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1
Ye, Jun. "Clustering Methods Using Distance-Based Similarity Measures of Single-Valued Neutrosophic Sets." Journal of Intelligent Systems 23, no. 4 (2014): 379–89. http://dx.doi.org/10.1515/jisys-2013-0091.
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AbstractClustering plays an important role in data mining, pattern recognition, and machine learning. Single-valued neutrosophic sets (SVNSs) are useful means to describe and handle indeterminate and inconsistent information that fuzzy sets and intuitionistic fuzzy sets cannot describe and deal with. To cluster the data represented by single-valued neutrosophic information, this article proposes single-valued neutrosophic clustering methods based on similarity measures between SVNSs. First, we define a generalized distance measure between SVNSs and propose two distance-based similarity measures of SVNSs. Then, we present a clustering algorithm based on the similarity measures of SVNSs to cluster single-valued neutrosophic data. Finally, an illustrative example is given to demonstrate the application and effectiveness of the developed clustering methods.
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Ye, Jun. "Single-Valued Neutrosophic Minimum Spanning Tree and Its Clustering Method." Journal of Intelligent Systems 23, no. 3 (2014): 311–24. http://dx.doi.org/10.1515/jisys-2013-0075.
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AbstractClustering plays an important role in data mining, pattern recognition, and machine learning. Then, single-valued neutrosophic sets (SVNSs) are a useful means to describe and handle indeterminate and inconsistent information, which fuzzy sets and intuitionistic fuzzy sets cannot describe and deal with. To cluster the data represented by single-value neutrosophic information, the article proposes a single-valued neutrosophic minimum spanning tree (SVNMST) clustering algorithm. Firstly, we defined a generalized distance measure between SVNSs. Then, we present an SVNMST clustering algorithm for clustering single-value neutrosophic data based on the generalized distance measure of SVNSs. Finally, two illustrative examples are given to demonstrate the application and effectiveness of the developed approach.
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Ye, Jun. "Improved Cross Entropy Measures of Single Valued Neutrosophic Sets and Interval Neutrosophic Sets and Their Multicriteria Decision Making Methods." Cybernetics and Information Technologies 15, no. 4 (2015): 13–26. http://dx.doi.org/10.1515/cait-2015-0051.
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Abstract Due to some drawbacks of the cross entropy between Single Valued Neutrosophic Sets (SVNSs) in dealing with decision-making problems, the existing single valued neutrosophic cross entropy indicates an asymmetrical phenomenon or may produce an undefined (unmeaningful) phenomenon in some situations. In order to overcome these disadvantages, this paper proposes an improved cross entropy measure of SVNSs and investigates its properties, and then extends it to a cross entropy measure between interval neutrosophic sets (INSs). Furthermore, the cross entropy measures are applied to multicriteria decision making problems with single valued neutrosophic information and interval neutrosophic information. In decision making methods, through the weighted cross entropy measure between each alternative and the the ideal alternative, one can obtain the ranking order of all alternatives and the best one. The decision-making methods using the proposed cross entropy measures can efficiently deal with decision making problems with incomplete, indeterminate and inconsistent information which exist usually in real situations. Finally, two illustrative examples are provided to demonstrate the application and efficiency of the developed decision making approaches under single valued neutrosophic and interval neutrosophic environments.
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Tian, Chao, Wen Yu Zhang, Shuai Zhang, and Juan Juan Peng. "An Extended Single-Valued Neutrosophic Projection-Based Qualitative Flexible Multi-Criteria Decision-Making Method." Mathematics 7, no. 1 (2019): 39. http://dx.doi.org/10.3390/math7010039.
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With respect to multi-criteria decision-making (MCDM) problems in which the criteria denote the form of single-valued neutrosophic sets (SVNSs), and the weight information is also fully unknown, a novel MCDM method based on qualitative flexible multiple criteria (QUALIFLEX) is developed. Firstly, the improved cosine measure of the included angle between two SVNSs is defined. Then, the improved single-valued neutrosophic projection is developed, and the corresponding improved single-valued neutrosophic bidirectional projection and single-valued neutrosophic bidirectional projection difference are investigated. Moreover, the partial ordering relation of SVNSs is developed. Secondly, an extended QUALIFLEX method based on an improved single-valued neutrosophic projection measure is proposed to handle MCDM problems in which the weights of criteria are completely unknown. Finally, an example for selection of a green supplier, as well as a performance comparison analysis, are provided to demonstrate the effectiveness of the proposed method.
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Fan, Changxing. "Correlation Coefficients of Refined-Single Valued Neutrosophic Sets and Their Applications in Multiple Attribute Decision-Making." Journal of Advanced Computational Intelligence and Intelligent Informatics 23, no. 3 (2019): 421–26. http://dx.doi.org/10.20965/jaciii.2019.p0421.
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The paper presents the correlation coefficient of refined-single valued neutrosophic sets (Refined-SVNSs) based on the extension of the correlation of single valued neutrosophic sets (SVNSs), and then a decision making method is proposed by the use of the weighted correlation coefficient of Refined-SVNSs. Through the weighted correlation coefficient between the ideal alternative and each alternative, we can rank all alternatives and the best one of all alternatives can be easily identified as well. Finally, to prove this decision making method proposed in this paper is useful to deal with the actual application, we use an example to illustrate it.
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Zhang, Huanying, Fei Wang, and Yushui Geng. "Multi-Criteria Decision-Making Method Based on Single-Valued Neutrosophic Schweizer–Sklar Muirhead Mean Aggregation Operators." Symmetry 11, no. 2 (2019): 152. http://dx.doi.org/10.3390/sym11020152.
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Schweizer–Sklar (SS) operation can make information aggregation more flexible, and the Muirhead mean (MM) operator can take into account the correlation between inputs by a variable parameter. Because traditional MM is only available for real numbers and single-valued neutrosophic set (SVNS) can better express incomplete and uncertain information in decision systems, in this paper, we applied MM operators to single-valued neutrosophic sets (SVNSs) and presented two new MM aggregation operators with the SS operation, i.e., a single-valued neutrosophic SS Muirhead mean (SVNSSMM) operator and a weighted single-valued neutrosophic SS MM (WSVNSSMM) operator. We listed some properties of them and some particular cases about various parameter values. We also proposed the multi-criteria decision-making method based on the WSVNSSMM operator in SVNS. At last, we illustrated the feasibility of this method using a numerical example of company investment.
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Ali, Mehboob, Zahid Hussain, and Miin-Shen Yang. "Hausdorff Distance and Similarity Measures for Single-Valued Neutrosophic Sets with Application in Multi-Criteria Decision Making." Electronics 12, no. 1 (2022): 201. http://dx.doi.org/10.3390/electronics12010201.
