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New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures,...
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New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic & Plithogenic Optimizations

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Computer".

Deadline for manuscript submissions: closed (31 December 2021) | Viewed by 48402

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editors

Prof. Dr. Florentin Smarandache

E-Mail Website
Guest Editor
Department of Mathematics, University of New Mexico, Gallup, NM 87301, USA
Interests: neutrosophic probability; neutrosophic statistics; neutrosophic algebraic structures; plithogenic set; unmatter; superluminal physics; paradoxism; quantum paradoxes
Special Issues, Collections and Topics in MDPI journals
Dr. Yanhui Guo

E-Mail Website
Guest Editor
Department of Data Analytics, University of Illinois Springfield, Springfield, IL 62703, USA
Interests: image processing; medical image processing; pattern recognition; computer vision; data science
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue invites state-of-the-art papers on new topics related of neutrosophic theories and their applications.

The fields of neutrosophic probability and neutrosophic statistics, neutrosophic algebraic structures, neutrosophic optimization, and neutrosophic applications in symmetry are getting more attention.

Prof. Dr. Florentin Smarandache
Dr. Yanhui Guo
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Neutrosophic algebraic structures
  • Neutrosophic triplet algebraic structures
  • Neutrosophic extended triplet algebraic structures
  • Neutrosophic algebraic hyperstructures
  • Neutrosophic triplet algebraic hyperstructures
  • Neutrosophic n-ary algebraic structures
  • Neutrosophic n-ary algebraic hyperstructures
  • Refined neutrosophic algebraic structures
  • Refined neutrosophic algebraic hyperstructures
  • Quadruple neutrosophic algebraic structures
  • Refined quadruple neutrosophic algebraic structures
  • Neutrosophic image processing
  • Neutrosophic image classification
  • Neutrosophic computer vision
  • eutrosophic machine learning
  • Neutrosophic Artificial Intelligence
  • Neutrosophic data analytics
  • Neutrosophic deep learning
  • Neutrosophic symmetry
  • Applications of neutrosophy

Published Papers (21 papers)

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Research

19 pages, 340 KiB  
Article
A Study on Some Properties of Neutrosophic Multi Topological Group
by Bhimraj Basumatary, Nijwm Wary, Dimacha Dwibrang Mwchahary, Ashoke Kumar Brahma, Jwngsar Moshahary, Usha Rani Basumatary and Jili Basumatary
Symmetry 2021, 13(9), 1689; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13091689 - 13 Sep 2021
Cited by 5 | Viewed by 1384
Abstract
In this paper, we studied some properties of the neutrosophic multi topological group. For this, we introduced the definition of semi-open neutrosophic multiset, semi-closed neutrosophic multiset, neutrosophic multi regularly open set, neutrosophic multi regularly closed set, neutrosophic multi continuous mapping, and then studied [...] Read more.
In this paper, we studied some properties of the neutrosophic multi topological group. For this, we introduced the definition of semi-open neutrosophic multiset, semi-closed neutrosophic multiset, neutrosophic multi regularly open set, neutrosophic multi regularly closed set, neutrosophic multi continuous mapping, and then studied the definition of a neutrosophic multi topological group and some of their properties. Moreover, since the concept of the almost topological group is very new, we introduced the definition of neutrosophic multi almost topological group. Finally, for the purpose of symmetry, we used the definition of neutrosophic multi almost continuous mapping to define neutrosophic multi almost topological group and study some of its properties. Full article
(This article belongs to the Special Issue New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic & Plithogenic Optimizations)
18 pages, 322 KiB  
Article
£-Single Valued Extremally Disconnected Ideal Neutrosophic Topological Spaces
by Fahad Alsharari
Symmetry 2021, 13(1), 53; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13010053 - 31 Dec 2020
Cited by 3 | Viewed by 1468
Abstract
This paper aims to mark out new concepts of r-single valued neutrosophic sets, called r-single valued neutrosophic £-closed and £-open sets. The definition of £-single valued neutrosophic irresolute mapping is provided and its characteristic properties are discussed. Moreover, [...] Read more.
