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The concept of q-rung orthopair neutrosophic set is introduced in this paper and fundamental properties of it are studied. Also the ordinary notion of topological space is extended to q-rung orthopair neutrosophic environment, as well as the fundamental concepts of convergence, continuity, compactness and Hausdorff topological space. All these generalizations are illustrated by suitable examples. [ABSTRACT FROM AUTHOR]

We use a neutrosophic set, instead of an intuitionistic fuzzy because the neutrosophic set is more general, and it allows for independent and partial independent components μ (χ) , γ (χ) , ζ (χ), while in an intuitionistic fuzzy set, all components are totally dependent. In this article, we present and demonstrate the concept of neutrosophic invariant subgroups. We delve into the exploration of this notion to establish and study the neutrosophic quotient group. Further, we give the concept of a neutrosophic normal subgroup as a novel concept. [ABSTRACT FROM AUTHOR]

Clustering is a crucial method for deciphering data structure and producing new information. Due to its significance in revealing fundamental connections between the human brain and events, it is essential to utilize clustering for cognitive research. Dealing with noisy data caused by inaccurate synthesis from several sources or misleading data production processes is one of the most intriguing clustering difficulties. Noisy data can lead to incorrect object recognition and inference. This research aims to innovate a novel clustering approach, named Picture-Neutrosophic Trusted Safe Semi-Supervised Fuzzy Clustering (PNTS3FCM), to solve the clustering problem with noisy data using neutral and refusal degrees in the definition of Picture Fuzzy Set (PFS) and Neutrosophic Set (NS). Our contribution is to propose a new optimization model with four essential components: clustering, outlier removal, safe semi-supervised fuzzy clustering and partitioning with labeled and unlabeled data. The effectiveness and flexibility of the proposed technique are estimated and compared with the state-of-art methods, standard Picture fuzzy clustering (FC-PFS) and Confidence-weighted safe semi-supervised clustering (CS3FCM) on benchmark UCI datasets. The experimental results show that our method is better at least 10/15 datasets than the compared methods in terms of clustering quality and computational time. [ABSTRACT FROM AUTHOR]

The traditional neutrosophic clustering method only performs cluster analysis on the data itself, and often ignores the supervision information of data. In order to solve the above problems, a label-guided weighted semi-supervised neutrosophic clustering algorithm is proposed in the paper. On the one hand, the paired constraint information is used to construct the supervision weight coefficient and the distance measurement learning is combined to re-measure the degree of membership of the data and the cluster center; On the other hand, by minimizing the sum of squares of error between membership matrix and label matrix, the purpose of clustering results guided by label information is realized. Experiments on various data sets and comparisons with other clustering algorithms show that the new clustering algorithm can make full use of supervisory information and improve the accuracy of clustering. [ABSTRACT FROM AUTHOR]

An extension of the Integrated Simple Weighted Sum Product (WISP) method is presented in this article, customized for the application of single-valued neutrosophic numbers. The extension is suggested to take advantage that the application of neutrosophic sets provides in terms of solving complex decision-making problems, as well as decision-making problems associated with assessments, prediction uncertainty, imprecision, and so on. In addition, an adapted questionnaire and appropriate linguistic variables are also proposed in the article to enable a simpler and more precise collection of respondents' attitudes using single-valued neutrosophic numbers. An approach for deneutrosophication, i.e. the transformation of a single-valued neutrosophic number into a crisp number is also proposed in the article. Detailed use and characteristics of the presented improvement are shown on an example of the evaluation of rural tourist tours. [ABSTRACT FROM AUTHOR]

Clustering research is an important field in machine learning, pattern recognition and other fields. The neutrosophic set characterizes the data through true membership functions, indeterminate membership functions and false membership functions. Data clustering using neutrosophic set has become one of the current research hotspots. In this paper, first, a new definition of data uncertainty in a neutrosophic set is proposed in this paper based on the density of data. Next, a clustering model based on the uncertainty value of neutrosophic set data is proposed by considering the main cluster (true membership) and the noise cluster (false membership) in the data set. The model takes into account the distance of the data points to the cluster centers and the indeterminacy value of each data point, and then minimizes the proposed cost function by the method of Lagrangian multipliers. The true membership value and false membership value of each data point can be obtained. Finally, the effectiveness of the method is demonstrated by experiments on the various datasets. Experimental results show that the cost function has more accurate membership degree when dealing with boundary points and outliers, and outperforms existing clustering methods on datasets. [ABSTRACT FROM AUTHOR]

