Single-valued Neutrosophic Numbers Research Articles

A novel framework for single-valued neutrosophic MADM and applications to English-blended teaching quality evaluation

Abstract In the context of “Internet plus,” college English-teaching resources are increasingly rich. Research has found that implementing a blended teaching model for college English based on the Super Star Learning Communication and Rain Classroom online teaching platform is beneficial for improving students’ enthusiasm and continuity in English learning. The English-blended teaching quality evaluation is a multiple attribute decision making (MADM). The single-valued neutrosophic set (SVNS) is a useful tool to depict uncertain information during the English-blended teaching quality evaluation. In such an article, the single-valued neutrosophic number Aczel–Alsina power geometric (SVNNAAPG) operator is produced based on the Aczel–Alsina operations and classical power geometric operator under SVNSs. The SVNNAAPG operator is built for MADM. Eventually, an example about English-blended teaching quality evaluation and some selected comparative analysis was used to depict the SVNNAAPG technique.

Bi-objective optimization of an EDM process with Cu-MWCNT composite tool using single-valued neutrosophic grey relational analysis

Purpose In many of today’s manufacturing industries, such as automobile, aerospace, defence, die and mould making, medical and electrical discharge machining (EDM) has emerged as an effective material removal process. In this process, a series of discontinuous electric discharges is used for removing material from the workpiece in the form of craters generating a replica of the tool into the workpiece in a dielectric environment. Appropriate selection of the tool electrode material and combination of input parameters is an important requirement for performance enhancement of an EDM process. This paper aims to optimize an EDM process using single-valued neutrosophic grey relational analysis using Cu-multi-walled carbon nanotube (Cu-MWCNT) composite tool electrode. Design/methodology/approach This paper proposes the application of grey relational analysis (GRA) in a single-valued neutrosophic fuzzy environment to identify the optimal parametric intermix of an EDM process while considering Cu-MWCNT composite as the tool electrode material. Based on Taguchi’s L9 orthogonal array, nine experiments are conducted at varying combinations of four EDM parameters, i.e. pulse-on time, duty factor, discharge current and gap voltage, with subsequent measurement of two responses, i.e. material removal rate (MRR) and tool wear rate (TWR). The electrodeposition process is used to fabricate the Cu-MWCNT composite tool. Findings It is noticed that both the responses would be simultaneously optimized at higher levels of pulse-on time (38 µs) and duty factor (8), moderate level of discharge current (5 A) and lower level of gap voltage (30 V). During bi-objective optimization (maximization of MRR and minimization of TWR) of the said EDM process, the achieved values of MRR and TWR are 243.74 mm3/min and 0.001034 g/min, respectively. Originality/value Keeping in mind the type of response under consideration, their measured values for each of the EDM experiments are expressed in terms of linguistic variables which are subsequently converted into single-valued neutrosophic numbers. Integration of GRA with single-valued neutrosophic sets would help in optimizing the said EDM process with the Cu-MWCNT composite tool while simultaneously considering truth-membership, indeterminacy membership and falsity-membership degrees in a human-centric uncertain decision-making environment.

LogTODIM framework for MAGDM with neutrosophic sets: Energy conservation and emission reduction case

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.

Multi-attribute decision-making methods based on Aczel-Alsina power aggregation operators for English blended teaching quality evaluation under single-valued neutrosophic sets

As a new form of teaching, blended teaching can integrate the advantages of classroom teaching and online teaching and improve the overall quality and effectiveness of English teaching under the premise of changing the orientation of teachers and students. The English blended teaching quality evaluation is a multiple attribute decision making (MADM) issue. Aczel-Alsina t-norm and t-conorm operations have the true advantage of changeability by adjusting a decision parameter. power averaging (PA) operator allowed decision attributes to strengthen each other through weight information during fusion, thereby eliminating the influence of subjective weights on the decision results. Motivate through classical Aczel-Alsina operators, PA operator and the single-valued neutrosophic sets (SVNSs), in this paper, the single-valued neutrosophic number Aczel-Alsina power averaging (SVNNAAPA) operator and the single-valued neutrosophic number Aczel-Alsina power weighted averaging (SVNNAAPWA) operator are constructed under SVNSs. The SVNNAAPWA operator is built for MADM. Eventually, an example about English blended teaching quality evaluation and some selected comparative decision analysis is used to depict the SVNNAAPWA method.