This paper aims to mark out new concepts of r-single valued neutrosophic sets, called r-single valued neutrosophic £-closed and £-open sets. The definition of £-single valued neutrosophic irresolute mapping is provided and its characteristic properties are discussed. Moreover, the concepts of £-single valued neutrosophic extremally disconnected and £-single valued neutrosophic normal spaces are established. As a result, a useful implication diagram between the r-single valued neutrosophic ideal open sets is obtained. Finally, some kinds of separation axioms, namely r-single valued neutrosophic ideal-Ri (r-SVNIRi, for short), where i={0,1,2,3}, and r-single valued neutrosophic ideal-Tj (r-SVNITj, for short), where j={1,2,212,3,4}, are introduced. Some of their characterizations, fundamental properties, and the relations between these notions have been studied. Full article
(This article belongs to the Special Issue New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic & Plithogenic Optimizations)
29 pages, 393 KiB  
Article
Topological Structures via Interval-Valued Neutrosophic Crisp Sets
by Dongsik Jo, S. Saleh, Jeong-Gon Lee, Kul Hur and Chen Xueyou
Symmetry 2020, 12(12), 2050; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12122050 - 10 Dec 2020
Cited by 1 | Viewed by 1839
Abstract
In this paper, we introduce the new notion of interval-valued neutrosophic crisp sets providing a tool for approximating undefinable or complex concepts in real world. First, we deal with some of its algebraic structures. We also define an interval-valued neutrosophic crisp (vanishing) point [...] Read more.
In this paper, we introduce the new notion of interval-valued neutrosophic crisp sets providing a tool for approximating undefinable or complex concepts in real world. First, we deal with some of its algebraic structures. We also define an interval-valued neutrosophic crisp (vanishing) point and obtain some of its properties. Next, we define an interval-valued neutrosophic crisp topology, base (subbase), neighborhood, and interior (closure), respectively and investigate some of each property, and give some examples. Finally, we define an interval-valued neutrosophic crisp continuity and quotient topology and study some of each property. Full article
(This article belongs to the Special Issue New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic & Plithogenic Optimizations)
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23 pages, 1080 KiB  
Article
A Novel MCDM Method Based on Plithogenic Hypersoft Sets under Fuzzy Neutrosophic Environment
by Muhammad Rayees Ahmad, Muhammad Saeed, Usman Afzal and Miin-Shen Yang
Symmetry 2020, 12(11), 1855; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12111855 - 10 Nov 2020
Cited by 16 | Viewed by 2386
Abstract
In this paper, we advance the study of plithogenic hypersoft set (PHSS). We present four classifications of PHSS that are based on the number of attributes chosen for application and the nature of alternatives or that of attribute value degree of appurtenance. These [...] Read more.
In this paper, we advance the study of plithogenic hypersoft set (PHSS). We present four classifications of PHSS that are based on the number of attributes chosen for application and the nature of alternatives or that of attribute value degree of appurtenance. These four PHSS classifications cover most of the fuzzy and neutrosophic cases that can have neutrosophic applications in symmetry. We also make explanations with an illustrative example for demonstrating these four classifications. We then propose a novel multi-criteria decision making (MCDM) method that is based on PHSS, as an extension of the technique for order preference by similarity to an ideal solution (TOPSIS). A number of real MCDM problems are complicated with uncertainty that require each selection criteria or attribute to be further subdivided into attribute values and all alternatives to be evaluated separately against each attribute value. The proposed PHSS-based TOPSIS can be used in order to solve these real MCDM problems that are precisely modeled by the concept of PHSS, in which each attribute value has a neutrosophic degree of appurtenance corresponding to each alternative under consideration, in the light of some given criteria. For a real application, a parking spot choice problem is solved by the proposed PHSS-based TOPSIS under fuzzy neutrosophic environment and it is validated by considering two different sets of alternatives along with a comparison with fuzzy TOPSIS in each case. The results are highly encouraging and a MATLAB code of the algorithm of PHSS-based TOPSIS is also complied in order to extend the scope of the work to analyze time series and in developing algorithms for graph theory, machine learning, pattern recognition, and artificial intelligence. Full article
(This article belongs to the Special Issue New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic & Plithogenic Optimizations)
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22 pages, 1889 KiB  
Article
A Novel Framework Using Neutrosophy for Integrated Speech and Text Sentiment Analysis
by Kritika Mishra, Ilanthenral Kandasamy, Vasantha Kandasamy W. B. and Florentin Smarandache
Symmetry 2020, 12(10), 1715; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12101715 - 18 Oct 2020
Cited by 12 | Viewed by 2939
Abstract
With increasing data on the Internet, it is becoming difficult to analyze every bit and make sure it can be used efficiently for all the businesses. One useful technique using Natural Language Processing (NLP) is sentiment analysis. Various algorithms can be used to [...] Read more.
