scholarly journals Fixed Point Results in Orthogonal Neutrosophic Metric Spaces

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Umar Ishtiaq ◽  
Khalil Javed ◽  
Fahim Uddin ◽  
Manuel de la Sen ◽  
Khalil Ahmed ◽  
...  
Keyword(s):  
Fixed Point ◽  
Fuzzy Set ◽  
Metric Space ◽  
Metric Spaces ◽  
Intuitionistic Fuzzy Set ◽  
Neutrosophic Set ◽  
Imprecise Data ◽  
Intuitionistic Fuzzy ◽  
Neutrosophic Logic ◽  
The Relationship

Neutrosophy deals with neutrosophic logic, probability, and sets. Actually, the neutrosophic set is a generalization of the classical set, fuzzy set, and intuitionistic fuzzy set. A neutrosophic set is a mathematical notion serving issues containing inconsistent, indeterminate, and imprecise data. The notion of intuitionistic fuzzy metric space is useful in modelling some phenomena, where it is necessary to study the relationship between two probability functions. In this study, the concept of an orthogonal neutrosophic metric space is initiated. It is a generalization of the neutrosophic metric space. Some fixed point results are investigated in this setting. For the validity of the obtained results, some nontrivial examples are given.

scholarly journals MBJ-neutrosophic subalgebras and filters in $ BE $-algebras

2022 ◽  
Vol 7 (4) ◽  
pp. 6016-6033
Author(s):  
Rajab Ali Borzooei ◽  
◽  
Hee Sik Kim ◽  
Young Bae Jun ◽  
Sun Shin Ahn ◽  
...  
Keyword(s):  
Membership Function ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Neutrosophic Set ◽  
Neutrosophic Sets ◽  
Intuitionistic Fuzzy ◽  
The Relationship ◽  
Interval Valued

<abstract><p>The concept of a neutrosophic set, which is a generalization of an intuitionistic fuzzy set and a para consistent set etc., was introduced by F. Smarandache. Since then, it has been studied in various applications. In considering a generalization of the neutrosophic set, Mohseni Takallo et al. used the interval valued fuzzy set as the indeterminate membership function because interval valued fuzzy set is a generalization of a fuzzy set, and introduced the notion of MBJ-neutrosophic sets, and then they applied it to BCK/BCI-algebras. The aim of this paper is to apply the concept of MBJ-neutrosophic sets to a $ BE $-algebra, which is a generalization of a BCK-algebra. The notions of MBJ-neutrosophic subalgebras and MBJ-neutrosophic filters of $ BE $-algebras are introduced and related properties are investigated. The conditions under which the MBJ-neutrosophic set can be a MBJ-neutrosophic subalgebra/filter are searched. Characterizations of MBJ-neutrosophic subalgebras and MBJ-neutrosophic filters are considered. The relationship between an MBJ-neutrosophic subalgebra and an MBJ-neutrosophic filter is established.</p></abstract>

scholarly journals Stability of intuitionistic fuzzy set-valued maps and solutions of integral inclusions

2021 ◽  
Vol 7 (1) ◽  
pp. 315-333
Author(s):  
Maysaa Al-Qurashi ◽  
◽  
Mohammed Shehu Shagari ◽  
Saima Rashid ◽  
Y. S. Hamed ◽  
...  
Keyword(s):  
Fixed Point ◽  
Fuzzy Set ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Intuitionistic Fuzzy Set ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Fixed Point ◽  
Functional Inclusion

<abstract><p>In this paper, new intuitionistic fuzzy fixed point results for sequence of intuitionistic fuzzy set-valued maps in the structure of $ b $-metric spaces are examined. A few nontrivial comparative examples are constructed to keep up the hypotheses and generality of our obtained results. Following the fact that most existing concepts of Ulam-Hyers type stabilities are concerned with crisp mappings, we introduce the notion of stability and well-posedness of functional inclusions involving intuitionistic fuzzy set-valued maps. It is a familiar fact that solution of every functional inclusion is a subset of an appropriate space. In this direction, intuitionistic fuzzy fixed point problem involving $ (\alpha, \beta) $-level set of an intuitionistic fuzzy set-valued map is initiated. Moreover, novel sufficient criteria for existence of solutions to an integral inclusion are investigated to indicate a possible application of the ideas presented herein.</p></abstract>

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.

scholarly journals Some results on χ-single valued neutrosophic subgroups

2021 ◽  
Vol 23 (3) ◽  
pp. 1583
Author(s):  
M. Shazib Hameed ◽  
Zaheer Ahmad ◽  
Salman Mukhtar ◽  
Asad Ullah
Keyword(s):  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Vital Role ◽  
Neutrosophic Set ◽  
Pythagorean Fuzzy Set ◽  
Intuitionistic Fuzzy ◽  
Novel Structure ◽  
Fuzzy Subgroups