Multi-criteria decision making (MCDM) is the technique of selecting the best alternative from multiple alternatives and multiple conditions. The technique for order preference by similarity to an ideal solution (TOPSIS) is a crucial practical technique for ranking and selecting different options by using a distance measure. In this article, we protract the fuzzy TOPSIS technique to neutrosophic fuzzy TOPSIS and prove the accuracy of the method by explaining the MCDM problem with single-valued neutrosophic information and use the method for supplier selection in the production industry. We hope that this article will promote future scientific research on numerous existing issues based on multi-criteria decision making. [ABSTRACT FROM AUTHOR]

Multi-criteria decision-making (MCDM) focuses on coordination, choice and planning issues, including multi-criteria. the neutrosophic soft set cannot handle environments involving multiple attributes. In order to overcome these obstacles, the neutrosophic hypersoft set (NHSS) and Interval Value neutrosophic hypersoft set (IVNHSS) are defined. In this paper, we extend the concept of IVNHSS with basic properties. We also developed some basic operations on IVNHSS such as union, intersection, addition, difference, Truth-favorite, and False-favorite, etc. with their desirable properties. Finally, the necessity and possibility operations on IVNHSS with properties are presented in the following research. [ABSTRACT FROM AUTHOR]

Multi-criteria decision making (MCDM) is the technique of selecting the best alternative from multiple alternatives and multiple conditions. The technique for order preference by similarity to an ideal solution (TOPSIS) is a crucial practical technique for ranking and selecting different options by using a distance measure. In this article, we protract the fuzzy TOPSIS technique to neutrosophic fuzzy TOPSIS, and prove the accuracy of the method by explaining the MCDM problem with single-value neutrosophic information, and use the method for supplier selection in the production industry. We hope that this article will promote future scientific research on numerous existence issues based on multi-criteria decision making. [ABSTRACT FROM AUTHOR]

Raw data are classified using clustering techniques in a reasonable manner to create disjoint clusters. A lot of clustering algorithms based on specific parameters have been proposed to access a high volume of datasets. This paper focuses on cluster analysis based on neutrosophic set implication, i.e., a k-means algorithm with a threshold-based clustering technique. This algorithm addresses the shortcomings of the k-means clustering algorithm by overcoming the limitations of the threshold-based clustering algorithm. To evaluate the validity of the proposed method, several validity measures and validity indices are applied to the Iris dataset (from the University of California, Irvine, Machine Learning Repository) along with k-means and threshold-based clustering algorithms. The proposed method results in more segregated datasets with compacted clusters, thus achieving higher validity indices. The method also eliminates the limitations of threshold-based clustering algorithm and validates measures and respective indices along with k-means and thresholdbased clustering algorithms. [ABSTRACT FROM AUTHOR]

The main purpose of this article is to develop and study the notion of interval-valued neutrosophic subring. Also, we have studied some homomorphic characteristics of interval-valued neutrosophic subring. Again, we have defined the concept of product of two interval-valued neutrosophic subrings and analyzed some of its important properties. Furthermore, we have developed the notion of interval-valued neutrosophic normal subring and studied some of its basic characteristics and homomorphic properties. [ABSTRACT FROM AUTHOR]

Multi-criteria decision making (MCDM) is concerned about coordinating as well as looking after selection as well as planning problems which included multi-criteria. The neutrosophic soft set cannot handle the environment which involved more than one attribute. To overcome those hurdles neutrosophic hypersoft set (NHSS) is defined. In this paper, we proposed the generalized aggregate operators on NHSS such as extended union, extended intersection, OR-operation, ANDoperation, etc. with their properties. Finally, the necessity and possibility operations on NHSS with suitable examples and properties are presented in the following research. [ABSTRACT FROM AUTHOR]

