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This article explores the interconnections among the single-valued neutrosophic grill, single-valued neutrosophic primal and their stratification, uncovering their fundamental characteristics and correlated findings. By introducing the notion of a single-valued neutrosophic primal, a broader framework including the fuzzy primal and intuitionistic fuzzy primal is established. Additionally, the concept of a single-valued neutrosophic open local function for a single-valued neutrosophic topological space is presented. We introduce an operator based on a single-valued neutrosophic primal, illustrating that the single-valued neutrosophic primal topology is finer than the single-valued neutrosophic topology. Lastly, the concept of single-valued neutrosophic open compatibility between the single-valued neutrosophic primal and single-valued neutrosophic topologies is introduced, along with the establishment of several equivalent conditions related to this notion. [ABSTRACT FROM AUTHOR]

Using the strength of a single-valued neutrosophic set (SVNS) with the flexibility of a hesitant fuzzy set (HFS) yields a robust model named the single-valued neutrosophic hesitant fuzzy set (SVNHFS). Due to the ability to utilize three independent indexes (truthness, indeterminacy, and falsity), an SVNHFS is an efficient model for optimization and computational intelligence (CI) as well as an intelligent decision support system (IDSS). Taking advantage of the flexibility of operational parameters in Dombi's t-norm and t-conorm operations, new aggregation operators (AOs) are proposed, which are named the SVN fuzzy Dombi weighted averaging (SVNHFDWA) operator, SVN hesitant fuzzy Dombi ordered weighted averaging (SVNHFDOWA) operator, SVN hesitant fuzzy Dombi hybrid averaging (SVNHFDHWA) operator, SVN hesitant fuzzy Dombi weighted geometric (SVNHFDWG) operator, SVN hesitant fuzzy Dombi ordered weighted geometric (SVNHFDOWG) operator as well as SVN hesitant fuzzy Dombi hybrid weighted geometric (SVNHFDHWG) operator. The efficiency of these AOs is investigated in order to determine the best option using SVN hesitant fuzzy numbers (SVNHFNs) in an IDSS. Additionally, a practical application of SVNHFDWA and SVNHFDWG is also presented to examine symmetrical analysis in the selection of wireless charging station for vehicles. [ABSTRACT FROM AUTHOR]

Professional selection is a significant task for any organization that aims to select the most appropriate candidates to fill well-defined vacancies up. In the recruitment process, various individual characteristics are involved, such as leadership, analytical skills, independent thinking, innovation, stamina and personality, ambiguity and imprecision. It outlines staff contribution and therefore plays a significant part in human resources administration. Additionally, in the era of the Internet of Things and Big Data (IoTBD), professional selection would face several challenges not only to the safe selection and security but also to make wise and prompt decisions especially in the large-scale candidates and criteria from the Cloud. However, the process of professional selection is often led by experience, which contains vague, ambiguous and uncertain decisions. It is therefore necessary to design an efficient decision-making algorithm, which could be further escalated to IoTBD. In this paper, we propose a new hybrid neutrosophic multi criteria decision making (MCDM) framework that employs a collection of neutrosophic analytical network process (ANP), and order preference by similarity to ideal solution (TOPSIS) under bipolar neutrosophic numbers. The MCDM framework is applied for chief executive officer (CEO) selection in a case study at the Elsewedy Electric Group, Egypt. The proposed approach allows us to assemble individual evaluations of the decision makers and therefore perform accurate personnel selection. The outcomes of the proposed method are compared with those of the related works such as weight sum model (WSM), weight product model (WPM), analytical hierarchy process (AHP), multi-objective optimization based on simple ratio analysis (MOORA) and ANP methods to prove and validate the results. [ABSTRACT FROM AUTHOR]

The notion of a neutrosophic positive implicative N-ideal in BCK-algebras is introduced, and several properties are investigated. Relations between a neutrosophic N-ideal and a neutrosophic positive implicative N-ideal are discussed. Characterizations of a neutrosophic positive implicative N-ideal are considered. Conditions for a neutrosophic N-ideal to be a neutrosophic positive implicative N-ideal are provided. An extension property of a neutrosophic positive implicative N-ideal based on the negative indeterminacy membership function is discussed. [ABSTRACT FROM AUTHOR]

