A novel divergence measure and its based TOPSIS method for multi criteria decision-making under single-valued neutrosophic environment

MABAC method for multiple attribute group decision making under single-valued neutrosophic sets and applications to performance evaluation of sustainable microfinance groups lending

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.

Inspection of the Production Lot Using Two Successive Occasions Sampling Under Neutrosophy

The efficiency of the measuring tools and operators is a significant part of lot sentencing decisions. These tools have to pass some pre-specified quality levels to avoid problems during the quality assessment scenarios. These measurements have a serious risk to be encountered with any extent of ambiguity, doubt, or indeterminacy due to any of the factors like variation among the operating regimes, warming effects in the hot climatic conditions, the operators’ casual attitude, and so on. These factors as the most significant sources of extraneous variations can deeply affect the efficacy of lot sentencing decisions. Hence, the decision when based on the measurement through the operating tools and these tools have to pass which have fulfilled some adequate standards only then lot sentencing may avoid or save from the rejection of a good lot. The authors have put their focus on dealing with the factors that arise by measuring variability among the measured or determined values despite having the normal population distribution. In this study, the auxiliary information is used to estimate the variable of interest over the two successive occasions under the neutrosophic interval numbers and proved helpful to overcome this issue. The presented approach has discussed that in blurred, doubted, uncertain and undetermined datasets partially or completely, the efficacy of the decision for the whole lot cannot be decided on the single point crisped value. But the range of values around such a single crisp point in the form of neutrosophic theory is proved far better. In this context, the neutrosophic interval number successive sampling-based sampling plan is proposed which is the major contribution to the existing literature. It is explained in terms of operating characteristic function and the plan parameters are determined through the neutrosophic non-linear optimization approach. The comparative analysis is presented with the existing sampling plans and found efficient. Moreover, a real-life industrial dataset is used as an application of the concept.

A Novel Similarity Measure of Single-Valued Neutrosophic Sets Based on Modified Manhattan Distance and Its Applications

A single-valued neutrosophic (SVN) set contains three parameters, which can well describe three aspects of an objective thing. However, most previous similarity measures of SVN sets often encounter some counter-intuitive examples. Manhattan distance is a well-known distance, which has been applied in pattern recognition, image analysis, ad-hoc wireless sensor networks, etc. In order to develop suitable distance measures, a new distance measure of SVN sets based on modified Manhattan distance is constructed, and a new distance-based similarity measure also is put forward. Then some applications of the proposed similarity measure are introduced. First, we introduce a pattern recognition algorithm. Then a multi-attribute decision-making method is proposed, in which a weighting method is developed by building an optimal model based on the proposed similarity measure. Furthermore, a clustering algorithm is also put forward. Some examples are also used to illustrate these methods.

Arccosine and arctangent similarity measures of refined simplified neutrosophic indeterminate sets and their multicriteria decision-making method

In indeterminate and inconsistent setting, existing simplified neutrosophic indeterminate set (SNIS) can be depicted by the neutrosophic number (NN) functions of the truth, falsity and indeterminacy. Then, the three NN functions in SNIS lack their refined expressions and then the simplified neutrosophic indeterminate decision making (DM) method cannot carry out the multicriteria DM problems with both criteria and sub-criteria in the setting of SNISs. To overcome the flaws, this study first proposes a new notion of a refined simplified neutrosophic indeterminate set (RSNIS), which is described by the refined truth, falsity and indeterminate NN information regarding both elements and sub-elements in a universe set, as the extension of SNIS. Next, we propose the arccosine and arctangent similarity measures of RSNISs and their multicriteria DM method with various indeterminate risk ranges so as to carry out multicriteria DM problems with weight values of both criteria and sub-criteria in RSNIS setting. Lastly, the proposed DM method is applied to a multicriteria DM example of slope design schemes for an open pit mine to illustrate its application in the indeterminate DM problem with RSNISs. The decision results and comparative analysis indicate the rationality and efficiency of the proposed DM method with different indeterminate risk ranges.

T-spherical fuzzy power aggregation operators and their applications in multi-attribute decision making

The paper aims to present the concept of power aggregation operators for the T-spherical fuzzy sets (T-SFSs). T-SFS is a powerful concept, with four membership functions denoting membership, abstinence, non-membership and refusal degree, to deal with the uncertain information as compared to other existing fuzzy sets. On the other hand, the relationship between the different pairs of the attributes are well recorded in terms of power operators. Thus, keeping these advantages of T-SFSs and power operator, the objective of this work is to define several weighted averaging and geometric power aggregation operators. The stated operators named as T-spherical fuzzy weighted, ordered weighted, hybrid averaging and geometric operators for the collection of the T-SFSs. The various properties and the special cases of them are also derived. Further, the consequences of proposed new power aggregation operators are studied in view of some constraints. Finally, a multiple attribute decision making algorithm, based on the proposed operators, is established to solve the problems with uncertain information and illustrate with numerical examples. A comparative study, superiority analysis and discussion of the proposed approach are furnished to confirm the approach.