The idea behind the neutrosophic set is we can connect the concept by dynamics of opposite interacts and its neutral that are uncertain and get common parts. Automata theory is beneficial to solve computational complexity problem and also it is an in uential mathematical modeling tool in computer science. Inspired by the concepts of neutrosophic sets and automata theory, here, we are introducing and discussing the algebraic concept of neutrosophic finite automata based on the paper [10]. Generally, composite machines can be achieved by the output of the one machine that will be used as input for another machines. This paper introduced the concept of composite automata under the environment of the neutrosophic set and also examined the box function between the composite neutrosophic finite automata. [ABSTRACT FROM AUTHOR]

In a wide spectrum of mathematical issues, the presence of a fixed point (FP) is equal to the presence of a appropriate map solution. Thus in several fields of math and science, the presence of a fixed point is important. Furthermore, an interesting field of mathematics has been the study of the existence and uniqueness of common fixed point (CFP) and coincidence points of mappings fulfilling the contractive conditions. Therefore, the existence of a FP is of significant importance in several fields of mathematics and science. Results of the FP, coincidence point (CP) contribute conditions under which maps have solutions. The aim of this paper is to explore these conditions (mappings) used to obtain the FP, CP and CFP of a neutrosophic soft set. We study some of these mappings (conditions) such as contraction map, L-lipschitz map, non-expansive map, compatible map, commuting map, weakly commuting map, increasing map, dominating map, dominated map of a neutrosophic soft set. Moreover we introduce some new points like a coincidence point, common fixed point and periodic point of neutrosophic soft mapping. We establish some basic results, particular examples on these mappings and points. In these results we show the link between FP and CP. Moreover we show the importance of mappings for obtaining the FP, CP and CFP of neutrosophic soft mapping. [ABSTRACT FROM AUTHOR]

Neutrophic offsets are neutrosophic sets whose truth-values lie outside the interval [0, 1].Uninorms are aggregation operators defined in fuzzy logic to generalize t-norms and t-conorms. They satisfy the axioms of symmetry, associativity, monotony and the existence of a neutral element. Fuzzy uninorms have been generalized to intuitionistic fuzzy sets, neutrosophic sets, and neutrosophic offsets, which are called offuninorms in the latter case. This paper aims to demonstrate that offsets and offuninorms can be used in digital image processing, especially for image segmentation and edge detection, moreover algorithms and examples are also provided. [ABSTRACT FROM AUTHOR]

A neutrosophic set is a part of neutrosophy that studies the origin, nature and scope of neutralities as well as their interactions with different ideational spectra. In this present paper first we have introduced the concept of a neutrosophic soft set having incomplete data with suitable examples. Then we have tried to explain the consistent and inconsistent association between the parameters. We have introduced few new definitions, namely- consistent association number between the parameters, consistent association degree, inconsistent association number between the parameters and inconsistent association degree to measure these associations. Lastly we have presented a data filling algorithm. An illustrative example is employed to show the feasibility and validity of our algorithm in practical situation. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to make known to a new concept of generalised neutrosophic bipolar vague sets and also defined neutrosophic bipolar vague topology in topological spaces. Also, we introduce generalized neutrosophic bipolar vague closed sets and conferred its properties. [ABSTRACT FROM AUTHOR]

The most widely used technique for solving and optimizing a real-life problem is linear programming (LP), due to its simplicity and efficiency. However, in order to handle the impreciseness in the data, the neutrosophic set theory plays a vital role which makes a simulation of the decision-making process of humans by considering all aspects of decision (i.e., agree, not sure and disagree). By keeping the advantages of it, in the present work, we have introduced the neutrosophic LP models where their parameters are represented with a trapezoidal neutrosophic numbers and presented a technique for solving them. The presented approach has been illustrated with some numerical examples and shows their superiority with the state of the art by comparison. Finally, we conclude that proposed approach is simpler, efficient and capable of solving the LP models as compared to other methods. [ABSTRACT FROM AUTHOR]

