scholarly journals Refined Neutrosophy and Lattices vs. Pair Structures and YinYang Bipolar Fuzzy Set

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 353 ◽  
Author(s):  
Florentin Smarandache
Keyword(s):  
Fuzzy Set ◽  
Infinite Number ◽  
Neutrosophic Set ◽  
Lattice Structures

In this paper, we present the lattice structures of neutrosophic theories. We prove that Zhang-Zhang’s YinYang bipolar fuzzy set is a subclass of the Single-Valued bipolar neutrosophic set. Then we show that the pair structure is a particular case of refined neutrosophy, and the number of types of neutralities (sub-indeterminacies) may be any finite or infinite 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.

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 Multiple-attribute Decision-Making Method under a Single-Valued Neutrosophic Hesitant Fuzzy Environment

2015 ◽  
Vol 24 (1) ◽  
pp. 23-36 ◽  
Author(s):  
Jun Ye
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Weighted Averaging ◽  
Hesitant Fuzzy Set ◽  
Neutrosophic Set ◽  
Fuzzy Environment ◽  
Cosine Measure ◽  
Multiple Attribute

AbstractOn the basis of the combination of single-valued neutrosophic sets and hesitant fuzzy sets, this article proposes a single-valued neutrosophic hesitant fuzzy set (SVNHFS) as a further generalization of the concepts of fuzzy set, intuitionistic fuzzy set, single-valued neutrosophic set, hesitant fuzzy set, and dual hesitant fuzzy set. Then, we introduce the basic operational relations and cosine measure function of SVNHFSs. Also, we develop a single-valued neutrosophic hesitant fuzzy weighted averaging (SVNHFWA) operator and a single-valued neutrosophic hesitant fuzzy weighted geometric (SVNHFWG) operator and investigate their properties. Furthermore, a multiple-attribute decision-making method is established on the basis of the SVNHFWA and SVNHFWG operators and the cosine measure under a single-valued neutrosophic hesitant fuzzy environment. Finally, an illustrative example of investment alternatives is given to demonstrate the application and effectiveness of the developed approach.

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 A note on different types of product of neutrosophic graphs

2021 ◽  
Author(s):  
Kartick Mohanta ◽  
Arindam Dey ◽  
Anita Pal
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Real World ◽  
Real Life ◽  
Neutrosophic Set ◽  
Total Degree ◽  
Decision Making Problem ◽  
Different Types ◽  
Neutrosophic Graph ◽  
Real World Problems

AbstractFuzzy set and neutrosophic set are two efficient tools to handle the uncertainties and vagueness of any real-world problems. Neutrosophic set is more capable than fuzzy set to deal the uncertainties of a real-life problem. This research paper introduces some new concept of single-valued neutrosophic graph (SVNG). We have also presented some different operations on SVNG such as rejection, symmetric difference, maximal product, and residue product with appropriate examples, and some of their important theorems are also described. Then, we have described the concept of total degree of a neutrosophic graph with some interesting examples. We have also presented an efficient approach to solve a decision-making problem using SVNG.

scholarly journals A study on a new method for solving interval neutrosophic linear programming problems

2021 ◽  
Vol 5 (2) ◽  
pp. 48-54
Author(s):  
Mohamed Assarudeen S N ◽  
Ulaganathan D
Keyword(s):  
Linear Programming ◽  
Set Theory ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
New Method ◽  
Neutrosophic Set ◽  
Engineering Applications ◽  
Standard Methods ◽  
Linear Programming Problems ◽  
Science Activities

Neutrosophic set theory is a generalization of the intuitionistic fuzzy set which can be considered as a powerful tool to express the indeterminacy and inconsistent information that exist commonly in engineering applications and real meaningful science activities. In this paper an interval neutrosophic linear programming (INLP) model will be presented, where its parameters are represented by triangular interval neutrosophic numbers (TINNs) and call it INLP problem. Afterward, by using a ranking function we present a technique to convert the INLP problem into a crisp model and then solve it by standard methods

scholarly journals Cross Entropy Measures of Bipolar and Interval Bipolar Neutrosophic Sets and Their Application for Multi-Attribute Decision Making

2018 ◽  
Author(s):  
Surapati Pramanik ◽  
Partha Pratim Dey ◽  
Florentin Smarandache ◽  
Jun Ye
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Cross Entropy ◽  
Neutrosophic Set ◽  
Membership Functions ◽  
Neutrosophic Sets ◽  
Entropy Measures ◽  
Multi Attribute Decision Making ◽  
Important Extension ◽  
The Ideal

Bipolar neutrosophic set is an important extension of bipolar fuzzy set. This set is a hybridization of bipolar fuzzy set and neutrosophic set. Every element of a bipolar neutrosophic set consists of three independent positive membership functions and three independent negative membership functions. In this paper, we develop cross entropy measures of bipolar neutrosophic sets and prove its properties. We also define cross entropy measures of interval bipolar neutrosophic sets and prove its properties. Thereafter, we develop two novel multi-attribute decision making methods based on the proposed cross entropy measures. In the decision making framework, we calculate the weighted cross entropy measures between each alternative and the ideal alternative to rank the alternatives and choose the best one. We solve two illustrative examples of multi-attribute decision making problems and compare the obtained result with the results of other existing methods to show the applicability and effectiveness of the developed method. In the end, the main conclusion and future scope of research are summarized.

scholarly journals Indeterminacy in Neutrosophic Theories and their Applications

2021 ◽  
Author(s):  
Florentin Smarandache ◽  
Keyword(s):  
Fuzzy Set ◽  
Neutrosophic Set ◽  
Algebraic Structures ◽  
Classical Probability ◽  
Broad Definition ◽  
Practical Applications ◽  
Intuitionistic Fuzzy ◽  
Classical Statistics ◽  
Definition Of

Indeterminacy makes the main distinction between fuzzy/intuitionistic fuzzy (and other extensions of fuzzy) set/logic vs. neutrosophic set/logic, and between classical probability and neutrosophic probability. Also, between classical statistics vs. neutrosophic and plithogenic statistics, between classical algebraic structures vs. neutrosophic algebraic structures, between crisp numbers vs. neutrosophic numbers. We present a broad definition of indeterminacy, various types of indeterminacies, and many practical applications.

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.

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