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The fuzziness and complexity of evaluation information are common phenomenon in practical decision-making problem, interval neutrosophic sets (INSs) is a power tool to deal with ambiguous information. Similarity measure plays an important role in judging the degree between ideal and each alternative in decision-making process, the purpose of this paper is to establish a multi-criteria decision-making method based on similarity measure under INSs.

Based on an extension of existing cosine similarity, this paper first introduces an improved cosine similarity measure between interval neutosophic numbers, which considers the degrees of the truth membership, the indeterminacy membership and the falsity membership of the evaluation values. And then a multi-criteria decision-making method is established based on the improved cosine similarity measure, in which the ordered weighted averaging (OWA) is adopted to aggregate the neutrosophic information related to each alternative. Finally, an example on supplier selection is given to illustrate the feasibility and practicality of the presented decision-making method.

In the whole process of research and practice, it was realized that the application field of the proposed similarity measure theory still should be expanded, and the development of interval number theory is one of further research direction.

The main contributions of this paper are as follows: this study presents an improved cosine similarity measure under INSs, in which the weights of the three independent components of an interval number are taken into account; OWA are adopted to aggregate the neutrosophic information related to each alternative; and a multi-criteria decision-making method using the proposed similarity is developed under INSs.

In 2005, Smarandache generalized the Atanassov's intuitionistic fuzzy sets (IFSs) to neutrosophic sets (NS), and other researchers introduced the notion of interval neutrosophic set (INSs), which is an instance of NS, and studied various properties. The notion of neutrosophic topology on the non‐standard interval is also due to Smarandache. The purpose of this paper is to study relations between INSs and topology.

The paper investigates the possible relations between INSs and topology.

Relations on INSs and neutrosophic topology.

Clearly, the paper is confined to IFSs and NSs.

The main applications are in the mathematical field.

The paper shows original results on fuzzy sets and topology.

This paper aims to present a new term weighting approach for text classification as a text mining task. The original method, neutrosophic term frequency – inverse term frequency (NTF-IDF), is an extended version of the popular fuzzy TF-IDF (FTF-IDF) and uses the neutrosophic reasoning to analyze and generate weights for terms in natural languages. The paper also propose a comparative study between the popular FTF-IDF and NTF-IDF and their impacts on different machine learning (ML) classifiers for document categorization goals.

After preprocessing textual data, the original Neutrosophic TF-IDF applies the neutrosophic inference system (NIS) to produce weights for terms representing a document. Using the local frequency TF, global frequency IDF and text N's length as NIS inputs, this study generate two neutrosophic weights for a given term. The first measure provides information on the relevance degree for a word, and the second one represents their ambiguity degree. Next, the Zhang combination function is applied to combine neutrosophic weights outputs and present the final term weight, inserted in the document's representative vector. To analyze the NTF-IDF impact on the classification phase, this study uses a set of ML algorithms.

Practicing the neutrosophic logic (NL) characteristics, the authors have been able to study the ambiguity of the terms and their degree of relevance to represent a document. NL's choice has proven its effectiveness in defining significant text vectorization weights, especially for text classification tasks. The experimentation part demonstrates that the new method positively impacts the categorization. Moreover, the adopted system's recognition rate is higher than 91%, an accuracy score not attained using the FTF-IDF. Also, using benchmarked data sets, in different text mining fields, and many ML classifiers, i.e. SVM and Feed-Forward Network, and applying the proposed term scores NTF-IDF improves the accuracy by 10%.

The novelty of this paper lies in two aspects. First, a new term weighting method, which uses the term frequencies as components to define the relevance and the ambiguity of term; second, the application of NL to infer weights is considered as an original model in this paper, which also aims to correct the shortcomings of the FTF-IDF which uses fuzzy logic and its drawbacks. The introduced technique was combined with different ML models to improve the accuracy and relevance of the obtained feature vectors to fed the classification mechanism.

ISM technique is one of the tools of interest in soft operations research. The soft nature of this technique has made inevitable use of indeterminacy theories. The present research attempts to develop ISM technique and MICMAC analysis in a neutrosophic space due to the complexity and uncertainty of the decision-making environment.

In this study, single-valued triangular neutrosophic numbers is used to develop Neutrosophic ISM (NISM) and Neutrosophic MICMAC (NMICMAC). First, the general algorithm of NISM and NMICMAC is provided. In the following, the complete description of NISM steps including level value determination, Factor Leveling Algorithm and NISM digraph algorithm are presented. Finally, a description of the NMICMAC steps is described.