Strategic outsourcing in reverse logistics: Neutrosophic integrated approach with a hierarchical and interactive quality function deployment

The efficiency of strategic outsourcing in reverse logistics (RL) depends on stakeholder requirements (SRs) directing organization development and experts’ knowledge decomposing and reconstructing strategic decision, which urges the adoption of hierarchical and interactive quality function deployment (QFD). Considering the uncertainty within a QFD, single valued neutrosophic number (SVNN) is introduced to capture both indeterminacy and inconsistency hidden in quantitive votes and qualitative judgments of stakeholders and experts. With unknown weight assignments, two maximum deviation models are constructed to obtain the priority of SRs and Shapley weights of experts. An SVNN-enabled grey relational analysis is extended to identify the interdependence priority of engineer characterizers (ECs). Due to the interactions among components such as experts in a group or ECs in QFD, two information aggregation tools under neutrosophic environments are presented based on fuzzy integral delineating the positive or negative effect. Built on these, we propose an integrated neutrosophic approach composed of a transformation module, weight module, integration module and QFD analysis module to support the outsourcing decision. Finally, an illustration example is used to confirm the practicality of the proposed approach. Sensitivity analysis and comparative analysis with multiple views have been conducted to show the flexibility and superiority of the given decision.

Enhanced EDAS technique for colleges business English teaching quality evaluation based on Euclid distance and cosine similarity measure

With the development of national economy and the increase of foreign trade, Business English has become one of the most popular majors in universities. In order to cultivate business English talents for the national society and adapt to the requirements of the times, the innovation of English teaching concepts and the reform of teaching techniques are the only way for business English majors teaching in universities. The colleges business English teaching quality evaluation is considered as a multi-attribute group decision making (MAGDM). In this paper, the EDAS technique is expanded to the single-valued neutrosophic sets (SVNSs) and the single-valued neutrosophic number EDAS (SVNN-EDAS) technique based on Euclid distance and cosine similarity measure (CSM) is constructed to manage MAGDM. The CRITIC technique is employed to achieve the weight information based on Euclid distance and CSM technique under SVNSs. Finally, the colleges business English teaching quality evaluation is employed to demonstrate the SVNN-EDAS technique and some comparative analysis is employed to demonstrate the SVNN-EDAS. Thus, the main research contribution of this work is then constructed: (1) the CRITIC technique is built to get the attribute’s weight based on Euclid distance and CSM technique; (2) the SVNN-EDAS technique is constructed under SVNNs based on Euclid distance and CSM technique; (3) an example for colleges business English teaching quality evaluation is employed to verify SVNN-EDAS technique and several decision comparative analysis are employed to verify the SVNN-EDAS.

Method for multiple attribute decision making with single-valued neutrosophic information and application to development level evaluation of rural preschool education

The development of rural preschool education (RPE) is not only related to the healthy growth of rural preschool children, but also to social fairness and sustainable development. Therefore, the development of RPE not only involves the expansion of quantity, but also the improvement of its quality. At present, in China’s RPE, the determination of value goals There are still many obstacles in terms of source supply, institutional mechanism construction, development mode selection, and external environment construction, which make the high-quality development of RPE lack good internal motivation and external support. In view of this situation, some researchers have begun to explore the high-quality and sustainable development of RPE differently. However, the high-quality development of RPE is a systematic reform project that needs to start from the present. From multiple perspectives such as reality and history, internal and external education, this paper examines the systematic and global nature of RPE reform and development. The development level evaluation of RPE is a MADM. In this paper, the generalized weighted Bonferroni mean (GWBM) decision operator and power average (PA) is designed to manage the MADM under single-valued neutrosophic sets (SVNSs). Then, the generalized single-valued neutrosophic number power WBM (GSVNNPWBM) decision operator is constructed and the MADM model are constructed based on GSVNNPWBM decision operator. Finally, a decision example for development level evaluation of RPE and some useful comparative studies were constructed to verify the GSVNNPWBM decision operator.