With increasing data on the Internet, it is becoming difficult to analyze every bit and make sure it can be used efficiently for all the businesses. One useful technique using Natural Language Processing (NLP) is sentiment analysis. Various algorithms can be used to classify textual data based on various scales ranging from just positive-negative, positive-neutral-negative to a wide spectrum of emotions. While a lot of work has been done on text, only a lesser amount of research has been done on audio datasets. An audio file contains more features that can be extracted from its amplitude and frequency than a plain text file. The neutrosophic set is symmetric in nature, and similarly refined neutrosophic set that has the refined indeterminacies I1 and I2 in the middle between the extremes Truth T and False F. Neutrosophy which deals with the concept of indeterminacy is another not so explored topic in NLP. Though neutrosophy has been used in sentiment analysis of textual data, it has not been used in speech sentiment analysis. We have proposed a novel framework that performs sentiment analysis on audio files by calculating their Single-Valued Neutrosophic Sets (SVNS) and clustering them into positive-neutral-negative and combines these results with those obtained by performing sentiment analysis on the text files of those audio. Full article
(This article belongs to the Special Issue New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic & Plithogenic Optimizations)
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20 pages, 811 KiB  
Article
Connectedness and Stratification of Single-Valued Neutrosophic Topological Spaces
by Yaser Saber, Fahad Alsharari, Florentin Smarandache and Mohammed Abdel-Sattar
Symmetry 2020, 12(9), 1464; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12091464 - 07 Sep 2020
Cited by 15 | Viewed by 1946
Abstract
This paper aims to introduce the notion of r-single-valued neutrosophic connected sets in single-valued neutrosophic topological spaces, which is considered as a generalization of r-connected sets in Šostak’s sense and r-connected sets in intuitionistic fuzzy topological spaces. In addition, it [...] Read more.
This paper aims to introduce the notion of r-single-valued neutrosophic connected sets in single-valued neutrosophic topological spaces, which is considered as a generalization of r-connected sets in Šostak’s sense and r-connected sets in intuitionistic fuzzy topological spaces. In addition, it introduces the concept of r-single-valued neutrosophic separated and obtains some of its basic properties. It also tries to show that every r-single-valued neutrosophic component in single-valued neutrosophic topological spaces is an r-single-valued neutrosophic component in the stratification of it. Finally, for the purpose of symmetry, it defines the so-called single-valued neutrosophic relations. Full article
(This article belongs to the Special Issue New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic & Plithogenic Optimizations)
18 pages, 9066 KiB  
Article
A New Multi-Sensor Fusion Target Recognition Method Based on Complementarity Analysis and Neutrosophic Set
by Yuming Gong, Zeyu Ma, Meijuan Wang, Xinyang Deng and Wen Jiang
Symmetry 2020, 12(9), 1435; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12091435 - 31 Aug 2020
Cited by 11 | Viewed by 2177
Abstract
To improve the efficiency, accuracy, and intelligence of target detection and recognition, multi-sensor information fusion technology has broad application prospects in many aspects. Compared with single sensor, multi-sensor data contains more target information and effective fusion of multi-source information can improve the accuracy [...] Read more.
To improve the efficiency, accuracy, and intelligence of target detection and recognition, multi-sensor information fusion technology has broad application prospects in many aspects. Compared with single sensor, multi-sensor data contains more target information and effective fusion of multi-source information can improve the accuracy of target recognition. However, the recognition capabilities of different sensors are different during target recognition, and the complementarity between sensors needs to be analyzed during information fusion. This paper proposes a multi-sensor fusion recognition method based on complementarity analysis and neutrosophic set. The proposed method mainly has two parts: complementarity analysis and data fusion. Complementarity analysis applies the trained multi-sensor to extract the features of the verification set into the sensor, and obtain the recognition result of the verification set. Based on recognition result, the multi-sensor complementarity vector is obtained. Then the sensor output the recognition probability and the complementarity vector are used to generate multiple neutrosophic sets. Next, the generated neutrosophic sets are merged within the group through the simplified neutrosophic weighted average (SNWA) operator. Finally, the neutrosophic set is converted into crisp number, and the maximum value is the recognition result. The practicality and effectiveness of the proposed method in this paper are demonstrated through examples. Full article
(This article belongs to the Special Issue New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic & Plithogenic Optimizations)
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14 pages, 845 KiB  
Article
Single-Valued Neutrosophic Set Correlation Coefficient and Its Application in Fault Diagnosis
by Shchur Iryna, Yu Zhong, Wen Jiang, Xinyang Deng and Jie Geng
Symmetry 2020, 12(8), 1371; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12081371 - 17 Aug 2020
Cited by 8 | Viewed by 2139
Abstract
With the increasing automation of mechanical equipment, fault diagnosis becomes more and more important. However, the factors that cause mechanical failures are becoming more and more complex, and the uncertainty and coupling between the factors are getting higher and higher. In order to [...] Read more.