In the last decade, characterizing the energy in MANET based on its acceptation, rejection and uncertain part is addressed as one of the major issues by the researchers. An efficient energy routing protocol for MANET is another issue. To resolve these issues current paper focuses on utilizing the properties of neutrosophic technique. The essential idea of the protocol is to choose an energy efficient route with respect to neutrosophic technique. In this neutrosophic set, we have three components such as (T, I, F). Each parameter such as energy and distance is taken from these neutrosophic sets to determine the efficient energy route in MANET. After taking a brief survey about energy efficient routing for MANET using various methods, we are trying to implement the neutrosophic set technique to find the efficient energy route for MANET which provides the better energy route in uncertain situations. The comparative analysis between vague set MANET and neutrosophic MANET for the values of energy functions and distance functions is done by using Matlab and the result is discussed graphically. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), which is a set whose elements are characterized by many attributes' values. An attribute value v has a corresponding (fuzzy, intuitionistic fuzzy, or neutrosophic) degree of appurtenance d(x,v) of the element x, to the set P, with respect to some given criteria. In order to obtain a better accuracy for the plithogenic aggregation operators in the plithogenic set, and for a more exact inclusion (partial order), a (fuzzy, intuitionistic fuzzy, or neutrosophic) contradiction (dissimilarity) degree is defined between each attribute value and the dominant (most important) attribute value. The plithogenic intersection and union are linear combinations of the fuzzy operators tnorm and tconorm, while the plithogenic complement, inclusion (inequality), equality are influenced by the attribute values contradiction (dissimilarity) degrees. This article offers some examples and applications of these new concepts in our everyday life. [ABSTRACT FROM AUTHOR]

In this paper, we first propose the concept of divergence measure on neutrosophic sets. We also provide some formulas for the divergence measure for neutrosophic sets. After that, we investigate the properties of proposed neutrosophic divergence measure. Finally, we also apply these formulas in medical problem and the classification problem. [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]

Neutrosophic set is a generalization of classical set, fuzzy set, and intuitionistic fuzzy set by employing a degree of truth (T), a degree of indeterminacy (I), and a degree of falsehood (F) associated with an element of the dataset. One of the most essential problems is studying set-theoretic operators in order to be applied to practical applications. Developing Matlab toolboxes for computing the operational matrices in neutrosophic environments is essential to gain more widely-used of neutrosophic algorithms. In this paper, we propose some computing procedures in Matlab for neutrosophic operational matrices, especially i) computing the single-valued neutrosophic matrix; ii) determining complement of a single-valued neutrosophic matrix; iii) computing max-min-min and min-maxmax of two single-valued neutrosophic matrices; v) computing power of a single-valued neutrosophic matrix; vi) computing additional operation and subtraction of two single-valued neutrosophic matrices; and ix) computing transpose of a singlevalued neutrosophic matrix. Numerical examples are given to illustrate their applicability. [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]

In this paper, we generalize the definition of Neutrosophic sets and present a method for extending crisp functions on Neutrosophic sets and study some properties of such extended functions. [ABSTRACT FROM AUTHOR]

Neutrosophic set is a new mathematical tool for handling problems involving imprecise, indeterminacy and inconsistent data. Pseudo-BCI algebra is a kind of non-classical logic algebra in close connection with various non-commutative fuzzy logics. Recently, we applied neutrosophic set theory to pseudo-BCI algebras. In this paper, we study neutrosophic filters in pseudo-BCI algebras. The concepts of neutrosophic regular filter, neutrosophic closed filter and fuzzy regular filter in pseudo-BCI algebras are introduced, and some basic properties are discussed. Moreover, the relationships among neutrosophic regular filter, fuzzy filters and anti-grouped neutrosophic filters are presented, and the results are proved: a neutrosophic filter (fuzzy filter) is a neutrosophic regular filter (fuzzy regular filter), if and only if it is both a neutrosophic closed filter (fuzzy closed filter) and an anti-grouped neutrosophic filter (fuzzy anti-grouped filter). [ABSTRACT FROM AUTHOR]