A decision-making framework for China’s rare earth industry security evaluation by neutrosophic soft CoCoSo method

The rare earth industry is a crucial strategic industry that is related to the national economy and national security. In the context of economic globalization, international competition is becoming increasingly fierce, and the rare earth industry is facing a more severe survival and development environment than ever before. Although China is the greatest world’s rare earth country in rare earth reserves, production, consumption and export volume, it is not a rare earth power. The rare earth industry has no right to speak in the international market. The comparative advantage is weakening and the security of rare earth industry appears. Therefore, studying the rare earth industry security has important theoretical and practical significance. When measuring the China’s rare earth industry security, the primary problem involves tremendous uncertainty. Neutrosophic soft set (NSS), depicted by the parameterized form of truth membership, falsity membership and indeterminacy membership, is a more serviceable pattern for capturing uncertainty. In this paper, five dimensions of rare earth industry security are identified and then prioritized against twelve different criteria relevant to structure, organization, layout, policy and ecological aspects of industry security. Then, the objective weight is computed by CRITIC (Criteria Importance Through Inter-criteria Correlation) method while the integrated weight is determined by concurrently revealing subjective weight and objective weight. Later, neutrosophic soft decision making method based CoCoSo (Combined Compromise Solution) is explored for settling the issue of low discrimination. Lastly, the feasibility and validity of the developed algorithm is verified by the issue of China’s rare earth industry security evaluation.

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 New Approach to Fuzzy TOPSIS Method Based on Entropy Measure under Spherical Fuzzy Information

Spherical fuzzy set (SFS) is one of the most important and extensive concept to accommodate more uncertainties than existing fuzzy set structures. In this article, we will describe a novel enhanced TOPSIS-based procedure for tackling multi attribute group decision making (MAGDM) issues under spherical fuzzy setting, in which the weights of both decision-makers (DMs) and criteria are totally unknown. First, we study the notion of SFSs, the score and accuracy functions of SFSs and their basic operating laws. In addition, defined the generalized distance measure for SFSs based on spherical fuzzy entropy measure to compute the unknown weights information. Secondly, the spherical fuzzy information-based decision-making technique for MAGDM is presented. Lastly, an illustrative example is delivered with robot selection to reveal the efficiency of the proposed spherical fuzzy decision support approach, along with the discussion of comparative results, to prove that their results are feasible and credible.

Some Novel Interactive Hybrid Weighted Aggregation Operators with Pythagorean Fuzzy Numbers and Their Applications to Decision Making

A Pythagorean fuzzy set (PFS) is one of the extensions of the intuitionistic fuzzy set which accommodate more uncertainties to depict the fuzzy information and hence its applications are more extensive. In the modern decision-making process, aggregation operators are regarded as a useful tool for assessing the given alternatives and whose target is to integrate all the given individual evaluation values into a collective one. Motivated by these primary characteristics, the aim of the present work is to explore a group of interactive hybrid weighted aggregation operators for assembling Pythagorean fuzzy sets to deal with the decision information. The proposed aggregation operators include interactive the hybrid weighted average, interactive hybrid weighted geometric and its generalized versions. The major advantages of the proposed operators to address the decision-making problems are (i) to consider the interaction among membership and non-membership grades of the Pythagorean fuzzy numbers, (ii) it has the property of idempotency and simple computation process, and (iii) it possess an adjust parameter value and can reflect the preference of decision-makers during the decision process. Furthermore, we introduce an innovative multiple attribute decision making (MADM) process under the PFS environment based on suggested operators and illustrate with numerous numerical cases to verify it. The comparative analysis as well as advantages of the proposed framework confirms the supremacies of the method.

Linguistic neutrosophic power Muirhead mean operators for safety evaluation of mines

Safety is the fundamental guarantee for the sustainable development of mining enterprises. As the safety evaluation of mines is a complex system engineering project, consistent and inconsistent, even hesitant evaluation information may be contained simultaneously. Linguistic neutrosophic numbers (LNNs), as the extensions of linguistic terms, are effective means to entirely and qualitatively convey such evaluation information with three independent linguistic membership functions. The aim of our work is to investigate several mean operators so that the safety evaluation issues of mines are addressed under linguistic neutrosophic environment. During the safety evaluation process of mines, many influence factors should be considered, and some of them may interact with each other. To this end, the Muirhead mean (MM) operators are adopted as they are powerful tools to deal with such situation. On the other hand, to diminish the impacts of irrational data provided by evaluators, the power average (PA) operators are under consideration. Thus, with the combination of MM and PA, the power MM operators and weighted power MM operators are proposed to aggregate linguistic neutrosophic information. Meanwhile, some key points and special cases are studied. The advantages of these operators are that not only the interrelations among any number of inputs can be reflected, but also the effects of unreasonable information can be reduced. Thereafter, a new linguistic neutrosophic ranking technique based on these operators is developed to evaluate the mine safety. Moreover, in-depth discussions are made to show the robust and flexible abilities of our method. Results manifest that the proposed method is successful in dealing with mine safety evaluation issues within linguistic neutrosophic circumstances.