Derivatives and indefinite integrals of single valued neutrosophic functions

<abstract><p>With the continuous development of the fuzzy set theory, neutrosophic set theory can better solve uncertain, incomplete and inconsistent information. As a special subset of the neutrosophic set, the single-valued neutrosophic set has a significant advantage when the value expressing the degree of membership is a set of finite discrete numbers. Therefore, in this paper, we first discuss the change values of single-valued neutrosophic numbers when treating them as variables and classifying these change values with the help of basic operations. Second, the convergence of sequences of single-valued neutrosophic numbers are proposed based on subtraction and division operations. Further, we depict the concept of single-valued neutrosophic functions (SVNF) and study in detail their derivatives and differentials. Finally, we develop the two kinds of indefinite integrals of SVNF and give the relevant examples.</p></abstract>

Application of the Neutrosophic TOPSIS for the Analysis of the Violation of Due Process in Ecuadorian Adolescents

Due to the increase in violence in Ecuador involving juvenile offenders, an analysis of the situation is proposed from a neutrosophic approach to address the violation of due process in adolescents in Ecuador, highlighting the importance of considering the complexities and ambiguities of the juvenile penal system. Challenges are identified and classified through the PESTEL technique related to legal deficiencies, economic constraints, and socio-environmental factors contributing to juvenile delinquency, which are processed hermeneutically in a TOPSIS that uses single-valued neutrosophic numbers. The processing's main outcome is the influence of legal and economic aspects, thus the need to promote legal reforms, strengthen institutional capacities, invest in preventive programs, and support social reintegration and the responsible use of information technologies. The conclusions emphasize the importance of a comprehensive and coordinated approach to improve juvenile justice in Ecuador, ensuring respect for due process and the rights of adolescents.

Grey relational analysis-driven optimization of neutrosophic MAGDM for cloud SaaS credibility evaluation

In the basic cloud service delivery model, since SaaS (Software as a Service) is located at the application layer, if a relatively complete cloud service credibility comprehensive evaluation framework can be established from the perspective of SaaS cloud service consumers and combined with their trust context, it can not only effectively solve the trust problem between cloud service consumers (CSC) and cloud service provider (CSP), but also has very important practical significance for the popularization and promotion of SaaS service applications. The credibility evaluation of SaaS services in cloud computing environment is often considered as a multi-attribute group decision making (MAGDM) problem. In this paper, the grey relational analysis (GRA) method is extended to the single-valued neutrosophic sets (SVNSs) setting to deal with MAGDM with incomplete weight information. First, the SVNSs are reviewed. In addition, the single-valued neutrosophic number GRA (SVNN-GRA) is established for MAGDM with incomplete weight information, and the computational steps for all designs are listed. Finally, the credibility evaluation of SaaS services in cloud computing environment is given to demonstrate the SVNN-GRA model and some comparative analysis is done to demonstrate the SVNN-GRA.

Smart algorithmic solutions for neutrosophic multiple-attribute decision-making and applications to chair furniture comfort design evaluation

The activities in public places are becoming increasingly frequent, and public seats have become an important component of public space and an “auxiliary tool” for work, life, and leisure. The demand for such furniture in China is gradually increasing, but the design and research work of public seats is lagging behind the development status and speed of other civil and office furniture. Usually, public seats can be divided into two parts based on their usage: public indoor seats and public outdoor seats. How to understand the role and impact of public seats on the indoor environment, and how to establish a new design method for public seats in the context of the overall environmental system, are currently urgent issues to be solved. The chair furniture comfort design evaluation is a classical MADM issues. In such paper, the generalized weighted Bonferroni mean (WBM) operator and power average (PA) is constructed for MADM with single-valued neutrosophic sets (SVNSs). Then, the generalized single-valued neutrosophic number power WBM (GSVNNPWBM) operator is built and then the MADM decision methods are proposed based on the GSVNNPWBM operator. Finally, an example about chair furniture comfort design evaluation and some comparative analysis were given to demonstrate the GSVNNPWBM method.