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Hausdorff distance is one of the important distance measures to study the degree of dissimilarity between two sets that had been used in various fields under fuzzy environments. Among those, the framework of single-valued neutrosophic sets (SVNSs) is the one that has more potential to explain uncertain, inconsistent and indeterminate information in a comprehensive way. And so, Hausdorff distance for SVNSs is important. Thus, we propose two novel schemes to calculate the Hausdorff distance and its corresponding similarity measures (SMs) for SVNSs. In doing so, we firstly develop the two forms of Hausdorff distance between SVNSs based on the definition of Hausdorff metric between two sets. We then use these new distance measures to construct several SMs for SVNSs. Some mathematical theorems regarding the proposed Hausdorff distances for SVNSs are also proven to strengthen its theoretical properties. In order to show the exact calculation behavior and distance measurement mechanism of our proposed methods in accordance with the decorum of Hausdorff metric, we utilize an intuitive numerical example that demonstrate the novelty and practicality of our proposed measures. Furthermore, we develop a multi-criteria decision making (MCDM) method under single-valued neutrosophic environment using the proposed SMs based on our defined Hausdorff distance measures, called as a single-valued neutrosophic MCDM (SVN-MCDM) method. In this connection, we employ our proposed SMs to compute the degree of similarity of each option with the ideal choice to identify the best alternative as well as to perform an overall ranking of the alternatives under study. We then apply our proposed SVN-MCDM scheme to solve two real world problems of MCDM under single-valued neutrosophic environment to show its effectiveness and application.
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Jiang, Wen, Zihan Zhang, and Xinyang Deng. "Multi-Attribute Decision Making Method Based on Aggregated Neutrosophic Set." Symmetry 11, no. 2 (2019): 267. http://dx.doi.org/10.3390/sym11020267.
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Multi-attribute decision-making refers to the decision-making problem of selecting the optimal alternative or sorting the scheme when considering multiple attributes, which is widely used in engineering design, economy, management and military, etc. But in real application, the attribute information of many objects is often inaccurate or uncertain, so it is very important for us to find a useful and efficient method to solve the problem. Neutrosophic set is proposed from philosophical point of view to handle inaccurate information efficiently, and a single-valued neutrosophic set (SVNS) is a special case of neutrosophic set, which is widely used in actual application fields. In this paper, a new method based on single-valued neutrosophic sets aggregation to solve multi-attribute decision making problem is proposed. Firstly, the neutrosophic decision matrix is obtained by expert assessment, a score function of single-valued neutrosophic sets (SVNSs) is defined to obtain the positive ideal solution (PIS) and the negative ideal solution (NIS). Then all alternatives are aggregated based on TOPSIS method to make decision. Finally numerical examples are given to verify the feasibility and rationality of the method.
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Liu, Donghai, Guangyan Liu, and Zaiming Liu. "Some Similarity Measures of Neutrosophic Sets Based on the Euclidean Distance and Their Application in Medical Diagnosis." Computational and Mathematical Methods in Medicine 2018 (November 28, 2018): 1–9. http://dx.doi.org/10.1155/2018/7325938.
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Similarity measure is an important tool in multiple criteria decision-making problems, which can be used to measure the difference between the alternatives. In this paper, some new similarity measures of single-valued neutrosophic sets (SVNSs) and interval-valued neutrosophic sets (IVNSs) are defined based on the Euclidean distance measure, respectively, and the proposed similarity measures satisfy the axiom of the similarity measure. Furthermore, we apply the proposed similarity measures to medical diagnosis decision problem; the numerical example is used to illustrate the feasibility and effectiveness of the proposed similarity measures of SVNSs and IVNSs, which are then compared to other existing similarity measures.
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Sharma, Sonam, and Surender Singh. "Single - valued neutrosophic Yager power aggregation operators and its application to MCDM." Yugoslav Journal of Operations Research, no. 00 (2025): 4. https://doi.org/10.2298/yjor240715004s.
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The notion of Single-valued neutrosophic sets (SVNSs) being a generalization of fuzzy sets, intuitionistic fuzzy sets and picture fuzzy sets enhances implications of these methods in various interdisciplinary problems. Aggregation operator is a prevalent tool for unifying the data from various sources and applied to solve the problems of decision-making. In this article, the Yager's operations and power averaging operator are utilized to formulate and investigate some single-valued neutrosophic Yager power operators, i.e., single-valued neutrosophic Yager power weighted averaging (SVNYPWA) operators, single-valued neutrosophic Yager power order weighted averaging (SVNYPOWA) operator, single-valued neutrosophic Yager power weighted geometric averaging (SVNYPWGA) operator, and single-valued neutrosophic Yager power ordered weighted geometric averaging (SVNYPOWGA). Some important properties of the suggested operators are discussed. Furthermore, SVNYPWA and SVNYPWGA operators in the SVN environment are applied to solve the multi-criteria decision-making (MCDM) problem for selecting a suitable road construction company. Also, the proposed method has been verified using the multi-attributive border approximation area comparison (MABAC) method. Finally, a comparative analysis has been done, to establish the advantage of the proposed approach over the existing methods.
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Shakir, Taif Khalid, and Ahmed N. Al Masri. "Single Valued Neutrosophic Set for Selection of Water Supply in Intelligent Farming." International Journal of Advances in Applied Computational Intelligence 2, no. 2 (2022): 37–44. http://dx.doi.org/10.54216/ijaaci.020204.
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One of the most difficult problems in the water business is the oversight and strategic planning of basin-based water supplies. Governments are concerned with ensuring equitable growth by addressing issues like water scarcity, improving agricultural products, and supporting nutritional health. The primary contribution of this research is the introduction of a methodology for assessing agricultural water delivery systems that allow for collaboration among all stakeholders. The managing the water supply is a MADM. Multi-attribute decision-making (MADM) issues, which are characterized by inadequacy and ambiguity, may be efficiently described using single-valued neutrosophic sets (SVNSs). Several strategies, including the PROMETHEE strategy, are offered to address the MADM issue in SVNSs. The PROMETHEE technique ranks potential solutions by first having the decision maker pick a preferred function for every criterion. In this paper, the SVNS is integrated with the PROMETHEE method for water supply management in smart farming.
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Ali, Ahmed M. "A Multi-Criteria Decision-Making Approach for Piston Material Selection under Single-Valued Trapezoidal Neutrosophic Sets." Neutrosophic and Information Fusion 2, no. 1 (2023): 23–43. http://dx.doi.org/10.54216/nif.020102.
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It is one of the most difficult and time-consuming processes to develop and pick an acceptable material for the piston material that has a variety of attributes. Component failure is often caused by inappropriate material at some stage throughout the functioning process. In light of this, the piston material selection is performed in this article. The goal of this work is to found a technique for selecting the material of the piston for a new design engine by using the multi-criteria decision-making (MCDM) approach to find a solution to the issue of choosing the material for the piston. The purpose of the TOPSIS method is to pick the appropriate material for a piston based on the application it will be used in. The TOPSIS technique is stretched under neutrosophic sets to solve the vague and uncertain information in this process. The single-valued trapezoidal neutrosophic sets (SVTNSs) are used in this paper. The SVTNSs is a mixed with the trapezoidal neutrosophic sets (TNSs) and the single-valued neutrosophic sets (SVNSs). There are nine criteria and three alternatives used in this paper. The illustrative example is carried out The sensitivity analysis and comparative study are carried out to display the robustness and efficiency of the suggested model.
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Said, Shimaa, Mahmoud M. Ibrahim, and Mahmoud M. Ismail. "An Integrated Multi-Criteria Decision-Making Approach for Identification and Ranking Solar Drying Barriers under Single-Valued Triangular Neutrosophic Sets (SVTNSs)." Neutrosophic and Information Fusion 2, no. 1 (2023): 35–49. http://dx.doi.org/10.54216/nif.020103.
