Single-valued Neutrosophic Set Research Articles

H-Max Single-Valued Neutrosophic Distance Measure in Medical Diagnosis

As an instance of a neutrosophic set, a single-valued neutrosophic set (SVNS) can be used to handle uncertainty, inaccuracy, indeterminacy, and inconsistency. In this paper, a new not-so-sophisticated distance measure between two SVNSs is defined by considering the cross-assessment between characteristic functions for the forward and backward differences. Furthermore, a single-valued neutrosophic similarity measure, a single-valued neutrosophic entropy measure, and their basic properties are presented and proven. In addition, an application to medical diagnosis is shown to illustrate the effective applicability of the proposals.

Air Quality Index Analysis Using Single-Valued Neutrosophic Plithogenic Graph for Multi-Decision Process

Recently, Plithogenic set and its graphical structure visualization is stuide for dealing with multi-attribute data set. In this pocess a problem arises while characterization of uncertainty in tue, false and uncertain regions, independently. One of the suitable examples is Air Quality Index and its impact on human health contains multi-valued attributes. In this case the conflict may arise among two experts about acceptation, rejection and uncertain impact of AQI for human health. To resolve this issue a single-valued neutrosophic Plithogenic set and its graphical strcutue visualization is discussed in this paper with an illustrative example.

Similarity Measures and Multi-person TOPSIS Method Using m-polar Single-Valued Neutrosophic Sets

Similarity Measures and Multi-person TOPSIS Method Using m-polar Single-Valued Neutrosophic Sets

New similarity measures for single-valued neutrosophic sets with applications in pattern recognition and medical diagnosis problems

The single-valued neutrosophic set (SVNS) is a well-known model for handling uncertain and indeterminate information. Information measures such as distance measures, similarity measures and entropy measures are very useful tools to be used in many applications such as multi-criteria decision making (MCDM), medical diagnosis, pattern recognition and clustering problems. A lot of such information measures have been proposed for the SVNS model. However, many of these measures have inherent problems that prevent them from producing reasonable or consistent results to the decision makers. In this paper, we propose several new distance and similarity measures for the SVNS model. The proposed measures have been verified and proven to comply with the axiomatic definition of the distance and similarity measure for the SVNS model. A detailed and comprehensive comparative analysis between the proposed similarity measures and other well-known existing similarity measures has been done. Based on the comparison results, it is clearly proven that the proposed similarity measures are able to overcome the shortcomings that are inherent in existing similarity measures. Finally, an extensive set of numerical examples, related to pattern recognition and medical diagnosis, is given to demonstrate the practical applicability of the proposed similarity measures. In all numerical examples, it is proven that the proposed similarity measures are able to produce accurate and reasonable results. To further verify the superiority of the suggested similarity measures, the Spearman’s rank correlation coefficient test is performed on the ranking results that were obtained from the numerical examples, and it was again proven that the proposed similarity measures produced the most consistent ranking results compared to other existing similarity measures.

Correlation Coefficients of Consistency Neutrosophic Sets Regarding Neutrosophic Multi-valued Sets and Their Multi-attribute Decision-Making Method

To overcome the insufficiencies of existing information expression and operations of single-valued neutrosophic multisets (SVNMs) and multi-valued/hesitant neutrosophic sets (MVNSs), this study first introduces neutrosophic multi-valued sets (NMVSs), including SVNMs and MVNSs, as a general concept. Then, we propose a method that transforms NMVSs into consistency single-valued neutrosophic sets (CSVNSs) based on the average values and consistency degrees (complement of standard deviations) of the truth, indeterminacy, falsity multi-valued sequences in NMVSs. CSVNSs not only can realize the reasonable information expression and operation of different sequence lengths/cardinalities between neutrosophic multi-valued elements, but also can reflect the multi-valued sequences close to corresponding average levels in each neutrosophic multi-valued element. Next, we present two correlation coefficients between CSVNSs in the setting of NMVSs. Based on the correlation coefficients of CSVNSs, a decision-making (DM) approach is established in the NMVS setting. Lastly, an illustrative example and comparison with existing methods are presented to demonstrate the effectiveness and rationality of the established DM method in the NMVS setting. The developed DM approach not only makes the DM process more reasonable and credible, but also provides the new modeling method for multi-attribute DM problems in NMVS setting.