<p>In this study, we develop a novel structure χ-single valued neutrosophic set, which is a generalization of the intuitionistic set, inconsistent intuitionistic fuzzy set, Pythagorean fuzzy set, spherical fuzzy set, paraconsistent set, etc. Fuzzy subgroups play a vital role in vagueness structure, it differ from regular subgroups in that it is impossible to determine which group elements belong and which do not. In this paper, we investigate the concept of a χ-single valued neutrosophic set and χ-single valued neutrosophic subgroups. We explore the idea of χ-single valued neutrosophic set on fuzzy subgroups and several characterizations related to χ-single valued neutrosophic subgroups are suggested.</p>

scholarly journals A p-Ideal in BCI-Algebras Based on Multipolar Intuitionistic Fuzzy Sets

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 993
Author(s):  
Jeong-Gon Lee ◽  
Mohammad Fozouni ◽  
Kul Hur ◽  
Young Bae Jun
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Finite Degree ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Ideal ◽  
The Relationship

In 2020, Kang, Song and Jun introduced the notion of multipolar intuitionistic fuzzy set with finite degree, which is a generalization of intuitionistic fuzzy set, and they applied it to BCK/BCI-algebras. In this paper, we used this notion to study p-ideals of BCI-algebras. The notion of k-polar intuitionistic fuzzy p-ideals in BCI-algebras is introduced, and several properties were investigated. An example to illustrate the k-polar intuitionistic fuzzy p-ideal is given. The relationship between k-polar intuitionistic fuzzy ideal and k-polar intuitionistic fuzzy p-ideal is displayed. A k-polar intuitionistic fuzzy p-ideal is found to be k-polar intuitionistic fuzzy ideal, and an example to show that the converse is not true is provided. The notions of p-ideals and k-polar ( ∈ , ∈ ) -fuzzy p-ideal in BCI-algebras are used to study the characterization of k-polar intuitionistic p-ideal. The concept of normal k-polar intuitionistic fuzzy p-ideal is introduced, and its characterization is discussed. The process of eliciting normal k-polar intuitionistic fuzzy p-ideal using k-polar intuitionistic fuzzy p-ideal is provided.

scholarly journals On Intuitionistic Fuzzy 2-Metric Spaces

2018 ◽  
Vol 22 ◽  
pp. 01024
Author(s):  
Elif Güner ◽  
Vildan Çetkin ◽  
Halis Aygün
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Intuitionistic Fuzzy

In this study, we first recall the notion of an intuitionistic fuzzy 2-metric space and fundamental definitions with several illustrative examples. Then we define the notion of δ−chainable space and (δ,λ)−uniform locally contractive mapping between intuitionistic fuzzy 2-metric spaces. After that, by using the proposed concepts, we obtain a few fixed point theorems of self-mappings defined on this spaces.

scholarly journals Fixed point theorem for compatible mappings in intuitionistic fuzzy 3-metric spaces

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 371-376
Author(s):  
Hassan Abu-Donia ◽  
Hany Atia ◽  
Omnia Khater
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Main Idea ◽  
Intuitionistic Fuzzy ◽  
Uniqueness And Existence ◽  
The Fixed Point Theorem ◽  
Asymptotically Regular

In this paper, we introduced the concept of weak compatible of type (?) and asymptotically regular defined on intuitionistic fuzzy 3-metric space and proved the uniqueness and existence the fixed point theorem for five mappings from a complete intuitionistic fuzzy 3-metric space into itself under weak compatible of type (?) and asymptotically regular. The used definitions and theorem show the practice of our main idea.

Fixed Point Theorems for Faintly Compatible Mappings in Intuitionistic Fuzzy Metric Space

2017 ◽  
Vol 84 (1-2) ◽  
pp. 130 ◽  
Author(s):  
Kamal Wadhwa ◽  
Ved Prakash Bhardwaj
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Compatible Mappings ◽  
Fuzzy Metric ◽  
Intuitionistic Fuzzy ◽  
Continuous Mappings ◽  
Common Fixed Point Theorems

In this paper, we correct the contractive condition of Manro and Kang [16] and prove some common fixed point theorems for four faintly compatible mappings using subsequential continuous mappings in Intuitionistic Fuzzy metric spaces. We also provide an example in support of our main result. Our results improve and generalize the results of Manro and Kang [16].

scholarly journals Common Fixed Point Theorems in Modified Intuitionistic Fuzzy Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Saurabh Manro ◽  
Sanjay Kumar ◽  
S. S. Bhatia ◽  
Kenan Tas
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fuzzy Metric Space ◽  
Fuzzy Metric ◽  
Intuitionistic Fuzzy ◽  
Continuous Mappings ◽  
Common Fixed Point Theorems

This paper consists of main two sections. In the first section, we prove a common fixed point theorem in modified intuitionistic fuzzy metric space by combining the ideas of pointwiseR-weak commutativity and reciprocal continuity of mappings satisfying contractive conditions. In the second section, we prove common fixed point theorems in modified intuitionistic fuzzy metric space from the class of compatible continuous mappings to noncompatible and discontinuous mappings. Lastly, as an application, we prove fixed point theorems using weakly reciprocally continuous noncompatible self-mappings on modified intuitionistic fuzzy metric space satisfying some implicit relations.

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