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Solar dryers utilized in agriculture for the drying of food and crops are also utilized for drying operations in industrial settings. They have the potential to be shown as a very helpful tool in terms of the management of energy saving. It not only helps conserve energy, but it also helps save a lot of time, consumes less space, makes the procedure more effective, enhances the standard of the product, and safeguards the surroundings. Due to the many associated potential barriers, the acceptance of solar dryers has not yet reached a benchmark, although this was an expectation. In this body of work, a methodical framework that makes use of the MCDM tools has been proposed to identify and rank several obstacles in descending order of importance.The AHP can identify both quantitative and qualitative aspects by using comparison matrices to assign weights to them and rank them in order of importance. The AHP technique is used to calculate the weights and relationship of the solar drying barrier. To account for the lack of clarity and coherence in the data that is available in the actual world, we tested the suggested model in a neutrosophic set. We used the single-valued triangular neutrosophic sets (SVTNSs). SVTNSs are a type of neutrosophic set, integrated into triangular neutrosophic sets and SVNSs. The application of applying the SVNSs-AHP is performed.
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Ren, Shapu. "Multicriteria Decision-Making Method Under a Single Valued Neutrosophic Environment." International Journal of Intelligent Information Technologies 13, no. 4 (2017): 23–37. http://dx.doi.org/10.4018/ijiit.2017100102.
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A single valued neutrosophic set (SVNS) is a subclass of neutrosophic sets, which generalizes fuzzy sets, interval valued fuzzy set, and intuitionistic fuzzy set. It can be used to easily express incomplete, indeterminate and inconsistent information. This paper introduces the Dice similarity measure of single valued neutrosophic numbers (SVNNs) for ranking SVNNs and a single valued neutrosophic prioritized weighted geometric (SVNPWG) operator for aggregating single valued neutrosophic information. Based on the SVNPWG operator and the Dice similarity measure for SVNNs, a multicriteria decision-making method with different priority levels in the criteria is established in which the evaluation values of alternatives with respective to criteria are represented in the form of SVNNs. The ranking order of alternatives is performed through the Dice measure and the best one(s) can be determined as well. Finally, an illustrative example shows the application of the proposed method.
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Zhou, Xiaoyan, Mingwei Lin, and Weiwei Wang. "Statistical correlation coefficients for single-valued neutrosophic sets and their applications in medical diagnosis." AIMS Mathematics 8, no. 7 (2023): 16340–59. http://dx.doi.org/10.3934/math.2023837.
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<abstract> <p>The concept of single-valued neutrosophic sets (SVNSs) is considered as an attractive tool for dealing with highly ambiguous and uncertain information. The correlation coefficient of SVNSs acts as an important measure in the single-valued neutrosophic set theory and it has been applied in various fields, such as the pattern recognition, medical diagnosis, decision-making and also clustering analysis. To alleviate the weakness of the existing correlation coefficients, a novel statistical correlation coefficient is put forward to measure the degree of correlation between two SVNSs. This statistical correlation coefficient is developed based on the variance and covariance of SVNSs and its value is between −1 and 1. When solving the multicriteria decision making problems, the criteria show different weight values. To consider the weight information of multiple criteria, the weighted statistical correlation coefficient is developed for SVNSs. Afterwards, two numerical examples are given to show the effectiveness of the proposed statistical correlation coefficient in the pattern recognition, which can accurately classify unknown patterns into known patterns. Finally, the feasibility and practicability of the proposed correlation coefficient formula are illustrated by a practical multiple attribute decision making problem of traditional Chinese medicine diagnosis. The comparative results show that the proposed correlation coefficient formula is rational and effective.</p> </abstract>
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Ren, Haiping, Shixiao Xiao, and Hui Zhou. "A Chi-square Distance-based Similarity Measure of Single-valued Neutrosophic Set and Applications." International Journal of Computers Communications & Control 14, no. 1 (2019): 78–89. http://dx.doi.org/10.15837/ijccc.2019.1.3430.
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The aim of this paper is to propose a new similarity measure of singlevalued neutrosophic sets (SVNSs). The idea of the construction of the new similarity measure comes from Chi-square distance measure, which is an important measure in the applications of image analysis and statistical inference. Numerical examples are provided to show the superiority of the proposed similarity measure comparing with the existing similarity measures of SVNSs. A weighted similarity is also put forward based on the proposed similarity. Some examples are given to show the effectiveness and practicality of the proposed similarity in pattern recognition, medical diagnosis and multi-attribute decision making problems under single-valued neutrosophic environment.
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Zhang, Yingxin, Ting Li, Fan Yang, and Lei Qiao. "Modeling Uncertainties Through Employing Single-Valued Neutrosophic Multi-Attribute Decision-Making." International Journal of Decision Support System Technology 16, no. 1 (2025): 1–20. https://doi.org/10.4018/ijdsst.366207.
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The significance of performance evaluation for venture capital in small and medium-sized technology startups lies in helping investors understand the effectiveness of their capital investment and assess the company's growth potential and market prospects. The performance evaluation of risk investment in small and medium-sized high-technology venture enterprises involves the application of MADM. In this study, we explore the generalized weighted geometric Bonferroni mean (GWGBM) operator for MADM, utilizing single-valued neutrosophic sets (SVNSs) to handle uncertainty and vagueness in MADM processes. The study begins by introducing the single-valued neutrosophic number GWGBM (SVNNGWGBM) operator, which is specifically designed to aggregate decision-making criteria under SVNSs. Following this, MADM methods based on the SVNNGWGBM are developed and discussed. To demonstrate the practical application of this approach, an illustrative case study is provided, focusing on the performance evaluation of risk investment in small and medium-sized high-technology venture enterprises.
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Khan, Mohsin, Le Hoang Son, Mumtaz Ali, Hoang Thi Minh Chau, Nguyen Thi Nhu Na, and Florentin Smarandache. "Systematic Review of Decision Making Algorithms in Extended Neutrosophic Sets." Symmetry 10, no. 8 (2018): 314. http://dx.doi.org/10.3390/sym10080314.
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The Neutrosophic set (NS) has grasped concentration by its ability for handling indeterminate, uncertain, incomplete, and inconsistent information encountered in daily life. Recently, there have been various extensions of the NS, such as single valued neutrosophic sets (SVNSs), Interval neutrosophic sets (INSs), bipolar neutrosophic sets (BNSs), Refined Neutrosophic Sets (RNSs), and triangular fuzzy number neutrosophic set (TFNNs). This paper contains an extended overview of the concept of NS as well as several instances and extensions of this model that have been introduced in the last decade, and have had a significant impact in literature. Theoretical and mathematical properties of NS and their counterparts are discussed in this paper as well. Neutrosophic-set-driven decision making algorithms are also overviewed in detail.
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Chaudhary, Gopal, Amena .., and J. A. Lobo Marques. "Sentiment Analysis from Social Media Tweets Using Single-Valued Neutrosophic Sets and Fuzzy Sets." Journal of Neutrosophic and Fuzzy Systems 5, no. 2 (2023): 51–59. http://dx.doi.org/10.54216/jnfs.050205.
