scholarly journals Optimal Solutions for Constrained Bimatrix Games with Payoffs Represented by Single-Valued Trapezoidal Neutrosophic Numbers

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Mohamed Gaber ◽  
Majed G. Alharbi ◽  
Abd Alwahed Dagestani ◽  
El-Saeed Ammar
Keyword(s):  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Real Life ◽  
Optimal Strategies ◽  
Neutrosophic Set ◽  
Bimatrix Games ◽  
Comparison Analysis ◽  
Solution Approach ◽  
Mathematical Programming Problems ◽  
Life Decision

Single-valued neutrosophic set (SVNS) is considered as generalization and extension of fuzzy set, intuitionistic fuzzy set (IFS), and crisp set for expressing the imprecise, incomplete, and indeterminate information about real-life decision-oriented models. The theme of this research is to develop a solution approach to solve constrained bimatrix games with payoffs of single-valued trapezoidal neutrosophic numbers (SVTNNs). In this approach, the concepts and suitable ranking function of SVTNNs are defined. Hereby, the equilibrium optimal strategies and equilibrium values for both players can be determined by solving the parameterized mathematical programming problems, which are obtained from two novel auxiliary SVTNNs programming problems based on the proposed ranking approach of SVTNNs. Moreover, an application example is examined to verify the effectiveness and superiority of the developed algorithm. Finally, a comparison analysis between the proposed and the existing approaches is conducted to expose the advantages of our work.

scholarly journals On πgβ–Closed Sets and Mappings in Neutrosophic Topological Spaces

2019 ◽  
Vol 8 (12S) ◽  
pp. 505-510
Keyword(s):  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Real Life ◽  
Neutrosophic Set ◽  
Topological Spaces ◽  
Mathematical Tool ◽  
Neutrosophic Sets ◽  
Closed Sets ◽  
New Class ◽  
Closed Mappings

The real life situations always include indeterminacy. The Mathematical tool which is well known to deal with indeterminacy is Neutrosophy. The notion of Neutrosophic set is generally referred as the generalization of Intuitionistic fuzzy set. The Purpose of this article is to define the new class of sets called πgβ-closed sets in Neutrosophic topological spaces. The properties and characterizations of πgβclosed sets are discussed and its relationships with other Neutrosophic sets are studied. Further we define πgβ –closed mappings and πgβ –open sets and some of its properties are touched upon.

Transportation Problem in Neutrosophic Environment

2020 ◽  
pp. 180-212 ◽  
Author(s):  
Jayanta Pratihar ◽  
Ranjan Kumar ◽  
Arindam Dey ◽  
Said Broumi
Keyword(s):  
Linear Programming ◽  
Fuzzy Set ◽  
Transportation Problem ◽  
Intuitionistic Fuzzy Set ◽  
Real Life ◽  
Neutrosophic Set ◽  
Neutrosophic Sets ◽  
North West ◽  
Life Problems ◽  
The Cost

The transportation problem (TP) is popular in operation research due to its versatile applications in real life. Uncertainty exists in most of the real-life problems, which cause it laborious to find the cost (supply/demand) exactly. The fuzzy set is the well-known field for handling the uncertainty but has some limitations. For that reason, in this chapter introduces another set of values called neutrosophic set. It is a generalization of crisp sets, fuzzy set, and intuitionistic fuzzy set, which is handle the uncertain, unpredictable, and insufficient information in real-life problem. Here consider some neutrosophic sets of values for supply, demand, and cell cost. In this chapter, extension of linear programming principle, extension of north west principle, extension of Vogel's approximation method (VAM) principle, and extended principle of MODI method are used for solving the TP with neutrosophic environment called neutrosophic transportation problem (NTP), and these methods are compared using neutrosophic sets of value as well as a combination of neutrosophic and crisp value for analyzing the every real-life uncertain situation.

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 Fault diagnosis based on TOPSIS method with Manhattan distance

2019 ◽  
Vol 11 (3) ◽  
pp. 168781401983327 ◽  
Author(s):  
Wen Jiang ◽  
Meijuan Wang ◽  
Xinyang Deng ◽  
Linfeng Gou
Keyword(s):  
Fault Diagnosis ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Weighted Averaging ◽  
Manhattan Distance ◽  
Uncertain Information ◽  
Ideal Solution ◽  
Solution Approach ◽  
Intuitionistic Fuzzy ◽  
Fault Type

Fault diagnosis is important for the maintenance of machinery equipment. Due to the randomness and fuzziness of fault, the relationship between fault types and their characteristics are complicated. Therefore, the determination of fault type is a challenging part of machinery fault diagnosis with the traditional method. To tackle this problem, a fault diagnosis approach based on the technique for order performance by similarity to ideal solution with Manhattan distance is presented in this article. First, the similarity measure between the fault model and the detection sample is constructed based on the Manhattan distance. Then, the similarity is transformed into intuitionistic fuzzy set and the generated intuitionistic fuzzy set is fused by the intuitionistic fuzzy weighted averaging operator. On this basis, the technique for order performance by similarity to the ideal solution approach is utilized to obtain the final rank to ascertain the fault type. The proposed method can handle an intricate relationship between multiple fault types and their various fault characteristics and better express uncertain information. Finally, a fault diagnosis example of the machine rotor and comparative study are conducted to illustrate the application and the effectiveness of the proposed method.

A New Method for Solving Single- and Multi-Objective Capacitated Solid Minimum Cost Flow Problems under Uncertainty

2016 ◽  
Vol 25 (2) ◽  
pp. 159-183
Author(s):  
Manjot Kaur ◽  
Rehan Sadiq
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Real Life ◽  
Minimum Cost ◽  
Minimum Cost Flow ◽  
Multi Objective ◽  
Flow Problems ◽  
Cost Flow ◽  
Minimum Cost Flow Problems

AbstractIn real life, a person may assume that an object belongs to a set, but it is possible that he (she) is not sure about it. In other words, there may be hesitation or confusion whether an object belongs to a set or not. In fuzzy set theory, there is no means to incorporate such type of hesitation or confusion. A possible solution is to use intuitionistic fuzzy set [K. T. Atanassov, Intutionistic fuzzy sets, Fuzzy Sets Syst.20 (1986), 87–96]. In this article, the concept of unbalanced fully fuzzy multi-objective capacitated solid minimum cost flow (SMCF) problems is generalized by unbalanced intuitionistic fully fuzzy multi-objective capacitated SMCF (CSMCF) problems and new methods are proposed for solving these problems. The main advantage of the proposed methods over the existing methods is that all the unbalanced fully fuzzy single- and multi-objective CSMCF problems that can be solved by the existing methods can also be solved by the proposed method.

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.

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