A novel MABAC approach for multi-attribute group decision-making with single-valued neutrosophic sets: An application in assessing microfinance group lending performance

In the 40 years of global microcredit practice, loan technology has played a positive role in microcredit as one of the most important supporting elements. The development and evolution of microcredit institution lending technology is the result of comprehensive consideration of specific regional economic, social, cultural, and geographical factors. In the context of the diversified trend of microcredit technology, choosing loan technology reasonably, exploring flexible guarantee conditions, and innovating diversified loan technology combinations will become practical problems faced by microcredit institutions, and also the direction of theoretical research. The timely innovation of group loan technology in microcredit has practical value and theoretical significance for promoting the innovation of financial agricultural products in the implementation of China’s rural revitalization strategy, as well as bridging the theoretical controversy of microcredit loan technology. The performance evaluation of microfinance groups lending is a MAGDM issues. In this paper, the distances measures of single-valued neutrosophic sets (SVNSs) and maximizing deviation method (MDM) is used to obtain the attribute weight values. Based on the classical Multi-Attributive Border Approximation area Comparison (MABAC) method, the single-valued neutrosophic numbers MABAC (SVNN-MABAC) method is constructed for MAGDM under SVNSs. Finally, an example for performance evaluation of microfinance groups lending and some comparative decision analysis are constructed to verify the SVNN-MABAC model.

Intelligent acquisition of single-valued neutrosophic numbers based on emotional tendency analysis and its application in emergency decision making

With the rising incidences of emergencies, it is both challenging and meaningful to study how to make decisions quickly and take appropriate measures to control the spread and evolution of the situation. However, most current emergency decision-making focuses on mathematical model construction, whereas fuzzy decision-making is biased towards subjective assumptions, which are both insufficient for practicability. We studied the intelligent acquisition of single-valued neutrosophic numbers based on emotional tendency analysis and applied them to emergency decision-making. First, Python programming technology was used to crawl, preprocess, and statistically analyse the network comment data of emergencies, and a quantised single-value neutrosophic number was obtained. Second, the attribute values, represented as neutrosophic numbers, were uniformly converted into cloud droplets, and the weight of the attribute values was objectively determined according to the digital feature entropy in the cloud droplets. Subsequently, a case-based reasoning approach was used to calculate the combined weighted similarity between the alternatives and ideal solution (target case) to obtain a ranking of the alternatives and historical cases in the case base that best matches the target case. Finally, a typhoon disaster assessment was considered as an example to verify the feasibility and effectiveness of the proposed method, and the advantages of the proposed method were emphasised through multi-aspect and multi-angle comparative analyses. The relevant research can be used for public opinion monitoring during emergencies and emergency handling.

Method for multiple attribute group decision making with single-valued neutrosophic number and applications to service quality evaluation of urban public transport

In the process of urban development in our country, the traffic problem is a major problem that must be faced. At present, there are serious traffic jams in many cities, and with the use of a large number of private cars, the air environment in the cities is gradually deteriorated, which also brings a lot of energy consumption. Only by vigorously developing public transportation and encouraging and guiding citizens to choose the public transportation system as their travel mode can we give full play to the value of road resources. The service quality evaluation of urban public transport is viewed as the multiple attribute group decision making (MAGDM) issue. In this paper, the EDAS method is extended to the single-valued neutrosophic sets (SVNSs) setting to deal with MAGDM and the computational steps for all designs are listed. Finally, the service quality evaluation of urban public transport is given to demonstrate the SVNN-EDAS model and some good comparative analysis is done to demonstrate the SVNN-EDAS.