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In the last ten years, exciting work at the intersection of several academic disciplines has been done in the areas of view mining and sentiment analysis. The sheer amount of social media text that is now accessible for sentiment analysis has expanded by a factor of multiples with the development of social media networks, resulting in the creation of a formidable corpus. An examination of the sentiments included within tweets has been performed to measure the general public's perspective on breaking news, as well as a variety of laws, regulations, individuals, and political movements. In the assessment of the sentiment of Twitter data, fuzzy logic (FL) was used, but neutrosophy, which makes consideration the idea of indeterminacy, was not applied. Fuzzy logic (FL) was utilized since neutrosophy was not utilized to analyze tweets. In this study, we present the idea of single valued-neutrosophic sets (SVNSs) that may have positive, indeterminate, and negative memberships. We used the sanders dataset to apply the proposed methodology. The fuzzy set (FS) has the indeterminacy value opposite the NS. FS has two only degrees, truth, and falsity. This paper shows the difference between the NS and FS in the sample of data.
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Wu, Bin. "SVNN-Com-LogTODIM Technique for Risk Assessment of Battery Safety Operation in Energy Storage Power Stations Based on Single-Valued Neutrosophic MAGDM." International Journal of Decision Support System Technology 16, no. 1 (2024): 1–17. http://dx.doi.org/10.4018/ijdsst.361717.
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As the world transitions toward a more sustainable energy future, energy storage power plants play an increasingly crucial role in integrating renewable energy sources into the grid. However, ensuring the safety of battery operations in these facilities remains a critical concern. Assessing battery safety operations (BSO) in energy storage power stations is complex multiple-attribute group decision-making (MAGDM) task. Recently, the logarithmic TODIM (LogTODIM) technique was introduced to handle MAGDM challenges. Single-valued neutrosophic sets (SVNSs) have also emerged as tool for managing fuzzy data in BSO risk assessments. This study proposes the single-valued neutrosophic number combined LogTODIM (SVNN-Com-LogTODIM) technique to address MAGDM within the framework of SVNSs. A numerical case study on BSO risk assessment in energy storage power stations is provided to demonstrate the SVNN-Com-LogTODIM technique through comparative analysis.
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Al-Sharqi, Faisal Al, Ashraf Al Al-Quran, Badria A. Ali Yousif, et al. "Group decision-making algorithm based on AOs settings for single-valued neutrosophic fuzzy soft expert environment." International Journal of Neutrosophic Science 23, no. 3 (2024): 97–110. http://dx.doi.org/10.54216/ijns.230309.
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The incorporation of expert opinions and handling of data uncertainty are addressed by Al-Alkhazaleh through the introduction of a soft expert set. This extension of the soft set framework aims to enhance the analysis and decision-making processes by incorporating expert knowledge. On the other hand, the utilization of single neutrosophic sets (SVNSs) and fuzzy sets (FSs) has been introduced as models to effectively handle uncertain data. In this work, the authors propose a model that combines the essential characteristics of fuzzy sets (FSs) and single neutrosophic sets (SVNSs) within expert systems. Consequently, this model aims to offer decision-makers increased flexibility when interpreting uncertain information, empowering them in the decision-making process. From a scientific point of view, the process of evaluating this high-performance SVNFSES disappears. Therefore, in this paper, we initiated a new approach known as single-valued neutrosophic fuzzy soft expert sets (SVNFSESs) as a new development in a fuzzy soft computing environment. We investigate some fundamental operations on SVNFSESS along with their basic properties. Also, we investigate AND and OR operations between two SVNFSESS as well as several numerical examples to clarify the above fundamental operations. Finally, we have given an aggregation operator (AO) for SVNFSESs to construct a new algorithm to demonstrate the method’s effectiveness in handling some real-life applications.
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Zhao, Xia. "Enhanced EDAS framework for quality evaluation of cultural industry development under the background of digital economy based on SVNNCSM and SVNNCFSM techniques." International Journal of Knowledge-Based and Intelligent Engineering Systems 29, no. 2 (2024): 278–93. https://doi.org/10.1177/13272314241295918.
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With the advent of digital economy era, the high-quality development of cultural industry has received people's attention. How to take advantage of the favorable opportunities of rapid development of the digital economy to further promote the innovative development of cultural industry is an important problem that needs to be solved in development process of Chinese cultural industries. The quality evaluation of cultural industry development in the context of the digital economy is MAGDM. The single-valued neutrosophic sets (SVNSs) is useful tool to cope with uncertain information during the quality evaluation of cultural industry development in the context of the digital economy. In this paper, the single-valued neutrosophic number EDAS (SVNN-EDAS) model based on single-valued neutrosophic number cosine similarity measure (SVNNCSM) and SVNN cosine function similarity measure (SVNNCFSM) is formed to cope with the MAGDM. The CRITIC model is administrated to obtain the weight numbers in light with the SVNNCSM and SVNNCFSM under SVNSs. Finally, numerical example and different comparative analysis for quality evaluation of cultural industry development in the context of the digital economy is administrated to validate SVNN-EDAS model. The main contributions of this study are formed: (1) the CRITIC model is formed to obtain the weight numbers in light with SVNNCSM and SVNNCFSM; (2) the SVNN-EDAS model is formed in light with SVNNCSM and SVNNCFSM under SVNNs; (3) Finally, numerical example and comparative analysis for quality evaluation of cultural industry development in the context of the digital economy is administrated to validate SVNN-EDAS model.
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Singh, Surender, and Sonam Sharma. "Divergence Measures and Aggregation Operators for Single-Valued Neutrosophic Sets with Applications in Decision-Making Problems." Neutrosophic Systems with Applications 20 (August 1, 2024): 27–44. http://dx.doi.org/10.61356/j.nswa.2024.20281.
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Single-valued neutrosophic sets (SVNSs) facilitate the representation of uncertain information more extensively than conventional methods. The study of divergence measures of SVNSs is important due to their applications in different areas like multi-criteria decision-making (MCDM), pattern recognition, cluster analysis, machine learning, etc., In this paper, we introduce a divergence measure for SVNSs. The suggested divergence measure is applied to cluster analysis for the classification of imprecise data. For establishing the reasonability and advantage of the suggested divergence measure in a clustering problem over the existing measures, a comparative assessment is also presented. Furthermore, we introduce, an inferior ratio method for handling the MCDM problem in the SVN environment. The consistency of the results of the suggested method with existing approaches also supports the credibility of its practical usage.
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Peng, Tian, Zhang, Song, and Wang. "Single-Valued Neutrosophic Power Shapley Choquet Average Operators and Their Applications to Multi-Criteria Decision-Making." Mathematics 7, no. 11 (2019): 1081. http://dx.doi.org/10.3390/math7111081.
