds of representation of this principle are provided. Finally, a general framework of the algebraic operation between IFSs is given by using the multivariate extension principle.

scholarly journals Complex Atanassov's Intuitionistic Fuzzy Relation

2013 ◽  
Vol 2013 ◽  
pp. 1-18 ◽  
Author(s):  
Abd Ulazeez M. Alkouri ◽  
Abdul Razak Salleh
Keyword(s):  
Fuzzy Sets ◽  
Distance Measure ◽  
Cartesian Product ◽  
Real Life ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Relation ◽  
Mathematical Concepts ◽  
Intuitionistic Fuzzy ◽  
Real Life Situation ◽  
Atanassov’S Intuitionistic Fuzzy Sets

This paper presents distance measure between two complex Atanassov's intuitionistic fuzzy sets (CAIFSs). This distance measure is used to illustrate an application of CAIFSs in solving one of the most core application areas of fuzzy set theory, which is multiattributes decision-making (MADM) problems, in complex Atanassov's intuitionistic fuzzy realm. A new structure of relation between two CAIFSs, called complex Atanassov's intuitionistic fuzzy relation (CAIFR), is obtained. This relation is formally generalised from a conventional Atanassov's intuitionistic fuzzy relation, based on complex Atanassov's intuitionistic fuzzy sets, in which the ranges of values of CAIFR are extended to the unit circle in complex plane for both membership and nonmembership functions instead of [0, 1] as in the conventional Atanassov's intuitionistic fuzzy functions. Definition and some mathematical concepts of CAIFS, which serve as a foundation for the creation of complex Atanassov's intuitionistic fuzzy relation, are recalled. We also introduce the Cartesian product of CAIFSs and derive two properties of the product space. The concept of projection and cylindric extension of CAIFRs are also introduced. An example of CAIFR in real-life situation is illustrated in this paper. Finally, we introduce the concept of composition of CAIFRs.

scholarly journals New Concepts of Picture Fuzzy Graphs with Application

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 470 ◽  
Author(s):  
Cen Zuo ◽  
Anita Pal ◽  
Arindam Dey
Keyword(s):  
Fuzzy Set ◽  
Cartesian Product ◽  
Intuitionistic Fuzzy Set ◽  
Real Life ◽  
Fuzzy Graph ◽  
Intuitionistic Fuzzy ◽  
Strong Product ◽  
Fuzzy Graphs ◽  
Life Problems ◽  
Picture Fuzzy Set

The picture fuzzy set is an efficient mathematical model to deal with uncertain real life problems, in which a intuitionistic fuzzy set may fail to reveal satisfactory results. Picture fuzzy set is an extension of the classical fuzzy set and intuitionistic fuzzy set. It can work very efficiently in uncertain scenarios which involve more answers to these type: yes, no, abstain and refusal. In this paper, we introduce the idea of the picture fuzzy graph based on the picture fuzzy relation. Some types of picture fuzzy graph such as a regular picture fuzzy graph, strong picture fuzzy graph, complete picture fuzzy graph, and complement picture fuzzy graph are introduced and some properties are also described. The idea of an isomorphic picture fuzzy graph is also introduced in this paper. We also define six operations such as Cartesian product, composition, join, direct product, lexicographic and strong product on picture fuzzy graph. Finally, we describe the utility of the picture fuzzy graph and its application in a social network.

CARTESIAN PRODUCT OF INTUITIONISTIC FUZZY PMS-IDEALS OF PMS-ALGEBRAS

2020 ◽  
Vol 9 (3) ◽  
pp. 1459-1466
Author(s):  
C. Ragavan ◽  
M. Balamurugan ◽  
B. Thirumaran ◽  
S. Senthilkumar
Keyword(s):  
Cartesian Product ◽  
Intuitionistic Fuzzy
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