Novel Single-Valued Neutrosophic Combined Compromise Solution Approach for Sustainable Waste Electrical and Electronics Equipment Recycling Partner Selection

Waste electrical and electronics equipment (WEEE) recyclers have become a boon for countries as they assist to reduce carbon emissions by recycling the WEEE in the most ecofriendly way. The evaluation and choice of optimal WEEE recycling partner is a significant and multifaceted decision for the managerial experts because of the involvement of several qualitative and quantitative criteria. Thus, the aim of the article is to propose a novel methodology by integrating a combined compromise solution approach and similarity measure within the context of single-valued neutrosophic sets (SVNSs) and, then, used to solve the decision-making problem. In this approach, the criteria weights are evaluated by a new procedure based on a similarity measure. For this, a novel similarity measure is introduced for SVNSs and also presented its efficiency over existing similarity measures. To investigate the efficiency and practicality of the introduced approach, a case study of WEEE recycling partner selection is taken under the SVNSs environment. Finally, comparison and sensitivity analysis are made to check the robustness and stability of the developed methodology. The outcomes of this article exemplify that the developed approach is more suitable and well consistent with existing approaches.

Study on the Level of Knowledge in Dental Medical Emergencies of Dentistry Students through Neutrosophic Values

This research carries out an analysis of the level of knowledge in dental medical emergencies of tenth semester dentistry students at Universidad Regional Autonoma de los Andes UNIANDES, during the academic period April-August 2019, related to the reception of first aid courses. For this purpose, we made use of the neutrosophic theory, through the application of the single valued neutrosophic set (SVNS) associated to linguistic variables to evaluate the students' answers to the applied questionnaire. As a main result, we obtained a negative evaluation of the level of knowledge of dental medical emergencies for the students who have not received the first aid course.

A Novel Framework Using Neutrosophy for Integrated Speech and Text Sentiment Analysis

With increasing data on the Internet, it is becoming difficult to analyze every bit and make sure it can be used efficiently for all the businesses. One useful technique using Natural Language Processing (NLP) is sentiment analysis. Various algorithms can be used to classify textual data based on various scales ranging from just positive-negative, positive-neutral-negative to a wide spectrum of emotions. While a lot of work has been done on text, only a lesser amount of research has been done on audio datasets. An audio file contains more features that can be extracted from its amplitude and frequency than a plain text file. The neutrosophic set is symmetric in nature, and similarly refined neutrosophic set that has the refined indeterminacies I1 and I2 in the middle between the extremes Truth T and False F. Neutrosophy which deals with the concept of indeterminacy is another not so explored topic in NLP. Though neutrosophy has been used in sentiment analysis of textual data, it has not been used in speech sentiment analysis. We have proposed a novel framework that performs sentiment analysis on audio files by calculating their Single-Valued Neutrosophic Sets (SVNS) and clustering them into positive-neutral-negative and combines these results with those obtained by performing sentiment analysis on the text files of those audio.

A New Method Based on PROMETHEE and TODIM for Multi-Attribute Decision-Making with Single-Valued Neutrosophic Sets

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.

Multi-criteria group decision making model using single-valued neutrosophic set

Multi-criteria group decision making model using single-valued neutrosophic set

Integrated Weighted Distance Measure for Single-Valued Neutrosophic Linguistic Sets and Its Application in Supplier Selection

The purpose of this study is to propose an integrated distance-based methodology for multiple attribute group decision making (MAGDM) within single-valued neutrosophic linguistic (SVNL) environments. A new SVNL distance measure, namely the SVNL integrated weighted distance (SVNLIWD) measure, is first developed for achieving the aim. The remarkable feature of the SVNLIWD is that it integrates both merits of ordered weighting and average weighting into aggregating SVNL distances; therefore, it can account for both the importance of aggregated deviations as well as ordered positions. Thus, it can highlight the decision makers’ subjective risk attitudes and combine the importance of objective decision information. Some distinctive characteristics and special forms of the presented distance framework are then specifically studied. Moreover, a MAGDM model on the basis of the proposed SVNLIWD form is formulated. Finally, an illustrative numerical case regarding selecting low-carbon supplier is used to test the performance of the designed method.