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Single-valued neutrosophic sets (SVNSs), which involve in truth-membership, indeterminacy-membership and falsity-membership, play a significant role in describing the decision-makers’ preference information. In this study, a single-valued neutrosophic multi-criteria decision-making (MCDM) approach is developed based on Shapley fuzzy measures and power aggregation operator that takes a correlative relationship among criteria into account and also simultaneously reduces the effects of abnormal preference information. Firstly, two aggregation operators, namely, generalized weighted single-valued neutrosophic power Shapley Choquet average (GWSVNPSCA) operator and generalized weighted single-valued neutrosophic power Shapley Choquet geometric (GWSVNPSCG) operator, are accordingly defined, and the corresponding properties are discussed as well. Secondly, based on the proposed aggregation operators, an integrated MCDM approach is proposed to effectively solve single-valued neutrosophic problems where the weight information is incompletely known. A programming model is constructed to obtain the optimal Shapley fuzzy measure. Next, the proposed operators are utilized to aggregate the decision-makers’ preference information. Finally, a theoretical example with tourism attraction selection is provided to examine the efficacy of the developed approach, in which the results is found reasonable and credible.
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Abeer Eisa, M. Fattouh, and A. A. ElShabshery. "Single-Valued Neutrosophic Sets Based Score Function and WASPAS Method for Plant Location Selection Problem." Journal of Advanced Research in Applied Sciences and Engineering Technology 41, no. 2 (2024): 139–51. http://dx.doi.org/10.37934/araset.41.2.139151.
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In the context of single-valued neutrosophic sets (SVNSs), where the weights of the criteria are unknown, this work seeks to provide an integrated technique based on Entropy and Weighted Aggregate Sum Product Assessment (WASPAS) methodologies. A numerical case study (the plant site selection issue) is used to establish precise values for the criteria. We initially "fuzzify" the decision matrix before transforming it into an SVNS- decision matrix. The SVNS entropy weight technique is used to assign weights to each criterion. The scoring function is used by a tweaked version of the WASPAS algorithm to choose the optimal solution. The subject under study has also been applied to other MCDM methods, such as the more prevalent VIKOR and MOORA procedures. The SVNS-VIKOR technique has also been applied to the issue at hand. Using the same illustrative scenario, this study evaluates the strengths and weaknesses of several methods for verifying the accuracy of previously published data. The usefulness and efficiency of the used strategy are highlighted by the comparison study. When applied to real-world situations, the suggested method shines because it yields reliable findings even though the underlying data is plagued with issues such as uncertainty, imprecision, indeterminacy, and inconsistency.
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admin, admin, Ashraf Al Al-Quran, Hamiden Abd El Wahed Khalifa, et al. "Orthogonal distance and similarity for single-valued neutrosophic fuzzy soft expert environment and its application in decision-making." International Journal of Neutrosophic Science 23, no. 4 (2024): 08–22. http://dx.doi.org/10.54216/ijns.230401.
Full textAbstract:
A soft expert set(SES) is a concept that combines elements of soft sets and expert systems. It aims to incorporate expert knowledge and uncertainty-handling capabilities into the analysis and decision-making processes. On the other hand, the idea of single neutrosophic sets (SVNSs) and fuzzy sets (FSs) are imported models for handling the uncertainty data. In this work, the authors combine the critical features of FSs and SVNSs under expert systems in one model. Accordingly, this model worked to provide decision-makers with more flexibility in the process of interpreting uncertain information. From a scientific point of view, the process of evaluating this high-performance SVNFSES disappears. Therefore, in this paper, we initiated a new approach known as single-valued neutrosophic fuzzy soft expert sets (SVNFSESs) as a new development in a fuzzy soft computing environment. We investigate some fundamental operations on SVNFSESS along with their basic properties. Also, we investigate AND and OR operations between two SVNFSESS as well as several numerical examples to clarify the above fundamental operations. Finally, we have given an Orthogonal Distance and Similarity for SVNFSESs to construct a new algorithm to demonstrate the method’s effectiveness in handling some real-life applications.
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Abdullah, Lazim, Zheeching Ong, and Shalela Mohd Mahali. "Single-Valued Neutrosophic DEMATEL for Segregating Types of Criteria: A Case of Subcontractors’ Selection." Journal of Mathematics 2021 (April 15, 2021): 1–12. http://dx.doi.org/10.1155/2021/6636029.
Full textAbstract:
The decision-making trial and evaluation laboratory (DEMATEL) has been used to solve numerous multicriteria decision-making (MCDM) problems, where real numbers are utilised in defining linguistic variables. Although the DEMATEL has shown its success in solving many decision-making problems, researchers have not fully understood how the DEMATEL works on non-real-number linguistic variables. Recent discovery of single-valued neutrosophic sets (SVNSs) can offer a new method to solve decision-making problems, where three memberships of SVNSs are used to define experts’ linguistic judgment. This paper aims to propose a novel MCDM method, where SVNSs and the DEMATEL are fully utilised. Different from the DEMATEL, which directly utilises real numbers, this proposed method introduces SVNSs to better deal with truth, indeterminacy, and falsity in solving MCDM problem. As an application of the proposed method, subcontractors’ selection problem is investigated using the proposed method, where four types of criteria are developed. A group of experts were invited to provide opinions and linguistic judgment regarding the degree of influence between criteria of subcontractors’ selection. The linguistic evaluations defined in SVNSs were computed using the eight-step procedures of the proposed method. Based on the degree of influence, the computational results successfully segregated all ten criteria into four types, in which two to three criteria are grouped in each type. The results also suggest that “Experience” and “Quality” are the most influential criteria in subcontractors’ selection. The segregation based on degree of influence would be greatly significant for the practical implementation of the subcontractors’ selection.
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Faisal, Faisal, Ashraf Al Al-Quran, Agaeb Mahal Alanzi, et al. "Group decision-making based on distance measures settings for single-valued neutrosophic fuzzy soft expert environment." International Journal of Neutrosophic Science 23, no. 4 (2024): 88–103. http://dx.doi.org/10.54216/ijns.230407.
Full textAbstract:
A soft expert set is a concept that combines elements of soft sets and expert systems. It aims to incorporate expert knowledge and uncertainty-handling capabilities into the analysis and decision-making processes. On the other hand, the idea of single neutrosophic sets (SVNSs) and fuzzy sets (FSs) are imported models for handling the uncertainty data. In this work, the authors combine the critical features of FSs and SVNSs under expert systems in one model. Accordingly, this model worked to provide decision-makers with more flexibility in the process of interpreting uncertain information. From a scientific point of view, the process of evaluating this high-performance SVNFSES disappears. Therefore, in this paper, we initiated a new approach known as single-valued neutrosophic fuzzy soft expert sets (SVNFSESs) as a new development in a fuzzy soft computing environment. We investigate some fundamental operations on SVNFSESS along with their basic properties. Also, we investigate AND and OR operations between two SVNFSESS as well as several numerical examples to clarify the above fundamental operations. Finally, we have given distance measures (DM) between two SVNFSESs to construct a new algorithm that is used to demonstrate the effectiveness of the method in handling some real-life applications.
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Wang, Jingqian, and Xiaohong Zhang. "Two Types of Single Valued Neutrosophic Covering Rough Sets and an Application to Decision Making." Symmetry 10, no. 12 (2018): 710. http://dx.doi.org/10.3390/sym10120710.