An illustrative example – supplier selection problem – is given to verify the effectiveness of the proposed method and in the discussion section; the comparison and analysis of different aspects of the NISM with the previous methods are discussed.

In this study, NISM and NMICMAC are presented for the first time, so that each pairwise comparison judgment is provided as single valued triangular neutrosophic numbers. The development of the model is continued until the final stages of calculations with neutrosophic numbers, and only in the final stage the results are crispy presented. In addition, not only the factors of process are leveled, but at each level the factors are lined up and their importance is determined.

This research attempts to present a solid transportation problem (STP) mechanism in uncertain and indeterminate contexts, allowing decision makers to select their acceptance, indeterminacy and untruth levels.

Due to the lack of reliable information, changeable economic circumstances, uncontrolled factors and especially variable conditions of available resources to adapt to the real situations, the authors are faced with a kind of uncertainty and indeterminacy in constraints and the nature of the parameters of STP. Therefore, an approach based on neutrosophic logic is offered to make it more applicable to real-world circumstances. In this study, the triangular neutrosophic numbers (TNNs) have been utilized to represent demand, transportation capacity, accessibility and cost. Then, the neutrosophic STP was converted into an interval programming problem with the help of the variation degree concept. Then, two simple linear programming models were extracted to obtain the lower and upper bounds of the optimal solution.

The results reveal that the new model is not complicated but more flexible and more relevant to real-world issues. In addition, it is evident that the suggested algorithm is effective and allows decision makers to specify their acceptance, indeterminacy and falsehood thresholds.

Under the transportation literature, there are several solutions for TP and STP in crisp, fuzzy set (FS) and intuitionistic fuzzy set (IFS) conditions. However, the STP has never been explored in connection with neutrosophic sets to the best of the authors’ knowledge. So, this work tries to fill this gap by coming up with a new way to solve this model using NSs.

The Chinese believe that “man will conquer the sky” and “fighting with the sky brings endless joy”. Considering that disaster assessment can be regarded as a two-person, zero-sum game problem between nature and human beings, this paper proposes a multi-attribute decision-making method based on game theory and grey theory in a single-value neutrosophic set environment. Due to the complexity and uncertainty of the decision-making environment, the method builds a decision matrix based on single-valued neutrosophic numbers.

First, the authors use the single-value neutrosophic information entropy to calculate the attribute weights and the weighted decision matrix. Second, the optimal mixed strategy method based on linear programming solves the optimal mixed strategy for both sides of the game so that the expected payoff matrix can be obtained. Finally, grey correlation analysis is used to obtain the closeness coefficient of each alternative based on the expectation payoff matrix to identify the ranking result of the alternative.

An example is used to verify the effectiveness of the proposed method, and its rationality is verified through a comprehensive comparison and analysis of the various aspects.

The proposed decision-making method can be applied to typhoon disaster assessment. Such assessment results can provide intelligent decision support to the relevant disaster management departments, thereby reducing the negative impact of typhoon disasters on society, stabilizing society and improving people's happiness. Further, the method can be used for decision-making, recommendation and evaluation in other fields.

The proposed method uses single-value neutrosophic numbers to solve the information representation problem of decision-making in a complex environment. Under a new perspective, game theory is used to handle the decision matrix, while grey relational analysis converts inexact numbers to exact numbers for comparison and sorting. Thus, the proposed method can be used to make reasonable decisions while preserving information to the extent possible.

Entrepreneurship as a development engine has a distinct character in the economic growth of countries. Therefore, governments must support entrepreneurship in order to succeed in the future. The best way to improve the performance of this entrepreneurial advocacy is through efficient measurement methods. For this reason, the purpose of this paper is to propose a new integrated dynamic multi-attribute decision-making (MADM) model based on neutrosophic set (NS) for assessment of the government entrepreneurship support.

Due to the nature of entrepreneurship issues, which are multifaceted and full of uncertain, indeterminate and ambiguous dimensions, this measurement requires multi-criteria decision-making methods in spaces of uncertainty and indeterminacy. Also, due to the change in the size of indicators in different periods, researchers need a special type of decision model that can handle the dynamics of indicators. So, in this paper, the authors proposed a dynamic neutrosophic weighted geometric operator to aggregate dynamic neutrosophic information. Furthermore, in view of the deficiencies of current dynamic neutrosophic MADM methods a compromised model based on time degrees was proposed. The principle of time degrees was introduced, and the subjective and objective weighting methods were synthesized based on the proposed aggregated operator and a nonlinear programming problem based on the entropy concept was applied to determine the attribute weights under different time sequence.