This paper is the first study of the neutrosophic triplet loop (NTL) which was originally introduced by Florentin Smarandache. NTL originated from the neutrosophic triplet set X: a collection of triplets (x, neut(x), anti(x)) for an x ∈ X which obeys some axioms (existence of neutral(s) and opposite(s)). NTL can be informally said to be a neutrosophic triplet group that is not associative. That is, a neutrosophic triplet group is an NTL that is associative. In this study, NTL with inverse properties such as: right inverse property (RIP), left inverse property (LIP), right cross inverse property (RCIP), left cross inverse property (LCIP), right weak inverse property (RWIP), left weak inverse property (LWIP), automorphic inverse property (AIP), and anti-automorphic inverse property are introduced and studied. The research was carried out with the following assumptions: the inverse property (IP) is the RIP and LIP, cross inverse property (CIP) is the RCIP and LCIP, weak inverse property (WIP) is the RWIP and LWIP. The algebraic properties of neutrality and opposite in the aforementioned inverse property NTLs were investigated, and they were found to share some properties with the neutrosophic triplet group. The following were established: (1) In a CIPNTL (IPNTL), RIP (RCIP) and LIP (LCIP) were equivalent; (2) In an RIPNTL (LIPNTL), the CIP was equivalent to commutativity; (3) In a commutative NTL, the RIP, LIP, RCIP, and LCIP were found to be equivalent; (4) In an NTL, IP implied anti-automorphic inverse property and WIP, RCIP implied AIP and RWIP, while LCIP implied AIP and LWIP; (5) An NTL has the IP (CIP) if and only if it has the WIP and anti-automorphic inverse property (AIP); (6) A CIPNTL or an IPNTL was a quasigroup; (7) An LWIPNTL (RWIPNTL) was a left (right) quasigroup. The algebraic behaviours of an element, its neutral and opposite in the associator and commutator of a CIPNTL or an IPNTL were investigated. It was shown that (ℤp, *) where x * y = (p - 1)(x + y) for any prime p, is a non-associative commutative CIPNTL and IPNTL. The application of some of these varieties of inverse property NTLs to cryptography is discussed. [ABSTRACT FROM AUTHOR]

Over a period of seven months (August 2017--February 2018), the Special Issue dedicated to "Neutrosophic Information Theory and Applications" by the "Information" journal (ISSN 2078-2489), located in Basel, Switzerland, was a success. The Guest Editors, Prof. Dr. Florentin Smarandache from the University of New Mexico (USA) and Prof. Dr. Jun Ye from the Shaoxing University (China), were happy to select--helped by a team of neutrosophic reviewers from around the world, and by the "Information" journal editors themselves--and publish twelve important neutrosophic papers, authored by 27 authors and coauthors. There were a variety of neutrosophic topics studied and used by the authors and coauthors in Multi-Criteria (or Multi-Attribute and/or Group) Decision-Making, including Cross Entropy-Based MAGDM, Neutrosophic Hesitant Fuzzy Prioritized Aggregation Operators, Biparametric Distance Measures, Pattern Recognition and Medical Diagnosis, Intuitionistic Neutrosophic Graph, NC-TODIM-Based MAGDM, Neutrosophic Cubic Set, VIKOR Method, Neutrosophic Multiple Attribute Group Decision-Making, Competition Graphs, Intuitionistic Neutrosophic Environment, Neutrosophic Commutative N-Ideals, Neutrosophic N-Structures Applied to BCK/BCI-Algebras, Neutrosophic Similarity Score, Weighted Histogram, Robust Mean-Shift Tracking, and Linguistic Neutrosophic Cubic Numbers. [ABSTRACT FROM AUTHOR]

Neutrosophic sets (NSs) handle uncertain information while fuzzy sets (FSs) and intuitionistic fuzzy sets (IFs) fail to handle indeterminate information. Soft set theory, neutrosophic set theory, and rough set theory are different mathematical models for handling uncertainties and they are mutually related. The neutrosophic soft rough set (NSRS) model is a hybrid model by combining neutrosophic soft sets with rough sets. We apply neutrosophic soft rough sets to graphs. In this research paper, we introduce the idea of neutrosophic soft rough graphs (NSRGs) and describe different methods of their construction. We consider the application of NSRG in decision-making problems. In particular, we develop efficient algorithms to solve decision-making problems. [ABSTRACT FROM AUTHOR]

Soft sets (SSs), neutrosophic sets (NSs), and rough sets (RSs) are different mathematical models for handling uncertainties, but they are mutually related. In this research paper, we introduce the notions of soft rough neutrosophic sets (SRNSs) and neutrosophic soft rough sets (NSRSs) as hybrid models for soft computing. We describe a mathematical approach to handle decision-making problems in view of NSRSs. We also present an efficient algorithm of our proposed hybrid model to solve decision-making problems. [ABSTRACT FROM AUTHOR]