With the increasing automation of mechanical equipment, fault diagnosis becomes more and more important. However, the factors that cause mechanical failures are becoming more and more complex, and the uncertainty and coupling between the factors are getting higher and higher. In order to solve the given problem, this paper proposes a single-valued neutrosophic set ISVNS algorithm for processing of uncertain and inaccurate information in fault diagnosis, which generates neutrosophic set by triangular fuzzy number and introduces the formula of the improved weighted correlation coefficient. Since both the single-valued neutrosophic set data and the ideal neutrosophic set data are considered, the proposed method solves the fault diagnosis problem more effectively. Finally, experiments show that the algorithm can significantly improve the accuracy degree of fault diagnosis, and can better satisfy the diagnostic requirements in practice. Full article
(This article belongs to the Special Issue New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic & Plithogenic Optimizations)
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17 pages, 298 KiB  
Article
Combination of the Single-Valued Neutrosophic Fuzzy Set and the Soft Set with Applications in Decision-Making
by Ahmed Mostafa Khalil, Dunqian Cao, Abdelfatah Azzam, Florentin Smarandache and Wedad R. Alharbi
Symmetry 2020, 12(8), 1361; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12081361 - 14 Aug 2020
Cited by 18 | Viewed by 2999
Abstract
In this article, we propose a novel concept of the single-valued neutrosophic fuzzy soft set by combining the single-valued neutrosophic fuzzy set and the soft set. For possible applications, five kinds of operations (e.g., subset, equal, union, intersection, and complement) on single-valued neutrosophic [...] Read more.
In this article, we propose a novel concept of the single-valued neutrosophic fuzzy soft set by combining the single-valued neutrosophic fuzzy set and the soft set. For possible applications, five kinds of operations (e.g., subset, equal, union, intersection, and complement) on single-valued neutrosophic fuzzy soft sets are presented. Then, several theoretical operations of single-valued neutrosophic fuzzy soft sets are given. In addition, the first type for the fuzzy decision-making based on single-valued neutrosophic fuzzy soft set matrix is constructed. Finally, we present the second type by using the AND operation of the single-valued neutrosophic fuzzy soft set for fuzzy decision-making and clarify its applicability with a numerical example. Full article
(This article belongs to the Special Issue New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic & Plithogenic Optimizations)
19 pages, 499 KiB  
Article
Neutrosophic Modeling of Talcott Parsons’s Action and Decision-Making Applications for It
by Cahit Aslan, Abdullah Kargın and Memet Şahin
Symmetry 2020, 12(7), 1166; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12071166 - 13 Jul 2020
Cited by 11 | Viewed by 2185
Abstract
The grand theory of action of Parsons has an important place in social theories. Furthermore, there are many uncertainties in the theory of Parsons. Classical math logic is often insufficient to explain these uncertainties. In this study, we explain the grand theory of [...] Read more.
The grand theory of action of Parsons has an important place in social theories. Furthermore, there are many uncertainties in the theory of Parsons. Classical math logic is often insufficient to explain these uncertainties. In this study, we explain the grand theory of action of Parsons in neutrosociology for the first time. Thus, we achieve a more effective way of dealing with the uncertainties in the theory of Parsons as in all social theories. We obtain a similarity measure for single-valued neutrosophic numbers. In addition, we show that this measure of similarity satisfies the similarity measure conditions. By making use of this similarity measure, we obtain applications that allow finding the ideal society in the theory of Parsons within the theory of neutrosociology. In addition, we compare the results we obtained with the data in this study with the results of the similarity measures previously defined. Thus, we have checked the appropriateness of the decision-making application that we obtained. Full article
(This article belongs to the Special Issue New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic & Plithogenic Optimizations)
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25 pages, 1154 KiB  
Article
Solution and Interpretation of Neutrosophic Homogeneous Difference Equation
by Abdul Alamin, Sankar Prasad Mondal, Shariful Alam, Ali Ahmadian, Soheil Salahshour and Mehdi Salimi
Symmetry 2020, 12(7), 1091; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12071091 - 01 Jul 2020
Cited by 11 | Viewed by 2130
Abstract
In this manuscript, we focus on the brief study of finding the solution to and analyzingthe homogeneous linear difference equation in a neutrosophic environment, i.e., we interpreted the solution of the homogeneous difference equation with initial information, coefficient and both as a neutrosophic [...] Read more.
