Interval Neutrosophic Sets Research Articles

Research on the evaluation method of whole process engineering consulting service modes based on uncertain multiple-attribute group decision-making

With the continuous development of the economy and society, the engineering construction industry has experienced rapid growth, and higher requirements have been put forward for engineering consulting services. Currently, most engineering consulting service enterprises in China only provide relevant consulting services for engineering construction at a certain stage, lacking overall planning and overall control over the entire lifecycle of engineering construction. In order to improve the scientific level of fixed assets investment decision-making and construction management, it is of great value to explore professional engineering consulting services covering the whole process of project construction in the project decision-making stage and implementation stage to achieve the optimization of project quality and economic benefits. The whole process engineering consulting service modes (ECSM) evaluation is a multiple-attribute group decision-making (MAGDM). Recently, the TODIM technique and MACONT technique was created to put forward MAGDM. The interval neutrosophic sets (INSs) are created as a tool for managing fuzzy information during the whole process ECSM evaluation. In this work, the interval neutrosophic number TODIM-MACONT (INN-TODIM-MACONT) technique is created to put forward the MAGDM under INSs. Finally, a numerical analysis for whole process ECSM evaluation is given to validate the proposed technique. The main contributions are outlined: (1) the TODIM and MACONT technique was enhanced under INSs; (2) Information Entropy is created to conduct the weight information under INSs. (3) the INN-TODIM-MACONT technique is created to implement the MAGDM under INSs; (4) a numerical example for whole process ECSM evaluation and some comparative analysis is created to verify the INN-TODIM-MACONT technique.

Interval Neutrosophic Cubic Bézier Curve Approximation Model for Complex Data

Complex data is defined as data that has the qualities of huge data, a lack of data information, and uncertainty. This paper discussed constructing the interval neutrosophic cubic Bézier curve (INCBC) approximation model for complex data. To construct the interval neutrosophic data point (INDP) based on the definition of interval neutrosophic set (INS), interval neutrosophic relation (INR) and interval neutrosophic point (INP). Next is the introduction of an interval neutrosophic control point (INCP) that blends with the theory of interval neutrosophic set and the Bernstein basis function. Later, the interval neutrosophic cubic Bézier curve (INCBC) model is visualizing with a four-by-four control points relation approximates the curves for truth, false, and indeterminacy membership. At the end of this paper will demonstrate the algorithm for the creation of the interval neutrosophic cubic Bézier curve (INCBC). The scientific value of this work is the acceptance of complex uncertainty data. As a result, due to the fact it combines fuzzy geometric modelling, this approach has the potential to make a significant contribution to complex uncertainty modelling by using this spline which is Bézier curve model.

Cloud service prioritization using a Multi-Criteria Decision-Making technique in a cloud computing environment

Many companies are now moving their business to the cloud because the cloud provides user with unlimited resources and uninterrupted service. The aim of the paper is to rank services provided by a set of cloud-providers based on multi-criteria decision-making (MCDM) methods. The ranking of the cloud-providers set is based on the Interval neutrosophic set theory (INS). The paper proposes INS and TOPSIS techniques to help users and experts express their evaluations and rank cloud-providers based on various criteria. INS is used to deal with the imprecise knowledge, generated by the ambiguity from the experts' evaluations. To demonstrate the effectiveness of the framework, the closeness index (CI) values of CSPs were ranked in decreasing order. A numerical example for a case study for a set 6 CSP and 10 criteria is presented. The numerical results show that SoftLayer's is the best cloud-provider with a CI value equal to 0.69. The worst cloud-provider is Microsoft Azure with a CI value equal to 0.20. A sensitivity analysis was performed to check the consistency and robustness of the model.