A neutrosophic number (a + bI) is a significant mathematical tool to deal with indeterminate and incomplete information which exists generally in real-world problems, where a and bI denote the determinate component and indeterminate component, respectively. We define score functions and accuracy functions for ranking neutrosophic numbers. We then define a cosine function to determine the unknown weight of the criteria. We define the neutrosophic number harmonic mean operators and prove their basic properties. Then, we develop two novel multi-criteria group decision-making (MCGDM) strategies using the proposed aggregation operators. We solve a numerical example to demonstrate the feasibility, applicability, and effectiveness of the two proposed strategies. Sensitivity analysis with the variation of "I" on neutrosophic numbers is performed to demonstrate how the preference ranking order of alternatives is sensitive to the change of "I". The efficiency of the developed strategies is ascertained by comparing the results obtained from the proposed strategies with the results obtained from the existing strategies in the literature. [ABSTRACT FROM AUTHOR]

A rough neutrosophic set model is a hybrid model which deals with vagueness by using the lower and upper approximation spaces. In this research paper, we apply the concept of rough neutrosophic sets to graphs. We introduce rough neutrosophic digraphs and describe methods of their construction. Moreover, we present the concept of self complementary rough neutrosophic digraphs. Finally, we consider an application of rough neutrosophic digraphs in decision-making. [ABSTRACT FROM AUTHOR]

Graph theory has numerous applications in various disciplines, including computer networks, neural networks, expert systems, cluster analysis, and image capturing. Rough neutrosophic set (NS) theory is a hybrid tool for handling uncertain information that exists in real life. In this research paper, we apply the concept of rough NS theory to graphs and present a new kind of graph structure, rough neutrosophic digraphs. We present certain operations, including lexicographic products, strong products, rejection and tensor products on rough neutrosophic digraphs. We investigate some of their properties. We also present an application of a rough neutrosophic digraph in decision-making. [ABSTRACT FROM AUTHOR]

A single-valued neutrosophic set has king power to express uncertainty characterized by indeterminacy, inconsistency and incompleteness. Most of the existing single-valued neutrosophic cross entropy bears an asymmetrical behavior and produces an undefined phenomenon in some situations. In order to deal with these disadvantages, we propose a new cross entropy measure under a single-valued neutrosophic set (SVNS) environment, namely NS-cross entropy, and prove its basic properties. Also we define weighted NS-cross entropy measure and investigate its basic properties. We develop a novel multi-attribute group decision-making (MAGDM) strategy that is free from the drawback of asymmetrical behavior and undefined phenomena. It is capable of dealing with an unknown weight of attributes and an unknown weight of decision-makers. Finally, a numerical example of multi-attribute group decision-making problem of investment potential is solved to show the feasibility, validity and efficiency of the proposed decision-making strategy. [ABSTRACT FROM AUTHOR]

The notion of a neutrosophic commutative N-ideal in BCK-algebras is introduced, and several properties are investigated. Relations between a neutrosophic N-ideal and a neutrosophic commutative N-ideal are discussed. Characterizations of a neutrosophic commutative N-ideal are considered. [ABSTRACT FROM AUTHOR]

Neutrosophic N-structures with applications in BCK/BCI-algebras is discussed. The notions of a neutrosophic N-subalgebra and a (closed) neutrosophic N-ideal in a BCK/BCI-algebra are introduced, and several related properties are investigated. Characterizations of a neutrosophic N-subalgebra and a neutrosophic N-ideal are considered, and relations between a neutrosophic N-subalgebra and a neutrosophic N-ideal are stated. Conditions for a neutrosophic N-ideal to be a closed neutrosophic N-ideal are provided. [ABSTRACT FROM AUTHOR]

Hough transform (HT) is a useful tool for both pattern recognition and image processing communities. In the view of pattern recognition, it can extract unique features for description of various shapes, such as lines, circles, ellipses, and etc. In the view of image processing, a dozen of applications can be handled with HT, such as lane detection for autonomous cars, blood cell detection in microscope images, and so on. As HT is a straight forward shape detector in a given image, its shape detection ability is low in noisy images. To alleviate its weakness on noisy images and improve its shape detection performance, in this paper, we proposed neutrosophic Hough transform (NHT). As it was proved earlier, neutrosophy theory based image processing applications were successful in noisy environments. To this end, the Hough space is initially transferred into the NS domain by calculating the NS membership triples (T, I, and F). An indeterminacy filtering is constructed where the neighborhood information is used in order to remove the indeterminacy in the spatial neighborhood of neutrosophic Hough space. The potential peaks are detected based on thresholding on the neutrosophic Hough space, and these peak locations are then used to detect the lines in the image domain. Extensive experiments on noisy and noise-free images are performed in order to show the efficiency of the proposed NHT algorithm. We also compared our proposed NHT with traditional HT and fuzzy HT methods on variety of images. The obtained results showed the efficiency of the proposed NHT on noisy images. [ABSTRACT FROM AUTHOR]