An extended intelligent technique for multiple-attribute decision-making under single-valued neutrosophic sets and applications to sustainable development evaluation of rural ecotourism

With the development of society and the times, the socialist modernization cause in China is constantly developing, and the improvement of the economy has also driven the development of rural ecotourism industry in China. The unique natural terrain and cultural customs in rural areas have promoted the continuous development of local ecotourism industry, which has had a positive impact on the economic development of rural areas and not only solved the employment problem of the majority of the population in rural areas. It can also bring a continuous stream of economic benefits and continuously improve the living standards of local residents. Rural ecotourism refers to a rural tourism activity that takes place in rural areas, supported by the agricultural industry, and attracted by the rural environment and typical rural ecotourism resources, with the concept of ecotourism. Rural ecotourism mainly takes the form of rural scenery, agricultural participation, and folk experience, integrating sightseeing experience, cognition, and tourism activities. The main principles of rural tourism development are agricultural support, people-oriented, ecological protection, community participation, income feedback, and ecological home construction. The sustainable development evaluation of rural ecotourism is a classical multiple-attribute decision-making (MADM) issue. In such paper, the generalized weighted Bonferroni mean (GWBM) operator and power average (PA) is constructed for MADM with single-valued neutrosophic sets (SVNSs). Then, the single-valued neutrosophic number power generalized BM (SVNNPGBM) operator is built and then the MADM decision methods are proposed based on the SVNNPGBM operator. Finally, an example for sustainable development evaluation of rural ecotourism and some comparative analysis were given to demonstrate the SVNNPGBM method.

An extended technique for multiple attribute decision making under single-valued neutrosophic sets and applications to grain fermentation process quality evaluation

Fermentation engineering is a technology that uses engineering technology to produce useful biological products for human beings by using certain functions of organisms (mainly microorganisms) and active isolated enzymes, or to directly control certain industrial production processes with the participation of microorganisms. With the progress of science and technology, fermentation technology has also developed greatly, and has entered the stage of modern fermentation engineering that can artificially control and modify microorganisms to make these microorganisms produce products for human beings. As an important part of modern biotechnology, modern fermentation engineering has a broad application prospect. The grain fermentation process quality evaluation is a classical MADM issues. In such paper, the generalized weighted Bonferroni mean (WBM) operator is constructed for MADM with single-valued neutrosophic sets (SVNSs). Then, the generalized single-valued neutrosophic number WBM (GSVNNWBM) operator is built and then the MADM decision methods are proposed based on the GSVNNWBM operator. Finally, an example about grain fermentation process quality comprehensive evaluation and some comparative analysis were given to demonstrate the GSVNNWBM method.

An Aczel-Alsina aggregation-based outranking method for multiple attribute decision-making using single-valued neutrosophic numbers

The “single-valued neutrosophic set (SVNS)” is used to simulate scenarios with ambiguous, incomplete, or inaccurate information. In this article, with the aid of the Aczel-Alsina (AA) operations, we describe the aggregation operators (AOs) of SVNSs and how they work. AA t-norm (t-NM) and t-conorm (t-CNM) are first extended to single-valued neutrosophic (SVN) scenarios, and then we introduce several novel SVN operations, such as the AA sum, AA product, AA scalar multiplication, and AA exponentiation, by virtue of which we generate a few useful SVN AOs, for instance, the SVN AA weighted average (SVNAAWA) operator, SVN AA order weighted average (SVNAAOWA) operator, and SVN AA hybrid average (SVNAAHA) operator. Next, we create distinct features for such operators, group numerous exceptional cases together, and study the relationships between them. Following that, we created a way for “multiple attribute decision making (MADM)” in the SVN context using the SVNAAWA operator. We provided an illustration to substantiate the appropriateness and, additionally, the productiveness of the produced operators and strategy. Besides this, we contrasted the suggested strategy to the given procedures and conducted a comprehensive analysis of the new framework.