Enhanced computer network security assessment through employing an integrated LogTODIM-TOPSIS technique under interval neutrosophic sets

In the context of the development of the new era, computer network technology has become an indispensable and important technological means in people’s daily work and life. Through network technology, information resources can be collected, integrated, processed, and applied, thereby improving information analysis and mining capabilities, constructing big data environments for various industries, providing convenient and fast intelligent information services, and promoting social transformation and development. However, in practical development, network security issues seriously affect information security and social stability, and computer viruses and hackers pose a huge threat to computer systems. The computer network security evaluation is the MAGDM problems. Recently, the Logarithmic TODIM (LogTODIM) and TOPSIS technique has been utilized to cope with MAGDM issues. The interval neutrosophic sets (INSs) are utilized as a technique for characterizing uncertain information during the computer network security evaluation. In this paper, the interval neutrosophic number Logarithmic TODIM-TOPSIS (INN-LogTODIM-TOPSIS) technique is conducted to solve the MAGDM under INSs. Finally, a numerical case study for computer network security evaluation is utilized to validate the proposed technique. The prime contributions of this paper are put forward: (1) The entropy technique based on score values and accuracy value are conducted to obtain weight information under INSs; (2) an integrated INN-LogTODIM-TOPSIS technique is conducted to put forward the MAGDM issue; (3) An illustrative example for computer network security evaluation has been accomplished to put forward the INN-LogTODIM-TOPSIS technique.

Enhanced group decision-making framework for financial performance evaluation of high-tech enterprises under interval neutrosophic environment

The financial performance of enterprises has always been the key to their survival and development, especially for high-tech enterprises. Evaluating the financial performance of high-tech enterprises is beneficial for the management department to accurately understand the financial situation of the enterprise, timely identify financial problems, and study solutions based on this; On the other hand, the scientific evaluation of enterprise performance also provides useful assistance for other stakeholders such as the government, creditors, and enterprise employees to exercise their rights. With the development of the times and the progress of society, high-tech enterprises have developed rapidly. Studying the financial performance of high-tech enterprises has important theoretical and practical significance. The financial performance evaluation of high-tech enterprises is a classical MAGDM problems. Recently, the TODIM (TODIM) and (grey relational analysis) GRA technique has been employed to cope with MAGDM issues. The interval neutrosophic sets (INSs) are employed as a tool for characterizing uncertain information during the financial performance evaluation of high-tech enterprises. In this manuscript, the interval neutrosophic number TODIM-GRA (INN-TODIM-GRA) technique is implemented to solve the MAGDM under INSs. In the end, a numerical case study for financial performance evaluation of high-tech enterprises is employed to validate the proposed technique.

Smart algorithmic solutions for audience service quality evaluation for large-scale sports-events through harnessing interval neutrosophic EDAS and CRITIC Technique

Sports events, as large-scale events that provide products and services, have received widespread attention for their economic benefits and influence. Event organizers expect to achieve high efficiency by providing high-quality products and services. The quality of competition products and services is mainly evaluated through the subjective feelings of the audience, and usually the audience’s evaluation of service quality is vague. Therefore, this article intends to establish an evaluation index system for the quality of spectator service in sports events, in order to provide a reasonable evaluation of the service products provided by sports event organizers. The audience service quality evaluation for large-scale sports-events is a MAGDM problems. Recently, the EDAS and CRITIC technique has been employed to cope with MAGDM issues. The interval neutrosophic sets (INSs) are employed as a tool for characterizing uncertain information during the audience service quality evaluation for large-scale sports-events. In this paper, the interval neutrosophic number EDAS (INN-EDAS) technique based on the Hamming distance and Euclid distance is founded to manage the MAGDM under INSs. The CRITIC technique is employed to obtain the weight information based on the Hamming distance and Euclid distance under INSs. Finally, a numerical case study for audience service quality evaluation for large-scale sports-events is employed to validate the proposed technique. The main contributions of this paper are proposed: (1) The INN-EDAS technique based on the Hamming distance and Euclid distance is founded to manage the MAGDM under INSs; (2) The CRITIC technique is employed to obtain the weight information based on the Hamming distance and Euclid distance under INSs; (3) a numerical case study for audience service quality evaluation for large-scale sports-events is employed to validate the proposed technique.