Full textAbstract:
In this paper, to combine single valued neutrosophic sets (SVNSs) with covering-based rough sets, we propose two types of single valued neutrosophic (SVN) covering rough set models. Furthermore, a corresponding application to the problem of decision making is presented. Firstly, the notion of SVN β -covering approximation space is proposed, and some concepts and properties in it are investigated. Secondly, based on SVN β -covering approximation spaces, two types of SVN covering rough set models are proposed. Then, some properties and the matrix representations of the newly defined SVN covering approximation operators are investigated. Finally, we propose a novel method to decision making (DM) problems based on one of the SVN covering rough set models. Moreover, the proposed DM method is compared with other methods in an example.
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Ran, Hui. "MABAC method for multiple attribute group decision making under single-valued neutrosophic sets and applications to performance evaluation of sustainable microfinance groups lending." PLOS ONE 18, no. 1 (2023): e0280239. http://dx.doi.org/10.1371/journal.pone.0280239.
Full textAbstract:
As an important supplement to my country’s financial institutions, micro-loan companies serve "agriculture, rural areas and farmers", small and micro enterprises, and individuals, to a certain extent, alleviating the financing difficulties of such groups and regulating private finance. However, micro-loan companies only lend but do not deposit. In the process of lending, due to inadequate risk management, the risk problem has become increasingly prominent. With the continuous growth of the loan amount of rural credit and the continuous increase of microfinance groups lending customers, it faces certain problems in its risk management, which increases the risks of the company in all aspects. The performance evaluation of sustainable microfinance groups lending is a classical MAGDM issues. In such paper, the Hamming distances of single-valued neutrosophic sets (SVNSs) and maximizing deviation method (MDM) is used to obtain the attribute weights and the single-valued neutrosophic numbers MABAC(SVNN-MABAC) method is structured for MAGDM under SVNSs. Finally, an example about performance evaluation of sustainable microfinance groups lending and some comparative decision analysis are given to proof the SVNN-MABAC.
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Al-Qudah, Yousef Al. "A robust framework for the decision-making based on single-valued neutrosophic fuzzy soft expert setting." International Journal of Neutrosophic Science 23, no. 2 (2024): 195–210. http://dx.doi.org/10.54216/ijns.230216.
Full textAbstract:
A soft expert set is widely used as a tool to solve and model the problems appearing in computer science and operations research. It aims to incorporate expert knowledge and uncertainty-handling capabilities into the analysis and decision-making processes. On the other hand, the idea of single neutrosophic sets (SVNSs) and fuzzy sets (FSs) are imported models for handling the uncertainty data. In this work, the authors combine the critical features of FSs and SVNSs under expert systems in one model. Accordingly, this model worked to provide decision-makers with more flexibility in the process of interpreting uncertain information. From a scientific point of view, the process of evaluating this high-performance SVNFSES disappears. Therefore, in this paper, we initiated a new approach known as single-valued neutrosophic fuzzy soft expert sets (SVNFSESs) as a new development in a fuzzy soft computing environment. We investigate some fundamental operations on SVNFSESS along with their basic properties. Also, we investigate AND and OR operations between two SVNFSESS as well as several numerical examples to clarify the above fundamental operations. Finally, we have given distance measures (DM) between two SVNFSESs to construct a new algorithm that is used to demonstrate the effectiveness of the method in handling some real-life applications.
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Xu, Dongsheng, Xiaolan Wei, Hui Ding, and Hongqiong Bin. "A New Method Based on PROMETHEE and TODIM for Multi-Attribute Decision-Making with Single-Valued Neutrosophic Sets." Mathematics 8, no. 10 (2020): 1816. http://dx.doi.org/10.3390/math8101816.
Full textAbstract:
Single-valued neutrosophic sets (SVNSs) can effectively describe the multi-attribute decision-making (MADM) problems which are characterized by incompleteness and uncertainty. Aiming at the MADM problem of SVNSs, a series of methods are proposed to solve the problem, such as the TODIM and PROMETHEE methods. The main idea of the TODIM method is to establish a relative superiority function of scheme relative to other schemes based on the value function of prospect theory, and the ranking of alternatives is determined according to the obtained superiority. In the PROMETHEE method, the decision maker selects the preference function for each attribute according to their preference, and then calculates the priority index, inflow, outflow and net flow according to the difference of the attribute values of scheme, so as to determine the ranking of alternatives. In this paper, a new method based on PROMETHEE and TODIM is proposed to solve the MADM problem under the single-valued neutrosophic environment. Based on the calculation formula of inflow and outflow in PROMETHEE method, and the calculation formula of overall dominance in the TODIM method, a new integrated formula is obtained.
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Yang, Xiaoping, and Yefei Liu. "An Integrated Taxonomy Method Using Single-Valued Neutrosophic Number MAGDM for Evaluating the Physical Education Teaching Quality in Colleges and Universities." Mathematical Problems in Engineering 2022 (August 25, 2022): 1–11. http://dx.doi.org/10.1155/2022/2795788.
Full textAbstract:
Before the advent of the new era, my country has completed the popularization of higher education, and the country has gradually begun to pay attention to the quality of higher education. Under the background of Healthy China, the quality of physical education teaching in colleges and universities has become a hot topic of social concern. The quality of physical education teaching in colleges and universities directly determines the quality of physical education talents. A reasonable, complete, and scientific evaluation system of physical education teaching quality in colleges and universities is an effective measure to improve the quality of physical education teaching and the training of physical education talents. The physical education teaching quality evaluation in colleges and universities is frequently viewed as the multiple attribute group decision-making (MAGDM) issue. In such paper, taxonomy method is designed for solving the MAGDM under single-valued neutrosophic sets (SVNSs). First, the score function of SVNSs and criteria importance through intercriteria correlation (CRITIC) method is used to derive the attribute weights. Second, then, the optimal choice is obtained through calculating the smallest single-valued neutrosophic number development attribute values from the single-valued neutrosophic number positive ideal solution (SVNNPIS). Finally, a numerical example for physical education teaching quality evaluation in colleges and universities is given to illustrate the built method.
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Jiang, Pan. "LogTODIM framework for MAGDM with neutrosophic sets: Energy conservation and emission reduction case." International Journal of Knowledge-based and Intelligent Engineering Systems 28, no. 1 (2024): 149–61. http://dx.doi.org/10.3233/kes-230076.
Full textAbstract:
The significant acceleration of China’s urbanization process has greatly promoted economic development. At the same time, the massive construction of urban buildings has also caused many problems such as environmental pollution and increased energy consumption. Therefore, in architectural design, it is particularly important to pay attention to the sustainable development of the environment, handle the relationship between good people and nature under the guidance of the concept of green development, and focus on the recycling of resources. Focusing on resource utilization in architectural design and based on certain planning can better control the construction process of urban buildings, save energy consumption, reduce construction costs, and contribute to the green development of cities. The comprehensive evaluation of energy conservation and emission reduction of construction projects is a classical MAGDM problems. Recently, the Logarithmic TODIM (LogTODIM) method has been employed to cope with MAGDM issues. The single-valued neutrosophic sets (SVNSs) are used as a tool for characterizing uncertain information during the comprehensive evaluation of energy conservation and emission reduction of construction projects. In this paper, the single-valued neutrosophic number Logarithmic TODIM (SVNN-LogTODIM) method is built to solve the MAGDM under SVNSs. In the end, a numerical case study for comprehensive evaluation of energy conservation and emission reduction of construction projects is given to validate the proposed method.