Single-Valued Neutrosophic Set Correlation Coefficient and Its Application in Fault Diagnosis

With the increasing automation of mechanical equipment, fault diagnosis becomes more and more important. However, the factors that cause mechanical failures are becoming more and more complex, and the uncertainty and coupling between the factors are getting higher and higher. In order to solve the given problem, this paper proposes a single-valued neutrosophic set ISVNS algorithm for processing of uncertain and inaccurate information in fault diagnosis, which generates neutrosophic set by triangular fuzzy number and introduces the formula of the improved weighted correlation coefficient. Since both the single-valued neutrosophic set data and the ideal neutrosophic set data are considered, the proposed method solves the fault diagnosis problem more effectively. Finally, experiments show that the algorithm can significantly improve the accuracy degree of fault diagnosis, and can better satisfy the diagnostic requirements in practice.

Decision-making method based on new entropy and refined single-valued neutrosophic sets and its application in typhoon disaster assessment

This study proposes a multi-attribute decision-making method for the decision-making problems with attributes and sub-attribute where the attribute weight is unknown, based on information entropy and the evaluation based on distance from average solution (EDAS) method under a refined single-valued neutrosophic set environment. First, the new distance measure, similarity measure, and neutrosophic entropy based on refined single-valued neutrosophic sets are defined. Further, the relationship between them is discussed and the attribute weights are determined based on the new neutrosophic entropy. Then, the EDAS method is used to rank and select the best alternative. Finally, two illustrative examples of typhoon disaster assessment (typhoon disaster assessment with multi-layer indicators and dynamic assessment of typhoon disaster) are presented to demonstrate the feasibility, effectiveness, and practicality of the proposed method. The advantages of the proposed method are illustrated by sensitive analysis and comparative analysis with other methods.

A Further Study on Multiperiod Health Diagnostics Methodology under a Single-Valued Neutrosophic Set

Employing the concept and function of tangency with similarity measures and counterpart distances for reliable medical consultations has been extensively studied in the past decades and results in lots of isomorphic measures for application. We compared the majority of such isomorphic measures proposed by various researchers and classified them into (a) maximum norm and (b) one-norm categories. Moreover, we found that previous researchers used monotonic functions to transform an identity function and resulted in complicated expressions. In this study, we provide a theoretical foundation to explain the isomorphic nature of a newer measure proposed by the following research paper against its studied existing one in deriving the same pattern recognition results. Specifically, this study initially proposes two similarity measures using maximum norm, arithmetic mean, and aggregation operators and followed by a detailed discussion on their mathematical characteristics. Subsequently, a simplified version of such measures is presented for easy application. This study completely covers two previous methods to point out that the complex approaches used were unnecessary. The findings will help physicians, patients, and their family members to obtain a proper medical diagnosis during multiple examinations.

A Novel Extension of the TOPSIS Method Adapted for the Use of Single-Valued Neutrosophic Sets and Hamming Distance for E-Commerce Development Strategies Selection

Neutrosophic sets have been recognized as an effective approach in solving complex decision-making (DM) problems, mainly when such problems are related to uncertainties, as published in numerous articles thus far. The use of the three membership functions that can be used to express accuracy, inaccuracy, and indeterminacy during the evaluation of alternatives in multiple-criteria DM can be said to be a significant advantage of these sets. By utilizing these membership functions, neutrosophic sets provide an efficient and flexible approach to the evaluation of alternatives, even if DM problems are related to uncertainty and predictions. On the other hand, the TOPSIS method is a prominent multiple-criteria decision-making method used so far to solve numerous decision-making problems, and many extensions of the TOPSIS method are proposed to enable the use of different types of fuzzy as well as neutrosophic sets. Therefore, a novel extension of the TOPSIS method adapted for the use of single-valued neutrosophic sets was considered in this paper.