In this manuscript, we focus on the brief study of finding the solution to and analyzingthe homogeneous linear difference equation in a neutrosophic environment, i.e., we interpreted the solution of the homogeneous difference equation with initial information, coefficient and both as a neutrosophic number. The idea for solving and analyzing the above using the characterization theorem is demonstrated. The whole theoretical work is followed by numerical examples and an application in actuarial science, which shows the great impact of neutrosophic set theory in mathematical modeling in a discrete system for better understanding the behavior of the system in an elegant manner. It is worthy to mention that symmetry measure of the systems is employed here, which shows important results in neutrosophic arena application in a discrete system. Full article
(This article belongs to the Special Issue New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic & Plithogenic Optimizations)
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11 pages, 247 KiB  
Article
Neutrosophic Components Semigroups and Multiset Neutrosophic Components Semigroups
by Vasantha W. B., Ilanthenral Kandasamy and Florentin Smarandache
Symmetry 2020, 12(5), 818; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12050818 - 16 May 2020
Cited by 8 | Viewed by 1548
Abstract
Neutrosophic components (NC) under addition and product form different algebraic structures over different intervals. In this paper authors for the first time define the usual product and sum operations on NC. Here four different NC are defined using the four different intervals: (0, [...] Read more.
Neutrosophic components (NC) under addition and product form different algebraic structures over different intervals. In this paper authors for the first time define the usual product and sum operations on NC. Here four different NC are defined using the four different intervals: (0, 1), [0, 1), (0, 1] and [0, 1]. In the neutrosophic components we assume the truth value or the false value or the indeterminate value to be from the intervals (0, 1) or [0, 1) or (0, 1] or [0, 1]. All the operations defined on these neutrosophic components on the four intervals are symmetric. In all the four cases the NC collection happens to be a semigroup under product. All of them are torsion free semigroups or weakly torsion free semigroups. The NC defined on the interval [0, 1) happens to be a group under addition modulo 1. Further it is proved the NC defined on the interval [0, 1) is an infinite commutative ring under addition modulo 1 and usual product with infinite number of zero divisors and the ring has no unit element. We define multiset NC semigroup using the four intervals. Finally, we define n-multiplicity multiset NC semigroup for finite n and these two structures are semigroups under + modulo 1 and { M ( S ) , + , × } and { n - M ( S ) , + , × } are NC multiset semirings. Several interesting properties are discussed about these structures. Full article
(This article belongs to the Special Issue New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic & Plithogenic Optimizations)
20 pages, 1424 KiB  
Article
A Kind of Variation Symmetry: Tarski Associative Groupoids (TA-Groupoids) and Tarski Associative Neutrosophic Extended Triplet Groupoids (TA-NET-Groupoids)
by Xiaohong Zhang, Wangtao Yuan, Mingming Chen and Florentin Smarandache
Symmetry 2020, 12(5), 714; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12050714 - 02 May 2020
Cited by 4 | Viewed by 1768
Abstract
The associative law reflects symmetry of operation, and other various variation associative laws reflect some generalized symmetries. In this paper, based on numerous literature and related topics such as function equation, non-associative groupoid and non-associative ring, we have introduced a new concept of [...] Read more.