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Rani, Pratibha, and Arunodaya Raj Mishra. "Single-Valued Neutrosophic SWARA-TOPSIS-Based Group Decision-Making for Prioritizing Renewable Energy Systems." Computer and Decision Making: An International Journal 2 (January 24, 2025): 425–39. https://doi.org/10.59543/comdem.v2i.11227.
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In this paper, new outcomes on the evaluation of sustainability factors for Renewable Energy Sources (RESs) under Single Valued Neutrosophic Sets (SVNSs). Multiple Criteria Decision-Making (MCDM) model and the SVN-Stepwise Weight Assessment Ratio Analysis (SWARA) with SVN-Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) termed as ‘SVN-SWARA-TOPSIS’ are applied to solve the RESs selection problem. Five sustainability indicators RSTEE (resource, social, technology, environmental and economic) and twelve criteria are considered for RESs selection. In the proposed SVN-SWARA-TOPSIS method, three decision experts are selected for assessing the sustainability factors to the evaluation of RESs. In the developed framework, weight of the assessment of sustainability criteria are estimated by SVN-SWARA approach and preference order of RES options is determined by SVN-TOPSIS method on SVNSs setting. Finally, comparative and sensitivity assessments are discussed to analyse the validity of obtained result.
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Bathusha, S. N. Suber, та S. Angelin Kavitha Raj. "A Novel Approach on Energy of λJ-dominating Single-Valued Neutrosophic Graph Structure". Neutrosophic Systems with Applications 16 (6 квітня 2024): 48–66. http://dx.doi.org/10.61356/j.nswa.2024.16215.
Full textAbstract:
The concept of dominance is one of the most important ideas in graph theory for handling random events, and it has drawn the interest from many scholars. Research related to graph energy has garnered a lot focus recently. The application of single-valued neutrosophic graphs (SVNGs) for energy, Laplacian energy, and dominating energy has been recommended by previous studies. In this research, we apply the concepts of single-valued neutrosophic sets (SVNS) to graph structures (GSs) and investigate some intriguing features of single-valued neutrosophic graph structures (SVNGS). Moreover, the notions of λJ-dominating energy GS in an SVNGS environment are analyzed in this study. More specifically, illustrative examples are used to develop the adjacency matrix of a λJ-dominating SVNGS, as well as the spectrum of the adjacency matrix and their related theory. Further, the SVNGS λJ-dominating energy is determined. We go over various characteristics and constraints for the energy of SVNGS with λJ-dominating. Further, we introduce the idea of isomorphic and identical λJ-dominating SVNGS energy, which has been studied using relevant examples, and some of its established properties are presented.
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Cano, Allan, and Gaudencio Petalcorin. "Single-valued Neutrosophic Soft Sets in Hyper UP-Algebra." European Journal of Pure and Applied Mathematics 16, no. 1 (2023): 548–76. http://dx.doi.org/10.29020/nybg.ejpam.v16i1.4637.
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In this paper, the notions of SVN hyper UP-algebra and SVNS hyper UP-algebra are introduced, and some of their structural properties are investigated. Moreover, the Cartesian product of SVNS hyper UP-algebra is discussed and proved to be a SVNS hyper UP- algebra. Finally, the homomorphic image and preimage of SVNS hyper UP-algebra under SVNS functions are studied and showed also to be SVNS hyper UP-algebra.
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Hai-Long, Yang, Guo Zhi-Lian, and Liao Xiuwu. "On single valued neutrosophic relations." October 6, 2014. https://doi.org/10.5281/zenodo.23170.
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Smarandache initiated neutrosophic sets (NSs) which can be used as a mathematical tool for dealing with indeterminate and inconsistent information. In order to apply NSs conveniently, single valued neutrosophic sets (SVNSs) were proposed by Wang et al. In this paper, we propose single valued neutrosophic relations (SVNRs) and study their properties. The notions of anti-reflexive kernel, symmetric kernel, reflexive closure, and symmetric closure of a SVNR are introduced, respectively. Their accurate calculate formulas and some properties are explored. Finally, single valued neutrosophic relation mappings and inverse single valued neutrosophic relation mappings are introduced, and some interesting properties are also obtained.
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Jun, Ye. "Single valued neutrosophic minimum spanning tree and its clustering method." November 6, 2014. https://doi.org/10.5281/zenodo.34894.
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Clustering plays an important role in data mining, pattern recognition, and machine learning. Then, single valued neutrosophic sets (SVNSs) are useful means to describe and handle indeterminate and inconsistent information, which fuzzy sets and intuitionistic fuzzy sets cannot describe and deal with. To cluster the data represented by single value neutrosophic information, the paper proposes a single valued neutrosophic minimum spanning tree (SVNMST) clustering algorithm. Firstly, we defined a generalized distance measure between SVNSs. Then, we present a SVNMST clustering algorithm for clustering single value neutrosophic data based on the generalized distance measure of SVNSs. Finally, two illustrative examples are given to demonstrate the application and effectiveness of the developed approach.
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Dong-Sheng, Xu, Wei Cun, and Wei Gui-Wu. "TODIM Method for Single-Valued Neutrosophic Multiple Attribute Decision Making." September 12, 2018. https://doi.org/10.5281/zenodo.1413998.
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Recently, the TODIM has been used to solve multiple attribute decision making (MADM) problems. The single-valued neutrosophic sets (SVNSs) are useful tools to depict the uncertainty of the MADM. In this paper, we will extend the TODIM method to the MADM with the single-valued neutrosophic numbers (SVNNs).
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Jun, Ye, and Zhang Qiansheng. "Single Valued Neutrosophic Similarity Measures for Multiple Attribute Decision-Making." July 1, 2015. https://doi.org/10.5281/zenodo.22645.
Full textAbstract:
Similarity measures play an important role in data mining, pattern recognition, decision making, machine learning, image process etc. Then, single valued neutrosophic sets (SVNSs) can describe and handle the indeterminate and inconsistent information, which fuzzy sets and intuitionistic fuzzy sets cannot describe and deal with. Therefore, the paper proposes new similarity meas-ures between SVNSs based on the minimum and maxi-mum operators. Then a multiple attribute decision-making method based on the weighted similaritymeasure of SVNSs is established in which attribute values for alternatives are represented by the form of single valued neutrosophic values (SVNVs) and the attribute weights and the weights of the three independent elements (i.e., truthmembership degree, indeterminacy-membership degree, and falsity-membership degree) in a SVNV are considered in the decision-making method. In the decision making, we utilize the single-valued neutrosophic weighted similarity measure between the ideal alternative and an alternative to rank the alternatives corresponding to the measure values and to select the most desirable one(s). Finally, two practical examples are provided to demonstrate the applications and effectiveness of the single valued neutrosophic multiple attribute decision-making method.
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Han-Liang, Huang. "New Distance Measure of Single-Valued Neutrosophic Sets and Its Application." October 13, 2016. https://doi.org/10.5281/zenodo.236057.
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A single-valued neutrosophic set (SVNS) is an instance of a neutrosophic set, which can be used to handle uncertainty, imprecise, indeterminate, and inconsistent information in real life. In this paper, a new distance measure between two SVNSs is defined by the full consideration of truthmembership function, indeterminacy-membership function, and falsity-membership function for the forward and backward differences.