A flexible group decision-making method for informationization teaching ability evaluation of university teachers integrating ExpTODIM and GRA under interval neutrosophic environment

Today, information technology has penetrated into various fields of universities, and the development of information technology in teaching, scientific research, management, and services has become a catalyst for promoting changes in universities. In terms of teaching informatization, the Internet provides a powerful tool for knowledge dissemination and a huge platform for learning and communication between university teachers and students. Knowledge sharing has become easier, and the era of mutual interaction between teachers and students has arrived. University teachers need to quickly face this challenge, adapt to the new teaching and learning environment, improve their own literacy, enhance their information-based teaching ability, change their teaching behavior, and thereby improve the quality of university education and meet the needs of society for talent cultivation. The informationization teaching ability evaluation of university teachers is a classical MAGDM problems. Recently, the Exponential TODIM(ExpTODIM) and (grey relational analysis) GRA method has been used to cope with MAGDM issues. The interval neutrosophic sets (INSs) are used as a tool for characterizing uncertain information during the informationization teaching ability evaluation of university teachers. In this manuscript, the interval neutrosophic number Exponential TODIM-GRA (INN-ExpTODIM-GRA) method is built to solve the MAGDM under INSs. In the end, a numerical case study for informationization teaching ability evaluation of university teachers is given to validate the proposed method.

Neutrosophic Fuzzy Interval Sets and its Extension through MCDM and Applications in E-Management

we are introducing the model-type operators over Interval-Valued Fuzzy Neutrosophic Sets with time moments [IVFNS] and learn a few of their properties with numerical examples to demonstrate the defined operations and operators. Also introduce various distance measures over the extension of interval neutrosophic sets as well as apply the introduced measures in ecological management in this direct to decide the type of corrosion disturbing some towns for valuable management to be taken, using this normalized distance measures. The extensions of neutrosophic connection values and non-connection values be not used for all time probable positive to our fulfillment, but this concept IVTNFS part has more significant responsibility at this point since the time progress with IVN-fuzzy sets provide the accurate solution in factual situations similarly, conclusion making, career deciding and so on. This is the main reason for taking in the extensions of neutrosophic sets.

A generalized integrated group decision-making framework for computer network security evaluation with Interval Neutrosophic information

The rapid development of global information technology, especially the emergence and widespread application of the Internet, has enabled information technology to quickly penetrate into various fields of the economy and society. Informatization and networking have become important features of today’s era. However, while people enjoy the tremendous progress brought by information technology to humanity, the openness and security vulnerabilities of computer networks have also made network information security issues increasingly prominent. The invasion of hackers, the continuous generation and spread of computer virus, and the rampant use of rogue software have all caused great economic losses to individuals, enterprises, and countries. The computer network security evaluation is a multiple-attribute group decision making (MAGDM). Then, the TODIM and TOPSIS method has been established to deal with MAGDM issues. The interval neutrosophic sets (INSs) are established as an effective tool for representing uncertain information during the computer network security evaluation. In this manuscript, the interval neutrosophic number TODIM-TOPSIS (INN-TODIM-TOPSIS) method is established to solve the MAGDM under INSs. Finally, a numerical example study for computer network security evaluation is established to validate the INN-TODIM-TOPSIS method. The main research contribution of this paper is established: (1) the INN-TODIM-TOPSIS method is put up for MAGDM with INSs; (2) the INN-TODIM-TOPSIS method is put up for computer network security evaluation and were compared with existing methods; (3) Through the detailed comparison, it is evident that INN-TODIM-TOPSIS method for computer network security evaluation proposed in this paper are effective.

A novel multi-parameter similarity measure of interval neutrosophic sets for medical diagnosis

The use of similarity measures in interval-valued neutrosophic sets (IVNSs) theory is essential for comparing and assessing the degree of IVNSs difference. However, existing similarity measures for IVNSs suffer from several issues such as lacking precise axiomatic definitions, counterintuitive results, division by zero errors, inability to distinguish between positive and negative differences, and failure to satisfy the ranking definition. To address these limitations, we propose a novel multi-parameter similarity measure for IVNSs based on the tangent function. We demonstrate that our measure satisfies the axiomatic definition and apply it to medical diagnosis, achieving accurate diagnostic results. Additionally, we consider the interactions between symptoms, adjust the proposed similarity measure using Choquet integrals, and provide analytical comparisons to demonstrate the advantages of our improved similarity measure, highlighting its stability and high confidence in the field of medical diagnosis.This study contributes to the advancement of similarity measures in IVNSs theory and provides valuable insights for the field of medical diagnosis.