The associative law reflects symmetry of operation, and other various variation associative laws reflect some generalized symmetries. In this paper, based on numerous literature and related topics such as function equation, non-associative groupoid and non-associative ring, we have introduced a new concept of Tarski associative groupoid (or transposition associative groupoid (TA-groupoid)), presented extensive examples, obtained basic properties and structural characteristics, and discussed the relationships among few non-associative groupoids. Moreover, we proposed a new concept of Tarski associative neutrosophic extended triplet groupoid (TA-NET-groupoid) and analyzed related properties. Finally, the following important result is proved: every TA-NET-groupoid is a disjoint union of some groups which are its subgroups. Full article
(This article belongs to the Special Issue New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic & Plithogenic Optimizations)
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20 pages, 845 KiB  
Article
A Novel Dynamic Multi-Criteria Decision Making Method Based on Generalized Dynamic Interval-Valued Neutrosophic Set
by Nguyen Tho Thong, Florentin Smarandache, Nguyen Dinh Hoa, Le Hoang Son, Luong Thi Hong Lan, Cu Nguyen Giap, Dao The Son and Hoang Viet Long
Symmetry 2020, 12(4), 618; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12040618 - 14 Apr 2020
Cited by 14 | Viewed by 2711
Abstract
Dynamic multi-criteria decision-making (DMCDM) models have many meaningful applications in real life in which solving indeterminacy of information in DMCDMs strengthens the potential application of DMCDM. This study introduces an extension of dynamic internal-valued neutrosophic sets namely generalized dynamic internal-valued neutrosophic sets. Based [...] Read more.
Dynamic multi-criteria decision-making (DMCDM) models have many meaningful applications in real life in which solving indeterminacy of information in DMCDMs strengthens the potential application of DMCDM. This study introduces an extension of dynamic internal-valued neutrosophic sets namely generalized dynamic internal-valued neutrosophic sets. Based on this extension, we develop some operators and a TOPSIS method to deal with the change of both criteria, alternatives, and decision-makers by time. In addition, this study also applies the proposal model to a real application that facilitates ranking students according to attitude-skill-knowledge evaluation model. This application not only illustrates the correctness of the proposed model but also introduces its high potential appliance in the education domain. Full article
(This article belongs to the Special Issue New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic & Plithogenic Optimizations)
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14 pages, 415 KiB  
Article
Triangular Single Valued Neutrosophic Data Envelopment Analysis: Application to Hospital Performance Measurement
by Wei Yang, Lulu Cai, Seyed Ahmad Edalatpanah and Florentin Smarandache
Symmetry 2020, 12(4), 588; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12040588 - 08 Apr 2020
Cited by 49 | Viewed by 3173
Abstract
The foremost broadly utilized strategy for the valuation of the overall performance of a set of identical decision-making units (DMUs) that use analogous sources to yield related outputs is data envelopment analysis (DEA). However, the witnessed values of the symmetry or asymmetry of [...] Read more.
The foremost broadly utilized strategy for the valuation of the overall performance of a set of identical decision-making units (DMUs) that use analogous sources to yield related outputs is data envelopment analysis (DEA). However, the witnessed values of the symmetry or asymmetry of different types of information in real-world applications are sometimes inaccurate, ambiguous, inadequate, and inconsistent, so overlooking these conditions may lead to erroneous decision-making. Neutrosophic set theory can handle these occasions of data and makes an imitation of the decision-making procedure with the aid of thinking about all perspectives of the decision. In this paper, we introduce a model of DEA in the context of neutrosophic sets and sketch an innovative process to solve it. Furthermore, we deal with the problem of healthcare system evaluation with inconsistent, indeterminate, and incomplete information using the new model. The triangular single-valued neutrosophic numbers are also employed to deal with the mentioned data, and the proposed method is utilized in the assessment of 13 hospitals of Tehran University of Medical Sciences of Iran. The results exhibit the usefulness of the suggested approach and point out that the model has practical outcomes for decision-makers. Full article
(This article belongs to the Special Issue New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic & Plithogenic Optimizations)
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15 pages, 899 KiB  
Article
The Generalized Neutrosophic Cubic Aggregation Operators and Their Application to Multi-Expert Decision-Making Method
by Majid Khan, Muhammad Gulistan, Mumtaz Ali and Wathek Chammam
Symmetry 2020, 12(4), 496; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12040496 - 27 Mar 2020
Cited by 10 | Viewed by 2181
Abstract
In the modern world, the computation of vague data is a challenging job. Different theories are presented to deal with such situations. Amongst them, fuzzy set theory and its extensions produced remarkable results. Samrandache extended the theory to a new horizon with the [...] Read more.