The information of ten countries with the indicators such as connections (C), the country's level of education and experience (EE), cultural aspects (CA), government policies (GP) and funding (F) over four years was gathered and the proposed dynamic MADM model to assess the level of entrepreneurial support for these countries. The findings show that the flexibility of the model based on decision-making thought and we can see that the weights of the criteria have a considerable impact on the final evaluations.

In many decision areas the original decision information is usually collected at different periods. Thus, it is necessary to develop some approaches to deal with these issues. In the government entrepreneurship support problem, the researchers need tools to handle the dynamics of indicators in neutrosophic environments. Given that this issue is very important, nonetheless as far as is known, few studies have been done in this area. Furthermore, in view of the deficiencies of current dynamic neutrosophic MADM making methods a compromised model based on time degrees was proposed. Moreover, the presented neutrosophic aggregation operator is very suitable for aggregating the neutrosophic information collected at different periods. The developed approach can solve the several problems where all pieces of decision information take the form of neutrosophic information collected at different periods.

Single-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.

Einstein 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.

A 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.

The 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.

The study aims at evaluating the most appropriate transport project which is one of the critical concerns of transport infrastructure scheduling. This process will be applied considering a set of criteria and discussed alternatives with sustainable perspectives.

In this paper, a complex proportional assessment (COPRAS) framework is discussed to handle the sustainable transport investment project (STIP) assessment problem within a single-valued neutrosophic set (SVNSs). To form the procedure more useful in handling with uncertain features, a SVNS is applied as a valuable procedure to handle uncertainty. First, a new discrimination measure for SVNSs is introduced and discussed some elegant properties to determine the significance degree or weight values of criteria with the sustainabality perspectives. Second, an integrated approach is introduced based on the discrimination measure and the COPRAS method on SVNSs and named as SVN-COPRAS.

A case study of an STIP evaluation problem is used to confirm the practicality and effectiveness of the SVN-COPRAS framework. Lastly, comparative discussion and sensitivity investigation are illustrated to prove the strength and solidity of the proposed framework.

The SVNSs enrich the essence of linguistic information when a decision expert (DE) vacillates among different linguistic values (LVs) to measure a sustainable transport project alternative problem. The utilization of SVNSs provides a more stable procedure to describe DEs' evaluations. So, an elegant methodology is developed to incorporate the DEs' awareness and experience for electing the desired STIPs. The introduced methodology has higher operability than the single-valued neutrosophic set technique for order preference by similarity to an ideal solution (SVN-TOPSIS) procedure during the larger numbers of attribute(s) or option(s). For the SVN-COPRAS methodology, there is no need to estimate the single-valued neutrosophic ideal solution (SVN-IS) and single-valued neutrosophic anti-ideal solution (SVNA-IS). The outcomes are calculated with handling the realistic data, which elucidates that the introduced model can tackle more intricate and realistic multi-criteria decision-making issues.

Knowledge management (KM) significantly affects supply chain management (SCM) and its performance in today's highly competitive corporate climate. It is crucial to consider this relationship to achieve optimal supply chain performance (SCP). This study aims to assess this impact by defining and examining the multi-dimensional relationships between KM Process Elements (KMPEs) and SCP Evaluation Criteria (SCPEC) within a comprehensive theoretical framework.

Integrating KMPEs and SCPEC becomes an uncertain decision-making problem due to data deficiency and the vagueness of decision-makers’ judgments. To address uncertainties, this study uses interval-valued neutrosophic (IVN) sets and proposes an IVN model consisting of SWARA, which is one of the effective multi-criteria decision-making (MCDM) approaches, and house of quality (HOQ) methods. IVN-SWARA is used to weight the SCPEC while IVN-HOQ establishes relationships and prioritizes the KMPEs and SCPEC.

The results show that reliability is the most significant SCP evaluation criterion. Among the KMPEs, capitalization, sharing, and transfer exhibit stronger associations with the SCPEC compared to the other elements. Capitalization as one of the KMPEs was found to be the most critical one, and efficiency is the criterion most affected by all elements of the KM process.

This study uses innovative methodologies to evaluate the adoption of KM processes on SCP under uncertain environments and involving multi-decision-makers. The proposed integrated model demonstrates flexibility and practicality in combining KM and SCM, leading to improved SCP. Notably, this study presents the development of IVN-SWARA and the use of the integrated IVN-SWARA - IVN-HOQ decision tool, which are novel contributions to the existing literature.