scholarly journals Generalized Ideals of BCK/BCI-Algebras Based on Fuzzy Soft Set Theory

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
G. Muhiuddin ◽  
D. Al-Kadi ◽  
K. P. Shum ◽  
A. M. Alanazi
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Intuitionistic Fuzzy ◽  
Soft Point ◽  
Generalized Ideals

In the present paper, using Lukaswize triple-valued logic, we introduce the notion of α , β -intuitionistic fuzzy soft ideal of BCK / BCI -algebras, where α  and  β are the membership values between an intuitionistic fuzzy soft point and intuitionistic fuzzy set. Moreover, intuitionistic fuzzy soft ideals with thresholds are introduced, and their related properties are investigated.

scholarly journals An Intuitionistic Fuzzy Soft Set Theoretic Approach to Decision Making Problems

MATEMATIKA ◽  
2018 ◽  
Vol 34 (1) ◽  
pp. 49-58 ◽  
Author(s):  
Shiva Raj Singh ◽  
Surendra Singh Gautam ◽  
Abhishekh .
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Real Life ◽  
Construction Method ◽  
Soft Set ◽  
Theoretic Approach ◽  
Fuzzy Soft Set ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

In general most of real life problem of decision making involve imprecise parameters. In recent past the major emphasis of research workers in this area have been to develop the reliable models to deal with such imprecision and vagueness effectively. Several theories have been developed such as fuzzy set theory, interval valued fuzzy set, intuitionistic fuzzy set, and interval valued intuitionistic fuzzy set, rough set and soft set. The primary objectives of all the above developed theories are to deal with various kinds of uncertainty, imprecision and vagueness but unfortunately every theory has certain limitations. In the present paper we briefly introduced the notion of soft set, fuzzy soft set and intuitionistic fuzzy soft set. We extend the Jurio et al construction method of converting fuzzy set into intuitionistic fuzzy set to fuzzy soft set into intuitionistic fuzzy soft set. Here we consider a problem of decision making in fuzzy soft set and presented a method to generalize it into intuitionistic fuzzy soft set based decision making problem for modelling the problem in a better way. In the process we used the construction method and score function of intuitionistic fuzzy number.

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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