In the modern world, the computation of vague data is a challenging job. Different theories are presented to deal with such situations. Amongst them, fuzzy set theory and its extensions produced remarkable results. Samrandache extended the theory to a new horizon with the neutrosophic set (NS), which was further extended to interval neutrosophic set (INS). Neutrosophic cubic set (NCS) is the generalized version of NS and INS. This characteristic makes it an exceptional choice to deal with vague and imprecise data. Aggregation operators are key features of decision-making theory. In recent times several aggregation operators were defined in NCS. The intent of this paper is to generalize these aggregation operators by presenting neutrosophic cubic generalized unified aggregation (NCGUA) and neutrosophic cubic quasi-generalized unified aggregation (NCQGUA) operators. The accuracy and precision are a vital tool to minimize the potential threat in decision making. Generally, in decision making methods, alternatives and criteria are considered to evaluate the better outcome. However, sometimes the decision making environment has more components to express the problem completely. These components are named as the state of nature corresponding to each criterion. This complex frame of work is dealt with by presenting the multi-expert decision-making method (MEDMM). Full article
(This article belongs to the Special Issue New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic & Plithogenic Optimizations)
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17 pages, 2632 KiB  
Article
Study of Imaginative Play in Children Using Single-Valued Refined Neutrosophic Sets
by Vasantha W. B., Ilanthenral Kandasamy, Florentin Smarandache, Vinayak Devvrat and Shivam Ghildiyal
Symmetry 2020, 12(3), 402; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12030402 - 04 Mar 2020
Cited by 8 | Viewed by 2741
Abstract
This paper introduces Single Valued Refined Neutrosophic Set (SVRNS) which is a generalized version of the neutrosophic set. It consists of six membership functions based on imaginary and indeterminate aspect and hence, is more sensitive to real-world problems. Membership functions defined as complex [...] Read more.
This paper introduces Single Valued Refined Neutrosophic Set (SVRNS) which is a generalized version of the neutrosophic set. It consists of six membership functions based on imaginary and indeterminate aspect and hence, is more sensitive to real-world problems. Membership functions defined as complex (imaginary), a falsity tending towards complex and truth tending towards complex are used to handle the imaginary concept in addition to existing memberships in the Single Valued Neutrosophic Set (SVNS). Several properties of this set were also discussed. The study of imaginative pretend play of children in the age group from 1 to 10 years was taken for analysis using SVRNS, since it is a field which has an ample number of imaginary aspects involved. SVRNS will be more apt in representing these data when compared to other neutrosophic sets. Machine learning algorithms such as K-means, parallel axes coordinate, etc., were applied and visualized for a real-world application concerned with child psychology. The proposed algorithms help in analysing the mental abilities of a child on the basis of imaginative play. These algorithms aid in establishing a correlation between several determinants of imaginative play and a child’s mental abilities, and thus help in drawing logical conclusions based on it. A brief comparison of the several algorithms used is also provided. Full article
(This article belongs to the Special Issue New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic & Plithogenic Optimizations)
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15 pages, 1068 KiB  
Article
A Hybrid Approach of Interval Neutrosophic Vague Sets and DEMATEL with New Linguistic Variable
by Ashraf Al-Quran, Hazwani Hashim and Lazim Abdullah
Symmetry 2020, 12(2), 275; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12020275 - 12 Feb 2020
Cited by 18 | Viewed by 2566
Abstract
Nowadays, real world problems are complicated because they deal with uncertainty and incomplete information. Obviously, such problems cannot be solved by a single technique because of the multiple perspectives that may arise. Currently, the combination of DEMATEL and the neutrosophic environment are still [...] Read more.
Nowadays, real world problems are complicated because they deal with uncertainty and incomplete information. Obviously, such problems cannot be solved by a single technique because of the multiple perspectives that may arise. Currently, the combination of DEMATEL and the neutrosophic environment are still new and not fully explored. Previous studies of DEMATEL and this neutrosophic environment have been carried out based on numerical values to represent a new scale. Until now, little importance has been placed on the development of a linguistic variable for DEMATEL. It is important to develop a new linguistic variable to represent opinions based on human experience. Therefore, to fill this gap, the concept of Interval Neutrosophic Vague Sets (INVS) has been extended to the linguistic variable that can be used in the decision-making process. The INVS is useful tool to deal with uncertainty and incomplete information. Additionally, the advantages of the linguistic variable of INVS allows the greater range of value for membership functions. This study proposes a new framework for INVS and DEMATEL. In addition, a case study on the quality of hospital service has been evaluated to demonstrate the proposed approach. Finally, a comparative analysis to check the feasibility of the proposed method is presented. It demonstrates that different methods produce different relations and levels of importance. This is due to the inclusion of the INVS linguistic variable. Full article
(This article belongs to the Special Issue New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic & Plithogenic Optimizations)
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13 pages, 278 KiB  
Article
Single-Valued Neutrosophic Linguistic-Induced Aggregation Distance Measures and Their Application in Investment Multiple Attribute Group Decision Making
by Guansheng Yu, Shouzhen Zeng and Chonghui Zhang
Symmetry 2020, 12(2), 207; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12020207 - 02 Feb 2020
Cited by 8 | Viewed by 1625
Abstract
This paper studied the single-valued neutrosophic linguistic distance measures based on the induced aggregation method. Firstly, we proposed a single-valued neutrosophic linguistic-induced ordered weighted averaging distance (SVNLIOWAD) measure, which is a new extension of the existing distance measures based on the induced aggregation [...] Read more.