Enhanced TODIM method based on VIKOR for interval neutrosophic MAGDM and applications to brand competitiveness evaluation of manufacturing enterprises

A brand is an enterprise’s market image and huge intangible assets. A brand is an enterprise’s market image and huge intangible assets, and it is also a comprehensive embodiment of an enterprise’s core competitiveness. Therefore, continuous improvement of brand competitiveness undoubtedly has far-reaching significance for manufacturing enterprises. Using the brand competitiveness evaluation index system and selected evaluation methods of manufacturing enterprises constructed in this article, the brand competitiveness evaluation index system and selected evaluation methods can not only study the overall brand competitiveness of the participating enterprises, but also understand the advantages and disadvantages of the brand competitiveness of the participating enterprises from different perspectives, To help and guide manufacturing enterprises to strengthen brand building in a targeted manner and continuously improve the brand competitiveness of manufacturing enterprises. The brand competitiveness evaluation of manufacturing enterprises is a classical MAGDM problems. Recently, the TODIM and VIKOR method has been used to cope with MAGDM issues. The interval neutrosophic sets (INSs) are used as a tool for characterizing uncertain information during the brand competitiveness evaluation of manufacturing enterprises. In this manuscript, the interval neutrosophic number TODIM-VIKOR (INN-TODIM-VIKOR) method is built to solve the MAGDM under INSs. In the end, a numerical case study for brand competitiveness evaluation of manufacturing enterprises is given to validate the proposed method.

A novel group decision making model based on Interval neutrosophic sets for product modeling design quality evaluation

The energy consumption of mechanical products in China is enormous, and the energy utilization rate is low, which is increasingly receiving people’s attention. Conducting product design for energy optimization is of great significance for improving energy utilization efficiency. The scheme design of a product is the key to achieving innovation in product design, and the evaluation and decision-making of the design scheme directly affect the results of the later stage of the design. Therefore, correctly evaluating and making reliable decisions on product design schemes that are oriented towards fuzzy decision optimization is an important aspect of product innovation conceptual design. The product modeling design quality evaluation is a multiple attribute group decision making (MAGDM) problems. Recently, the Combined Compromise Solution (CoCoSo) method and information entropy method has been employed to cope with MAGDM issues. The interval neutrosophic sets (INSs) are employed as a tool for portraying uncertain information during the product modeling design quality evaluation. In this paper, the CoCoSo method is designed for MAGDM under INSs. Then, the interval neutrosophic numbers CoCoSo (INN-CoCoSo) method based on the Hamming distance and Euclidean distance is built for MAGDM. The information Entropy method is employed to produce the weight information based on the Hamming distance and Euclidean distance under INNSs. Finally, a practical numerical example for product modeling design quality evaluation is supplied to show the INN-CoCoSo method. The main contributions of this paper are constructed: (1) This paper builds the novel MAGDM based on CoCoSo model under INSs; (2) The information Entropy method is employed to produce the weight information based on the Hamming distance and Euclidean distance under INNSs; (3) The new MAGDM method is proposed for product modeling design quality evaluation based on INN-CoCoSo.

A decision support method for designing the blended teaching effectiveness evaluation of English courses in universities based on interval-valued neutrosophic information

The goal of internationalization, the actual needs of the new generation of college students, and the innovation of information technology have led to a shift from teaching English for general purposes (EGP) to teaching English courses. The blended teaching effectiveness evaluation of English courses in universities in an output-oriented perspective is viewed as the multiple attribute decision making (MADM). In this paper, Taxonomy method is designed for MADM under interval neutrosophic sets (INSs). Then, the interval neutrosophic numbers Taxonomy (INN-Taxonomy) method is formed to cope with MADM problem. Finally, a numerical decision example for blended teaching effectiveness evaluation of English courses in universities in an output-oriented perspective is given to demonstrate the INN-Taxonomy method.

Research and evaluation on comprehensive obstacle-avoiding behavior for unmanned vehicles based on the interval neutrosophic number multiple attribute group decision making