The notions of the neutrosophic triplet and neutrosophic duplet were introduced by Florentin Smarandache. From the existing research results, the neutrosophic triplets and neutrosophic duplets are completely different from the classical algebra structures. In this paper, we further study neutrosophic duplet sets, neutrosophic duplet semi-groups, and cancellable neutrosophic triplet groups. First, some new properties of neutrosophic duplet semi-groups are funded, and the following important result is proven: there is no finite neutrosophic duplet semi-group. Second, the new concepts of weak neutrosophic duplet, weak neutrosophic duplet set, and weak neutrosophic duplet semi-group are introduced, some examples are given by using the mathematical software MATLAB (MathWorks, Inc., Natick, MA, USA), and the characterizations of cancellable weak neutrosophic duplet semi-groups are established. Third, the cancellable neutrosophic triplet groups are investigated, and the following important result is proven: the concept of cancellable neutrosophic triplet group and group coincide. Finally, the neutrosophic triplets and weak neutrosophic duplets in BCI-algebras are discussed. [ABSTRACT FROM AUTHOR]

A bipolar single-valued neutrosophic (BSVN) graph structure is a generalization of a bipolar fuzzy graph. In this research paper, we present certain concepts of BSVN graph structures. We describe some operations on BSVN graph structures and elaborate on these with examples. Moreover, we investigate some related properties of these operations. [ABSTRACT FROM AUTHOR]

A fundus image is an effective tool for ophthalmologists studying eye diseases. Retinal vessel detection is a significant task in the identification of retinal disease regions. This study presents a retinal vessel detection approach using shearlet transform and indeterminacy filtering. The fundus image's green channel is mapped in the neutrosophic domain via shearlet transform. The neutrosophic domain images are then filtered with an indeterminacy filter to reduce the indeterminacy information. A neural network classifier is employed to identify the pixels whose inputs are the features in neutrosophic images. The proposed approach is tested on two datasets, and a receiver operating characteristic curve and the area under the curve are employed to evaluate experimental results quantitatively. The area under the curve values are 0.9476 and 0.9469 for each dataset respectively, and 0.9439 for both datasets. The comparison with the other algorithms also illustrates that the proposed method yields the highest evaluation measurement value and demonstrates the efficiency and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

Segmentation is considered as an important step in image processing and computer vision applications, which divides an input image into various non-overlapping homogenous regions and helps to interpret the image more conveniently. This paper presents an efficient image segmentation algorithm using neutrosophic graph cut (NGC). An image is presented in neutrosophic set, and an indeterminacy filter is constructed using the indeterminacy value of the input image, which is defined by combining the spatial information and intensity information. The indeterminacy filter reduces the indeterminacy of the spatial and intensity information. A graph is defined on the image and the weight for each pixel is represented using the value after indeterminacy filtering. The segmentation results are obtained using a maximum-flow algorithm on the graph. Numerous experiments have been taken to test its performance, and it is compared with a neutrosophic similarity clustering (NSC) segmentation algorithm and a graph-cut-based algorithm. The results indicate that the proposed NGC approach obtains better performances, both quantitatively and qualitatively. [ABSTRACT FROM AUTHOR]

k-nearest neighbors (k-NN), which is known to be a simple and efficient approach, is a non-parametric supervised classifier. It aims to determine the class label of an unknown sample by its k-nearest neighbors that are stored in a training set. The k-nearest neighbors are determined based on some distance functions. Although k-NN produces successful results, there have been some extensions for improving its precision. The neutrosophic set (NS) defines three memberships namely T, I and F. T, I, and F shows the truth membership degree, the false membership degree, and the indeterminacy membership degree, respectively. In this paper, the NS memberships are adopted to improve the classification performance of the k-NN classifier. A new straightforward k-NN approach is proposed based on NS theory. It calculates the NS memberships based on a supervised neutrosophic c-means (NCM) algorithm. A final belonging membership U is calculated from the NS triples as U = T + I - F. A similar final voting scheme as given in fuzzy k-NN is considered for class label determination. Extensive experiments are conducted to evaluate the proposed method's performance. To this end, several toy and real-world datasets are used. We further compare the proposed method with k-NN, fuzzy k-NN, and two weighted k-NN schemes. The results are encouraging and the improvement is obvious. [ABSTRACT FROM AUTHOR]