Some aggregation operators of parameterized single-valued neutrosophic numbers and their MADM approach in simplified neutrosophic indeterminate scenarios

Simplified neutrosophic indeterminate sets/numbers (SNISs/SNINs) can conveniently express the partially determinate and partially indeterminate information of truth, falsity, indeterminacy membership degrees, which shows its main merit. Then, the existing aggregation algorithms of SNINs lack a parameterized aggregation method to reach a flexible decision-making method subject to different decision risks. Therefore, this study proposed a MADM approach using some aggregation operators of parameterized single-valued neutrosophic numbers in a simplified neutrosophic indeterminate scenario. First, we presented a conversion technique from SNINs to parameterized single-valued neutrosophic numbers (PSVNNs) by an indeterminate parameter. Second, we proposed the score function of PSVNN and the parameterized single-valued neutrosophic weighted arithmetic averaging (PSVNWAA) and parameterized single-valued neutrosophic weighted geometric averaging (PSVNWGA) operators. Third, a multiple attribute decision-making (MADM) approach with the smaller, moderate and larger decision risks is developed by the PSVNWAA or PSVNWGA operator in a SNIS setting. Forth, the developed MADM approach is applied to the choice problem of clinical physicians as a numerical example. Generally, the developed MADM approach reveals the advantage of flexible decision making subject to the smaller, moderate, and larger decision risks of decision makers in a neutrosophic indeterminate scenario. However, this study reveals the main contributions in the aggregation algorithms of PSVNNs and flexible MADM approach in a SNIS setting.

Efficient Decision Making for Sustainable Energy Using Single-Valued Neutrosophic Prioritized Interactive Aggregation Operators

To reduce greenhouse gas emissions, conserve the environment, and reduce dependency on fossil fuels, the transition from fossil energy to renewable energy is deemed essential. Several companies around the globe, especially big conglomerates, were pioneers in the use of renewable energy. For sustainable growth, Pakistani businesses are growing increasingly interested in the use of green sources in manufacturing and economic activities. In recent years, there has been a growth in the number of companies that are eager to use renewable energies to produce products that correspond to green standards, therefore boosting their competitiveness. Yet, the selection of an appropriate energy source for any industrially complex project is not a simple task, as numerous qualitative and quantitative characteristics must be considered. To arrive at a feasible conclusion, this research provides a multi-criteria paradigm for sustainable energy selection in a single-valued neutrosophic environment. This work developed an innovative aggregation operators approach that interprets the input evaluation using single-valued neutrosophic numbers. For this, a “single-valued neutrosophic prioritized interactive weighted averaging operator and single-valued neutrosophic prioritized interactive weighted geometric operator” has been introduced. Several additional appealing features of these aggregation operators are also discussed. The application of the recommended operators for sustainable energy related to the industrial complex is discussed. A comparison analysis proves the empirical existence of the suggested methodology’s consistency and superiority.

Analysis Impact of Intrinsic and Extrinsic Motivation on Job Satisfaction in Logistics Service Sector: An Intelligent Neutrosophic Model


 The success of every company relies heavily on the happiness of its workforce, and the logistics service sector is no exception. The capacity of logistics suppliers to satisfy the demands of their clients depends on the efficiency and efficacy of operations, which in turn is affected by the level of employee satisfaction. This paper aims to analyze the factors of employee satisfaction in the logistic service industry to achieve productivity and a satisfied workforce. This paper used the multi-criteria decision-making (MCDM) methodology to handle various factors. The SWARA method is an MCDM method used to compute the importance of factors. The SWARA is integrated with the neutrosophic set to handle uncertain data. This paper used single-valued neutrosophic numbers to evaluate the factors by the experts. The application of the proposed methodology is conducted. We achieved the positive work ecological is essential to the success of any business, and this is especially true in the logistics service sector. When workers feel appreciated and supported, they are more likely to give their all at work, which in turn boosts output, morale, and retention. However, given that job security isn't the only element that influences employee happiness and retention, some would say that it's the least essential aspect. So this paper can aid any organization to increase productivity and employee satisfaction by showing the importance of various employee satisfaction in logistic services.