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Chao, Tian, Yu Zhang Wen, Zhang Shuai, and Juan Peng Juan. "An Extended Single-Valued Neutrosophic Projection-Based Qualitative Flexible Multi-Criteria Decision-Making Method." May 20, 2019. https://doi.org/10.5281/zenodo.3047157.
Full textAbstract:
With respect to multi-criteria decision-making (MCDM) problems in which the criteria denote the form of single-valued neutrosophic sets (SVNSs), and the weight information is also fully unknown, a novel MCDM method based on qualitative flexible multiple criteria (QUALIFLEX) is developed. Firstly, the improved cosine measure of the included angle between two SVNSs is defined.
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Rıdvan, Şahin. "Neutrosophic Hierarchical Clustering Algoritms." July 1, 2015. https://doi.org/10.5281/zenodo.22588.
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Interval neutrosophic set (INS) is a generalization of interval valued intuitionistic fuzzy set (IVIFS), whose the membership and non-membership values of elements consist of fuzzy range, while single valued neutrosophic set (SVNS) is regarded as extension of intuitionistic fuzzy set (IFS). In this paper, we extend the hierarchical clustering techniques proposed for IFSs and IVIFSs to SVNSs and INSs respectively. Based on the traditional hierarchical clustering procedure, the single valued neutrosophic aggregation operator, and the basic distance measures between SVNSs, we define a single valued neutrosophic hierarchical clustering algorithm for clustering SVNSs. Then we extend the algorithm to classify an interval neutrosophic data. Finally, we present some numerical examples in order to show the effectiveness and availability of the developed clustering algorithms.
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Ye, Jun. "Fault diagnoses of hydraulic turbine using the dimension root similarity measure of single-valued neutrosophic sets." August 28, 2016. https://doi.org/10.5281/zenodo.235686.
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This paper proposes a dimension root distance and its similarity measure of single-valued neutrosophic sets (SVNSs), and then develops the fault diagnosis method of hydraulic turbine by using the dimension root similarity measure of SVNSs. By the similarity measure between the fault diagnosis patterns and a testing sample with single-valued neutrosophic information and the relation indices, we can determine the fault type and rank faults.
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Jun, Ye. "Another Form of Correlation Coefficient between Single Valued Neutrosophic Sets and Its Multiple Attribute Decision- Making Method." July 1, 2015. https://doi.org/10.5281/zenodo.22428.
Full textAbstract:
A single valued neutrosophic set (SVNS), which is the subclass of a neutrosophic set, can be considered as a powerful tool to express the indeterminate and inconsistent information in the process of decision making. Then, correlation is one of the most broadly applied indices in many fields and also an important measure in data analysis and classification, pattern recognition, decision making and so on. Therefore, we propose another form of correlation coefficient between SVNSs and establish a multiple attribute decision making method using the correlation coefficient of SVNSs under single valued neutrosophic environment. Through the weighted correlation coefficient between each alternative and the ideal alternative, the ranking order of all alternatives can be determined and the best alternative can be easily identified as well. Finally, two illustrative examples are employed to illustrate the actual applications of the proposed decision-making approach.
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Huanying, Zhang, Wang Fei, and Geng Yushui. "Multi-Criteria Decision-Making Method Based on Single-Valued Neutrosophic Schweizer–Sklar Muirhead Mean Aggregation Operators." May 21, 2019. https://doi.org/10.5281/zenodo.3073904.
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Schweizer–Sklar (SS) operation can make information aggregation more flexible, and the Muirhead mean (MM) operator can take into account the correlation between inputs by a variable parameter. Because traditional MM is only available for real numbers and single-valued neutrosophic set (SVNS) can better express incomplete and uncertain information in decision systems, in this paper, we applied MM operators to single-valued neutrosophic sets (SVNSs) and presented two new MM aggregation operators with the SS operation, i.e., a single-valued neutrosophic SS Muirhead mean (SVNSSMM) operator and a weighted single-valued neutrosophic SS MM (WSVNSSMM) operator. We listed some properties of them and some particular cases about various parameter values. We also proposed the multi-criteria decision-making method based on the WSVNSSMM operator in SVNS. At last, we illustrated the feasibility of this method using a numerical example of company investment.
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Nancy, and Harish Garg. "A novel divergence measure and its based TOPSIS method for multi criteria decision-making under single-valued neutrosophic environment." May 20, 2019. https://doi.org/10.5281/zenodo.3047677.
Full textAbstract:
The theme of this work is to present an axiomatic definition of divergence measure for single-valued neutrosophic sets (SVNSs). The properties of the proposed divergence measure have been studied. Further, we develop a novel technique for order preference by similarity to ideal solution (TOPSIS) method for solving single-valued neutrosophic multi-criteria decision-making with incomplete weight information. Finally, a numerical example is presented to verify the proposed approach and to present its effectiveness and practicality.
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Farid, Hafiz Muhammad Athar, Harish Garg, Muhammad Riaz, and Gustavo Santos-García. "Multi-criteria group decision-making algorithm based on single-valued neutrosophic Einstein prioritized aggregation operators and its applications." Management Decision, June 21, 2022. http://dx.doi.org/10.1108/md-04-2022-0484.
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PurposeSingle-valued neutrosophic sets (SVNSs) are efficient models to address the complexity issues potentially with three components, namely indeterminacy, truthness and falsity. Taking advantage of SVNSs, this paper introduces some new aggregation operators (AOs) for information fusion of single-valued neutrosophic numbers (SVNNs) to meet multi-criteria group decision-making (MCGDM) challenges.Design/methodology/approachEinstein operators are well-known AOs for smooth approximation, and prioritized operators are suitable to take advantage of prioritized relationships among multiple criteria. Motivated by the features of these operators, new hybrid aggregation operators are proposed named as “single-valued neutrosophic Einstein prioritized weighted average (SVNEPWA) operator” and “single-valued neutrosophic Einstein prioritized weighted geometric (SVNEPWG) operators.” These hybrid aggregation operators are more efficient and reliable for information aggregation.FindingsA robust approach for MCGDM problems is developed to take advantage of newly developed hybrid operators. The effectiveness of the proposed MCGDM method is demonstrated by numerical examples. Moreover, a comparative analysis and authenticity analysis of the suggested MCGDM approach with existing approaches are offered to examine the practicality, validity and superiority of the proposed operators.Originality/valueThe study reveals that by choosing a suitable AO as per the choice of the expert, it will provide a wide range of compromise solutions for the decision-maker.
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Wentao, Xiong, and Cheng Jing. "A NovelMethod for Determining the AttributeWeights in the Multiple Attribute Decision-Making with Neutrosophic Information through Maximizing the Generalized Single-Valued Neutrosophic Deviation." June 7, 2018. https://doi.org/10.5281/zenodo.1412466.
Full textAbstract:
The purpose of this paper is to investigate the weights determination in the multiple attribute decision-making (MADM) with the single valued neutrosophic information. We first introduce a generalized single-valued neutrosophic deviation measure for a group of single valued neutrosophic sets (SVNSs), and then present a novel and simple nonlinear optimization model to determine the attribute weights by maximizing the total deviation of all attribute values, whether the attribute weights are partly known or completely unknown.