Extreme learning machine (ELM) is known as a kind of single-hidden layer feedforward network (SLFN), and has obtained considerable attention within the machine learning community and achieved various real-world applications. It has advantages such as good generalization performance, fast learning speed, and low computational cost. However, the ELM might have problems in the classification of imbalanced data sets. In this paper, we present a novel weighted ELM scheme based on neutrosophic set theory, denoted as neutrosophic weighted extreme learning machine (NWELM), in which neutrosophic c-means (NCM) clustering algorithm is used for the approximation of the output weights of the ELM. We also investigate and compare NWELM with several weighted algorithms. The proposed method demonstrates advantages to compare with the previous studies on benchmarks. [ABSTRACT FROM AUTHOR]

This manuscript aims to propose a new extension of the EDAS method, adapted for usage with single-valued neutrosophic numbers. By using single-valued neutrosophic numbers, the EDAS method can be more efficient for solving complex problems whose solution requires assessment and prediction, because truth- and falsity-membership functions can be used for expressing the level of satisfaction and dissatisfaction about an attitude. In addition, the indeterminacy-membership function can be used to point out the reliability of the information given with truth- and falsity-membership functions. Thus, the proposed extension of the EDAS method allows the use of a smaller number of complex evaluation criteria. The suitability and applicability of the proposed approach are presented through three illustrative examples. [ABSTRACT FROM AUTHOR]

The energy of a graph is defined as the sum of the absolute values of its eigenvalues. Recently, there has been a lot of interest in graph energy research. Previous literature has suggested integrating energy, Laplacian energy, and signless Laplacian energy with single-valued neutrosophic graphs (SVNGs). This integration is used to solve problems that are characterized by indeterminate and inconsistent information. However, when the information is endowed with both positive and negative uncertainty, then bipolar single-valued neutrosophic sets (BSVNs) constitute an appropriate knowledge representation of this framework. A BSVNs is a generalized bipolar fuzzy structure that deals with positive and negative uncertainty in real-life problems with a larger domain. In contrast to the previous study, which directly used truth and indeterminate and false membership, this paper proposes integrating energy, Laplacian energy, and signless Laplacian energy with BSVNs to graph structure considering the positive and negative membership degree to greatly improve decisions in certain problems. Moreover, this paper intends to elaborate on characteristics of eigenvalues, upper and lower bound of energy, Laplacian energy, and signless Laplacian energy. We introduced the concept of a bipolar single-valued neutrosophic graph (BSVNG) for an energy graph and discussed its relevant ideas with the help of examples. Furthermore, the significance of using bipolar concepts over non-bipolar concepts is compared numerically. Finally, the application of energy, Laplacian energy, and signless Laplacian energy in BSVNG are demonstrated in selecting renewable energy sources, while optimal selection is suggested to illustrate the proposed method. This indicates the usefulness and practicality of this proposed approach in real life. [ABSTRACT FROM AUTHOR]

The environment in which the decision-making process takes place is often characterized by uncertainty and vagueness and, because of that, sometimes it is very hard to express the criteria weights with crisp numbers. Therefore, the application of the Grey System Theory, i.e., grey numbers, in this case, is very convenient when it comes to determination of the criteria weights with partially known information. Besides, the criteria weights have a significant role in the multiple criteria decision-making process. Many ordinary multiple criteria decision-making methods are adapted for using grey numbers, and this is the case in this article as well. A new grey extension of the certain multiple criteria decision-making methods for the determination of the criteria weights is proposed. Therefore, the article aims to propose a new extension of the Step-wise Weight Assessment Ratio Analysis (SWARA) and PIvot Pairwise Relative Criteria Importance Assessment (PIPRECIA) methods adapted for group decision-making. In the proposed approach, attitudes of decision-makers are transformed into grey group attitudes, which allows taking advantage of the benefit that grey numbers provide over crisp numbers. The main advantage of the proposed approach in relation to the use of crisp numbers is the ability to conduct different analyses, i.e., considering different scenarios, such as pessimistic, optimistic, and so on. By varying the value of the whitening coefficient, different weights of the criteria can be obtained, and it should be emphasized that this approach gives the same weights as in the case of crisp numbers when the whitening coefficient has a value of 0.5. In addition, in this approach, the grey number was formed based on the median value of collected responses because it better maintains the deviation from the normal distribution of the collected responses. The application of the proposed approach was considered through two numerical illustrations, based on which appropriate conclusions were drawn. [ABSTRACT FROM AUTHOR]