With the advent of the information age, the development direction of automobiles has gradually changed, both from the domestic and foreign policy support attitude, or from the actual actions of the automotive industry and scientific research institutes’ continuous efforts, it is not difficult to see that driverless vehicle. At this time, the testing and evaluation of the intelligent behavior of driverless vehicles is particularly important. It is particularly important not only to regulate the intelligent behavior of unmanned vehicles, but also to promote the key It can not only regulate the intelligent behavior of unmanned vehicles, but also promote the improvement of key technologies of unmanned vehicles and the research and development of driver assistance systems. The evaluation of comprehensive obstacle-avoiding behavior for unmanned vehicles is often considered as a multi-attribute group decision making (MAGDM) problem. In this paper, the EDAS method is extended to the interval neutrosophic sets (INSs) setting to deal with MAGDM and the computational steps for all designs are listed. Then, the criteria importance through intercriteria correlation (CRITIC) is defined to obtain the attribute’s weight. Finally, the evaluation of comprehensive obstacle-avoiding behavior for unmanned vehicles is given to demonstrate the interval neutrosophic number EDAS (INN-EDAS) model and some good comparative analysis is done to demonstrate the advantages of INN-EDAS.

VIKOR and TOPSIS framework with a truthful-distance measure for the (t, s)-regulated interval-valued neutrosophic soft set.

This article introduces the structure of the -regulated interval-valued neutrosophic soft set (abbr. -INSS). The structure of -INSS is shown to be capable of handling the sheer heterogeneity and complexity of real-life situations, i.e. multiple inputs with various natures (hence neutrosophic), uncertainties over the input strength (hence interval-valued), the existence of different opinions (hence soft), and the perception at different strictness levels (hence -regulated). Besides, a novel distance measure for the -INSS model is proposed, which is truthful to the nature of each of the three membership (truth, indeterminacy, falsity) values present in a neutrosophic system. Finally, a Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and a Viekriterijumsko Kompromisno Rangiranje (VIKOR) algorithm that works on the -INSS are introduced. The design of the proposed algorithms consists of TOPSIS and VIKOR frameworks that deploy a novel distance measure truthful to its intuitive meaning. The conventional method of TOPSIS and VIKOR will be generalized for the structure of -INSS. The parameters and in the -INSS model take the role of strictness in accepting a collection of data subject to the amount of mutually contradicting information present in that collection of data. The proposed algorithm will then be subjected to rigorous testing to justify its consistency with human intuition, using numerous examples which are specifically made to tally with the various human intuitions. Both the proposed algorithms are shown to be consistent with human intuitions through all the tests that were conducted. In comparison, all other works in the previous literature failed to comply with all the tests for consistency with human intuition. The -INSS model is designed to be a conclusive generalization of Pythagorean fuzzy sets, interval neutrosophic sets, and fuzzy soft sets. This combines the advantages of all the three previously established structures, as well as having user-customizable parameters and , thereby enabling the -INSS model to handle data of an unprecedentedly heterogeneous nature. The distance measure is a significant improvement over the current disputable distance measures, which handles the three types of membership values in a neutrosophic system as independent components, as if from a Euclidean vector. Lastly, the proposed algorithms were applied to data relevant to the ongoing COVID-19 pandemic which proves indispensable for the practical implementation of artificial intelligence.

Similarity Measure for Interval Neutrosophic Sets and Its Decision Application in Resource Offloading of Edge Computing

Interval neutrosophic sets (INSs), characterized by truth, indeterminacy and falsity membership degrees, handle the uncertain and inconsistent information that commonly exists in real-life systems, and constitute an extension of the interval valued fuzzy set and interval valued intuitionistic fuzzy set. The existing works on similarity measures for INSs are mostly constructed by distance measures and entropies. Meanwhile, the degree of similarity is expressed as a single number, even if the interval-valued information is considered. This may lead to a loss of interval-valued information. In order to cope with these issues, in this paper, we introduce a new approach to constructing the similarity measures for INSs using fuzzy equivalencies. First, based on fuzzy equivalencies and aggregation operators, the definition of interval-valued fuzzy equivalence is generalized to interval neutrosophic values. Then, based on the framework of INSs, we propose the definition and construction method of the similarity measure using the interval neutrosophic fuzzy equivalence. The similarity degree is expressed as an interval and could retain more information than ever before. In addition, according to practical situations, one can obtain different similarities by selecting the parameters in fuzzy equivalence. Due to the increase in edge computing, it is necessary to reasonably offload the client’s resource and assign them to the edge server to balance the resource usage. The Similarity measure is conductive to select and match the client and edge server. Finally, an illustrative example verifies that the proposed method can find a reasonable client and edge server, as well as effectiveness in the edge computing application.