A multi‐criteria sustainable supplier selection framework based on neutrosophic fuzzy data and entropy weighting

AbstractThe gains in corporate sustainability are important for business development under the increasing competition and climate change. The importance of the green and sustainable supplier selection has increased due to the environmental concerns and regulations. The information for business decisions is often vague and imprecise. Therefore, this paper develops a fuzzy methodology for sustainable supplier selection based on fuzzy information. Single‐valued neutrosophic set (SVNS) is a very popular tool for processing potentially uncertain information provided by decision‐makers. Thus, SVNS is considered as a useful extension of the existing methods in uncertain complex situations. In order to facilitate the multi‐attribute decision‐making (MADM), this paper develops a new similarity measure for the SVNSs and explores its application possibilities. For achieving the aim, a single‐valued neutrosophic (SVN) hybrid weighted similarity (SVNHWS) measure is presented to reflect degree of similarity of SVNSs more effectively. Moreover, a method based on the SVNHWS and entropy measures is constructed for handling SVN MADM problems, in which, the entropy measure is used to derive the unknown weights information of attributes. Finally, an illustrative mathematical example dealing with the sustainable supplier selection is provided. The reliability of the proposed technique is tested by means of the comparative analysis.

A framework for prioritizing cloud services in neutrosophic environment

Cloud service selection assists cloud users to find the best cloud services as per their needs and minimizes the loss occurring due to improper selection of services. This paper aims to develop a cloud service selection framework for the neutrosophic environment using single-valued neutrosophic set (SVNS) theory and multi-criteria decision making (MCDM) based technique for order of preference by similarity to ideal solution (TOPSIS). The SVNS helps cloud users and experts to express their opinion in linguistic terms rather than crisp value due to partial knowledge involving some degree of truth, indeterminacy and falsehood. TOPSIS is used to rank cloud services efficiently. A case study has been performed on a real dataset obtained from CloudHarmony to demonstrate its practicality and usefulness. Sensitivity analysis has been carried out with the addition and deletion of cloud services to rank them and found that the framework is consistent and robust to rank reversal problem. The framework is also capable to strongly handle a fuzzy environment without rank reversal phenomenon in comparison with other MCDM based cloud service selection frameworks available in the literature.

Restoration Methods Selection for Wood Components of Chinese Ancient Architectures Based on TODIM with Single-Valued Neutrosophic Sets

The selection of restoration methods for ancient architectures is of great significance for the protection of human cultural heritage. This paper proposes a novel restoration methods selection approach for wood components of Chinese ancient architectures, in which a multicriteria group decision-making (MCGDM) method with decision-making information is in the form of single-valued neutrosophic sets (SNNSs). Firstly, it establishes an index system by comprehensively considering subjective and objective criteria. In addition, the best-worst method (BWM) and the entropy weight method are combined to produce index weights. Furthermore, the TODIM method is utilized by the single-valued neutrosophic sets to prioritize restoration methods. Finally, a specific case of wood component restoration is conducted to demonstrate the practicability of the proposed model. The robustness and effectiveness of the proposed method is verified by sensitivity analysis and comparison analysis.

Emergency Transportation Problem Based on Single-Valued Neutrosophic Set

Emergency events are full of large number of uncertain information. The existence of these uncertain information leads to less research on emergency logistics involving transshipment scenarios. In this paper, a new emergency transport model is proposed, which simulates the scenario of emergency transport from the logistics center to each disaster site and between each disaster site. The single-valued neutrosophic set (SVNS) is applied to transform the emergency transshipment problem into a multiattribute decision-making problem in ambiguous and uncertain environments. Technology for order preference by similarity to ideal solution (TOPSIS) is extended to the single-valued neutrosophic environment to rank and optimize the alternative transshipment routes. Firstly, the attribute weight is determined by using the entropy weight method; secondly, the scoring function of the single-valued neutrosophic fuzzy number is defined; thirdly, the TOPSIS method is used to rank the decision-making; finally, the feasibility and rationality of the proposed method are verified by an emergency operation example.

New similarity and entropy measures of single-valued neutrosophic sets with applications in multi-attribute decision making

Information measures play a fundamental role in single-valued neutrosophic set (SVNS) theory. The main purpose of this paper is to study the similarity and entropy measures of SVNS with applications in multi-attribute decision making. We proposed the axiomatic definitions of similarity and entropy for single-valued neutrosophic values (SVNVs) with respect to a new kind of inclusion relation between SVNVs. On the basis of Hamming distance, cosine function and cotangent function, three similarity measures and three entropies for SVNVs are constructed. Then, we extended the definitions and construction methods of similarity and entropy for SVNVs to SVNSs by using some aggregation operators. Finally, by using the new similarity and entropy measures we presented a SVNSs based multi-attribute decision making method. It demonstrated that the new information measures presented in this study are applicable and efficient.