Some decision-making problems, i.e., multi-criteria decision analysis (MCDA) problems, require taking into account the attitudes of a large number of decision-makers and/or respondents. Therefore, an approach to the transformation of crisp ratings, collected from respondents, in grey interval numbers form based on the median of collected scores, i.e., ratings, is considered in this article. In this way, the simplicity of collecting respondents' attitudes using crisp values, i.e., by applying some form of Likert scale, is combined with the advantages that can be achieved by using grey interval numbers. In this way, a grey extension of MCDA methods is obtained. The application of the proposed approach was considered in the example of evaluating the websites of tourism organizations by using several MCDA methods. Additionally, an analysis of the application of the proposed approach in the case of a large number of respondents, done in Python, is presented. The advantages of the proposed method, as well as its possible limitations, are summarized. [ABSTRACT FROM AUTHOR]

Neutrosophy, the study of neutralities, is a new branch of Philosophy that has applications in many different fields of science. Inspired by the idea of Neutrosophy, Smarandache introduced NeutroAlgebraicStructures (or NeutroAlgebras) by allowing the partiality and indeterminacy to be included in the structures' operations and/or axioms. The aim of this paper is to combine the concept of Neutrosophy with hyperstructures theory. In this regard, we introduce NeutroSemihypergroups as well as NeutroHv-Semigroups and study their properties by providing several illustrative examples. [ABSTRACT FROM AUTHOR]

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 I 1 and I 2 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. [ABSTRACT FROM AUTHOR]

In this paper, we develop the notion of the basis for a smooth neutrosophic topology in a more natural way. As a sequel, we define the notion of symmetric neutrosophic quasi-coincident neighborhood systems and prove some interesting results that fit with the classical ones, to establish the consistency of theory developed. Finally, we define and discuss the concept of product topology, in this context, using the definition of basis. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper we study and develop the Neutrosophic Triplet Topology (NTT) that was recently introduced by Sahin et al. Like classical topology, the NTT tells how the elements of a set relate spatially to each other in a more comprehensive way using the idea of Neutrosophic Triplet Sets. This article is important because it opens new ways of research resulting in many applications in different disciplines, such as Biology, Computer Science, Physics, Robotics, Games and Puzzles and Fiber Art etc. Herein we study the application of NTT in Biology. The Neutrosophic Triplet Set (NTS) has a natural symmetric form, since this is a set of symmetric triplets of the form , , where and are opposites of each other, while , being in the middle, is their axis of symmetry. Further on, we obtain in this paper several properties of NTT, like bases, closure and subspace. As an application, we give a multicriteria decision making for the combining effects of certain enzymes on chosen DNA using the developed theory of NTT. [ABSTRACT FROM AUTHOR]