A multi-criteria decision-making with regret theory-based MULTIMOORA method under interval neutrosophic environment

The MULTIMOORA (multiple multi-objective optimization by ratio analysis) method is useful for multiple criteria decision-making method. It is based on expected utility theory and assumes that decision makers are completely rational. However, some studies show that human beings are usually bounded rational, and their regret aversion behaviors play an important role in the decision-making process. Interval neutrosophic sets can more flexibly depict uncertain, incomplete and inconsistent information than single-valued neutrosophic sets. Therefore, this paper improves the traditional MULTIMOORA method by combining the regret theory under interval neutrosophic sets. Firstly, the regret theory is used to calculate the utility value and regret-rejoice value of each alternatives. Secondly, the criteria weights optimization model based on the maximizing deviation is constructed to obtain the weight vector. Then, the MULTIMOORA method is used to determine the order of the alternatives. Finally, an illustrative example about school selection is provided to demonstrate the feasibility of the proposed method. Sensitivity analysis shows the validity of the regret theory in the proposed method, and the ranking order change with different regret avoidance parameter. Comparisons are made with existing approaches to illustrate the advantage of the proposed method in reflecting decision makers’ psychological preference.

Diabetic Retinopathy Diagnosis Using Interval Neutrosophic Segmentation with Deep Learning Model

In recent times, Internet of Things (IoT) and Deep Learning (DL) models have revolutionized the diagnostic procedures of Diabetic Retinopathy (DR) in its early stages that can save the patient from vision loss. At the same time, the recent advancements made in Machine Learning (ML) and DL models help in developing Computer Aided Diagnosis (CAD) models for DR recognition and grading. In this background, the current research works designs and develops an IoT-enabled Effective Neutrosophic based Segmentation with Optimal Deep Belief Network (ODBN) model i.e., NS-ODBN model for diagnosis of DR. The presented model involves Interval Neutrosophic Set (INS) technique to distinguish the diseased areas in fundus image. In addition, three feature extraction techniques such as histogram features, texture features, and wavelet features are used in this study. Besides, Optimal Deep Belief Network (ODBN) model is utilized as a classification model for DR. ODBN model involves Shuffled Shepherd Optimization (SSO) algorithm to regulate the hyperparameters of DBN technique in an optimal manner. The utilization of SSO algorithm in DBN model helps in increasing the detection performance of the model significantly. The presented technique was experimentally evaluated using benchmark DR dataset and the results were validated under different evaluation metrics. The resultant values infer that the proposed INS-ODBN technique is a promising candidate than other existing techniques.

Ideal theory of interval neutrosophic sets in subtraction algebras

In this paper, we introduce the notion of interval neutrosophic ideals in subtraction algebras. Also, introduce the intersection and union of interval neutrosophic sets in subtraction algebras. We prove intersection of two-interval neutrosophic ideals is also an interval neutrosophic ideal. Some exciting properties and results based on such an ideal are discussed. Moreover, we define the homomorphism and homomorphism of interval neutrosophic sets. We prove the image of an interval neutrosophic subalgebra is also an interval neutrosophic sub-algebra.

Multi-attribute group decision-making method based on weighted partitioned Maclaurin symmetric mean operator and a novel score function under neutrosophic cubic environment

Neutrosophic cubic set is the generalized version of neutrosophic sets and interval neutrosophic sets. It can deal with the complex information by combining the neutrosophic set (NS) and cubic set (CS). Maclaurin symmetric mean operator is a classical aggregation operator in modern information fusion theory. Partitioned MSM operator can reflect the interrelationships among attributes in the same partition, but the attributes in different partitions are irrelevant. In order to efficiently gather NCS information where the attributes in the same partition are relevant but the attributes in different partitions are irrelevant, we extend the PMSM operator to neutrosophic cubic environment and define the neutrosophic cubic partitioned Maclaurin symmetric mean (NCPMSM) operator and neutrosophic cubic weighted partitioned Maclaurin symmetric mean operator. Later, in order to overcome the drawbacks of the existing score functions and effectively distinguish two NCSs, we define a novel score function of NCS. Next, based on NCWPMSM operator and the novel score function, we develop a multi-attribute group decision-making method. Finally, we give an example of supplier selection to illustrate the usefulness of the proposed MAGDM. At the same time, a comparative analysis is to show the effectiveness and advantages of the proposed method compared with the existing methods.