This paper studied the single-valued neutrosophic linguistic distance measures based on the induced aggregation method. Firstly, we proposed a single-valued neutrosophic linguistic-induced ordered weighted averaging distance (SVNLIOWAD) measure, which is a new extension of the existing distance measures based on the induced aggregation view. Then, based on the proposed SVNLIOWAD, a novel induced distance for single-valued neutrosophic linguistic sets, namely the single-valued neutrosophic linguistic weighted induced ordered weighted averaging distance (SVNLWIOWAD), was developed to eliminate the defects of the existing methods. The relationship between the two proposed distance measures was also explored. A multiple attribute group decision making (MAGDM) model was further presented based on the proposed SVNLWIOWAD measure. Finally, a numerical example concerning an investment selection problem was provided to demonstrate the usefulness of the proposed method under a single-valued neutrosophic linguistic environment and, then, a comparison analysis was carried out to verify the flexibility and effectiveness of the proposed work. Full article
(This article belongs to the Special Issue New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic & Plithogenic Optimizations)
21 pages, 329 KiB  
Article
On Single-Valued Neutrosophic Ideals in Šostak Sense
by Yaser Saber, Fahad Alsharari and Florentin Smarandache
Symmetry 2020, 12(2), 193; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12020193 - 25 Jan 2020
Cited by 20 | Viewed by 2384
Abstract
Neutrosophy is a recent section of philosophy. It was initiated in 1980 by Smarandache. It was presented as the study of origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. In this paper, we introduce the notion [...] Read more.
Neutrosophy is a recent section of philosophy. It was initiated in 1980 by Smarandache. It was presented as the study of origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. In this paper, we introduce the notion of single-valued neutrosophic ideals sets in Šostak’s sense, which is considered as a generalization of fuzzy ideals in Šostak’s sense and intuitionistic fuzzy ideals. The concept of single-valued neutrosophic ideal open local function is also introduced for a single-valued neutrosophic topological space. The basic structure, especially a basis for such generated single-valued neutrosophic topologies and several relations between different single-valued neutrosophic ideals and single-valued neutrosophic topologies, are also studied here. Finally, for the purpose of symmetry, we also define the so-called single-valued neutrosophic relations. Full article
(This article belongs to the Special Issue New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic & Plithogenic Optimizations)
13 pages, 744 KiB  
Article
New Results on Neutrosophic Extended Triplet Groups Equipped with a Partial Order
by Xin Zhou, Ping Li, Florentin Smarandache and Ahmed Mostafa Khalil
Symmetry 2019, 11(12), 1514; https://0-doi-org.brum.beds.ac.uk/10.3390/sym11121514 - 13 Dec 2019
Cited by 7 | Viewed by 2102
Abstract
Neutrosophic extended triplet group (NETG) is a novel algebra structure and it is different from the classical group. The major concern of this paper is to present the concept of a partially ordered neutrosophic extended triplet group (po-NETG), which is a NETG equipped [...] Read more.
Neutrosophic extended triplet group (NETG) is a novel algebra structure and it is different from the classical group. The major concern of this paper is to present the concept of a partially ordered neutrosophic extended triplet group (po-NETG), which is a NETG equipped with a partial order that relates to its multiplicative operation, and consider properties and structure features of po-NETGs. Firstly, in a po-NETG, we propose the concepts of the positive cone and negative cone, and investigate the structure features of them. Secondly, we study the specificity of the positive cone in a partially ordered weak commutative neutrosophic extended triplet group (po-WCNETG). Finally, we introduce the concept of a po-NETG homomorphism between two po-NETGs, construct a po-NETG on a quotient set by providing a multiplication and a partial order, then we discuss some fundamental properties of them. Full article
(This article belongs to the Special Issue New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic & Plithogenic Optimizations)
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