Plithogenic set is an extension of the crisp set, fuzzy set, intuitionistic fuzzy set, and neutrosophic sets, whose elements are characterized by one or more attributes, and each attribute can assume many values. Each attribute has a corresponding degree of appurtenance of the element to the set with respect to the given criteria. In order to obtain a better accuracy and for a more exact exclusion (partial order), a contradiction or dissimilarity degree is defined between each attribute value and the dominant attribute value. In this paper, entropy measures for plithogenic sets have been introduced. The requirements for any function to be an entropy measure of plithogenic sets are outlined in the axiomatic definition of the plithogenic entropy using the axiomatic requirements of neutrosophic entropy. Several new formulae for the entropy measure of plithogenic sets are also introduced. The newly introduced entropy measures are then applied to a multi-attribute decision making problem related to the selection of locations. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The coronavirus (COVID-19) pandemic is putting healthcare systems across the world under unprecedented and increasing pressure according to the World Health Organization (WHO). With the advances in computer algorithms and especially Artificial Intelligence, the detection of this type of virus in the early stages will help in fast recovery and help in releasing the pressure off healthcare systems. In this paper, a GAN with deep transfer learning for coronavirus detection in chest X-ray images is presented. The lack of datasets for COVID-19 especially in chest X-rays images is the main motivation of this scientific study. The main idea is to collect all the possible images for COVID-19 that exists until the writing of this research and use the GAN network to generate more images to help in the detection of this virus from the available X-rays images with the highest accuracy possible. The dataset used in this research was collected from different sources and it is available for researchers to download and use it. The number of images in the collected dataset is 307 images for four different types of classes. The classes are the COVID-19, normal, pneumonia bacterial, and pneumonia virus. Three deep transfer models are selected in this research for investigation. The models are the Alexnet, Googlenet, and Restnet18. Those models are selected for investigation through this research as it contains a small number of layers on their architectures, this will result in reducing the complexity, the consumed memory and the execution time for the proposed model. Three case scenarios are tested through the paper, the first scenario includes four classes from the dataset, while the second scenario includes 3 classes and the third scenario includes two classes. All the scenarios include the COVID-19 class as it is the main target of this research to be detected. In the first scenario, the Googlenet is selected to be the main deep transfer model as it achieves 80.6% in testing accuracy. In the second scenario, the Alexnet is selected to be the main deep transfer model as it achieves 85.2% in testing accuracy, while in the third scenario which includes two classes (COVID-19, and normal), Googlenet is selected to be the main deep transfer model as it achieves 100% in testing accuracy and 99.9% in the validation accuracy. All the performance measurement strengthens the obtained results through the research. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Cyclic associativity can be regarded as a kind of variation symmetry, and cyclic associative groupoid (CA-groupoid) is a generalization of commutative semigroup. In this paper, the various cancellation properties of CA-groupoids, including cancellation, quasi-cancellation and power cancellation, are studied. The relationships among cancellative CA-groupoids, quasi-cancellative CA-groupoids and power cancellative CA-groupoids are found out. Moreover, the concept of variant CA-groupoid is proposed firstly, some examples are presented. It is shown that the structure of variant CA-groupoid is very interesting, and the construction methods and decomposition theorem of variant CA-groupoids are established. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We introduce the notions of neutrosophic extended triplet LA-semihypergroup, neutrosophic extended triplet LA-hypergroup, which can reflect some symmetry of hyperoperation and discuss the relationships among them and regular LA-semihypergroups, LA-hypergroups, regular LA-hypergroups. In particular, we introduce the notion of strong pure neutrosophic extended triplet LA-semihypergroup, get some special properties of it and prove the construction theorem about it under the condition of asymmetry. The examples in this paper are all from Python programs. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A complex neutrosophic set is a useful model to handle indeterminate situations with a periodic nature. This is characterized by truth, indeterminacy, and falsity degrees which are the combination of real-valued amplitude terms and complex-valued phase terms. Hypergraphs are objects that enable us to dig out invisible connections between the underlying structures of complex systems such as those leading to sustainable development. In this paper, we apply the most fruitful concept of complex neutrosophic sets to theory of hypergraphs. We define complex neutrosophic hypergraphs and discuss their certain properties including lower truncation, upper truncation, and transition levels. Furthermore, we define T-related complex neutrosophic hypergraphs and properties of minimal transversals of complex neutrosophic hypergraphs. Finally, we represent the modeling of certain social networks with intersecting communities through the score functions and choice values of complex neutrosophic hypergraphs. We also give a brief comparison of our proposed model with other existing models. [ABSTRACT FROM AUTHOR]

The symmetry of hyperoperation is expressed by hypergroup, more extensive hyperalgebraic structures than hypergroups are studied in this paper. The new concepts of neutrosophic extended triplet semihypergroup (NET- semihypergroup) and neutrosophic extended triplet hypergroup (NET-hypergroup) are firstly introduced, some basic properties are obtained, and the relationships among NET- semihypergroups, regular semihypergroups, NET-hypergroups and regular hypergroups are systematically are investigated. Moreover, pure NET-semihypergroup and pure NET-hypergroup are investigated, and a strucuture theorem of commutative pure NET-semihypergroup is established. Finally, a new notion of weak commutative NET-semihypergroup is proposed, some important examples are obtained by software MATLAB, and the following important result is proved: every pure and weak commutative NET-semihypergroup is a disjoint union of some regular hypergroups which are its subhypergroups. [ABSTRACT FROM AUTHOR]

This paper aims to reveal the structure of idempotents in neutrosophic rings and neutrosophic quadruple rings. First, all idempotents in neutrosophic rings 〈 R ∪ I 〉 are given when R is C , R , Q , Z or Z n . Secondly, the neutrosophic quadruple ring 〈 R ∪ T ∪ I ∪ F 〉 is introduced and all idempotents in neutrosophic quadruple rings 〈 C ∪ T ∪ I ∪ F 〉 , 〈 R ∪ T ∪ I ∪ F 〉 , 〈 Q ∪ T ∪ I ∪ F 〉 , 〈 Z ∪ T ∪ I ∪ F 〉 and 〈 Z n ∪ T ∪ I ∪ F 〉 are also given. Furthermore, the algorithms for solving the idempotents in 〈 Z n ∪ I 〉 and 〈 Z n ∪ T ∪ I ∪ F 〉 for each nonnegative integer n are provided. Lastly, as a general result, if all idempotents in any ring R are known, then the structure of idempotents in neutrosophic ring 〈 R ∪ I 〉 and neutrosophic quadruple ring 〈 R ∪ T ∪ I ∪ F 〉 can be determined. [ABSTRACT FROM AUTHOR]

In this paper authors for the first time introduce the concept of Neutrosophic Quadruple (NQ) vector spaces and Neutrosophic Quadruple linear algebras and study their properties. Most of the properties of vector spaces are true in case of Neutrosophic Quadruple vector spaces. Two vital observations are, all quadruple vector spaces are of dimension four, be it defined over the field of reals R or the field of complex numbers C or the finite field of characteristic p, Z p ; p a prime. Secondly all of them are distinct and none of them satisfy the classical property of finite dimensional vector spaces. So this problem is proposed as a conjecture in the final section. [ABSTRACT FROM AUTHOR]

With the development of the social economy and enlarged volume of information, the application of multiple-attribute decision-making (MADM) has become increasingly complex, uncertain, and obscure. As a further generalization of hesitant fuzzy set (HFS), simplified neutrosophic hesitant fuzzy set (SNHFS) is an efficient tool to process the vague information and contains the ideas of a single-valued neutrosophic hesitant fuzzy set (SVNHFS) and an interval neutrosophic hesitant fuzzy set (INHFS). In this paper, we propose a decision-making approach based on the maximizing deviation method and TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) to solve the MADM problems, in which the attribute weight information is incomplete, and the decision information is expressed in simplified neutrosophic hesitant fuzzy elements. Firstly, we inaugurate an optimization model on the basis of maximizing deviation method, which is useful to determine the attribute weights. Secondly, using the idea of the TOPSIS, we determine the relative closeness coefficient of each alternative and based on which we rank the considered alternatives to select the optimal one(s). Finally, we use a numerical example to show the detailed implementation procedure and effectiveness of our method in solving MADM problems under simplified neutrosophic hesitant fuzzy environment. [ABSTRACT FROM AUTHOR]

Supply chain sustainability has become one of the most attractive decision management topics. There are many articles that have focused on this field presenting many different points of view. This research is centred on the evaluation of supply chain sustainability based on two critical dimensions. The first is the importance of evaluation metrics based on economic, environmental and social aspects, and the second is the degree of difficulty of information gathering. This paper aims to increase the accuracy of the evaluation. The proposed method is a combination of quality function deployment (QFD) with plithogenic aggregation operations. The aggregation operation is applied to aggregate: Firstly, the decision maker's opinions of requirements that are needed to evaluate the supply chain sustainability; secondly, the evaluation metrics based on the requirements; and lastly, the evaluation of information gathering difficulty. To validate the proposed model, this study presented a real world case study of Thailand's sugar industry. The results showed the most preferred and the lowest preferred metrics in order to evaluate the sustainability of the supply chain strategy. [ABSTRACT FROM AUTHOR]

The neutrosophic triplets in neutrosophic rings 〈 Q ∪ I 〉 and 〈 R ∪ I 〉 are investigated in this paper. However, non-trivial neutrosophic triplets are not found in 〈 Z ∪ I 〉 . In the neutrosophic ring of integers Z \ { 0 , 1 } , no element has inverse in Z. It is proved that these rings can contain only three types of neutrosophic triplets, these collections are distinct, and these collections form a torsion free abelian group as triplets under component wise product. However, these collections are not even closed under component wise addition. [ABSTRACT FROM AUTHOR]

In complex rings or complex fields, the notion of imaginary element i with i 2 = − 1 or the complex number i is included, while, in the neutrosophic rings, the indeterminate element I where I 2 = I is included. The neutrosophic ring 〈 R ∪ I 〉 is also a ring generated by R and I under the operations of R. In this paper we obtain a characterization theorem for a semi-idempotent to be in 〈 Z p ∪ I 〉 , the neutrosophic ring of modulo integers, where p a prime. Here, we discuss only about neutrosophic semi-idempotents in these neutrosophic rings. Several interesting properties about them are also derived and some open problems are suggested. [ABSTRACT FROM AUTHOR]