Interval-valued Neutrosophic Sets Research Articles

Theory and Application of Interval-Valued Neutrosophic Line Graphs

Neutrosophic graphs are used to model inconsistent information and imprecise data about any real-life problem. It is regarded as a generalization of intuitionistic fuzzy graphs. Since interval-valued neutrosophic sets are more accurate, compatible, and flexible than single neutrosophic sets, interval-valued neutrosophic graphs (IVNGs) were defined. The interval-valued neutrosophic graph is a fundamental issue in graph theory that has wide applications in the real world. Also, problems may arise when partial ignorance exists in the datasets of membership [0, 1], and then, the concept of IVNG is crucial to represent the problems. Line graphs of neutrosophic graphs are significant due to their ability to represent and analyze uncertain or indeterminate information about edge relationships and complex networks in graphs. However, there is a research gap on the line graph of interval-valued neutrosophic graphs. In this paper, we introduce the theory of an interval-valued neutrosophic line graph (IVNLG) and its application. In line with that, some mathematical properties such as weak vertex isomorphism, weak edge isomorphism, effective edge, and other properties of IVNLGs are proposed. In addition, we defined the vertex degree of IVNLG with some properties, and by presenting several theorems and propositions, the relationship between fuzzy graph extensions and IVNLGs was explored. Finally, an overview of the algorithm used to solve the problems and the practical application of the introduced graphs were provided.

Cross-entropy method for interval-valued neutrosophic number multiple attribute decision making for education quality management evaluation in higher education institutions

Under the premise of today’s socialist modernization construction, the development and progress of the country require more outstanding talents such as aspiring youth and intellectuals to participate, which puts forward higher requirements for education quality indicators and various aspects of operation. As the main institution and environment for implementing educational activities, the effectiveness of school management organization has a direct impact and even a decisive role on the quality of education. Therefore, how to improve the quality management of school education has become a hot topic in the education industry. The education quality management evaluation in higher education institutions is viewed as the multiple-attribute decision-making (MADM) issue. In this paper, the interval-valued neutrosophic number cross-entropy (IVNN-CE) technique is built under interval-valued neutrosophic sets (IVNSs) based on the traditional cross-entropy technique. Then, combine traditional cross-entropy technique with IVNSs, the IVNN-CE technique is constructed for MADM under IVNSs. Finally, the numerical example for education quality management evaluation in higher education institutions was constructed and some comparisons is employed to verify advantages of IVNN-CE technique. The main contribution of this paper is constructed: (1) the cross-entropy model is extended to IVNSs; (1) the CRITIC technique is employed to construct the attribute weights under IVNSs; (3) the IVNN-CE technique is constructed to manage the MADM under IVNSs; (4) a case study about education quality management evaluation in higher education institutions is constructed to show the built technique; (5) some comparative algorithms are constructed to verify the rationality of IVNN-CE technique.

Modified MABAC for MCGDM with interval-valued neutrosophic sets and application to design quality evaluation of digital cultural and creative products

With the development of digital creative industry and the use of more emerging digital technologies, the forms of digital cultural and creative design products are also increasingly diversified. Unlike traditional cultural and creative design products, digital cultural and creative design products are no longer limited to physical products, but appear more in the field of exhibition, virtual reality and product visualization. At the initial stage of the combination of digital information technology and cultural and creative content, digital cultural and creative design products, unlike ordinary cultural and creative design products, opened a new vision for users. The design quality evaluation of digital cultural and creative design products is viewed as a multi-criteria group decision-making (MCGDM). The single-value neutrosophic sets (SVNSs) concept and its interval-valued version (Interval-valued neutrosophic sets, IVNSs) are within the recent rapid developments for managing the uncertain representation problem in MCGDM. In SVNSs, decision makers (DMs) could portray membership, non-membership and hesitancy. IVNSs expands this useful feature through portraying intervals to these three information decision degrees. In this manner, the uncertainty, ambiguity and vagueness hidden in human judgements could be quantified more efficiently. IVNSs have been widely employed and researched in MCGDM. The main purpose of this paper is to proposed the Interval-valued neutrosophic number MABAC (IVNN-MABAC) technique based on prospect theory (PT) to address the MCGDM. Eventually, an example for design quality evaluation of digital cultural and creative design products and some comparative analysis was employed to demonstrate the superiority of the designed technique.

Extension of arithmetic and geometric aggregating operators using new type interval-valued neutrosophic sets.

The purpose of this article is to present a novel approach to the (δ,ε) interval-valued neutrosophic set (IVNS). This is an extension of the IVNS. As a result of this article, we will discuss the concept of (δ,ε) interval valued neutrosophic weighted averaging (IVNWA), (δ,ε) interval-valued neutrosophic weighted geometric (IVNWG), (δ,ε) generalized interval-valued neutrosophic weighted averaging (GIVNWA) and (δ,ε) generalized interval-valued neutrosophic weighted geometric (GIVNWG). Additionally, the (δ,ε) IVNS approach is characterized by idempotency, boundedness, commutativity and monotonicity.

Q-rung square root interval-valued neutrosophic sets with respect to aggregated operators using multiple attribute decision making

This paper introduces the concept of multiple attribute decision making (MADM) using q-rung square root interval valued neutrosophic sets (q-rung SRIVNS). The interval valued neutrosophic set (IVNS) and the q-rung square root neutrosophic set (q-rung SRNS) deals with the q-rung SRIVNS. The purpose of this article is to provide an analysis of several aggregating operations. In this article, we discuss a novel idea for the q-rung square root interval valued neutrosophic weighted averaging (q-rung SRIVNWA), q-rung ortho square root interval valued neutrosophic weighted geometric (q-rung SRIVNWG), generalized q-rung SRIVN weighted averaging (q-rung GSRIVNWA) and generalized q-rung SRIVN weighted geometric (q-rung GSRIVNWG). Using Euclidean distances and Hamming distances is illustrated with examples. These sets will be subjected to various algebraic operations in this communication. By doing this, models will be more accurate and will be closed to an integer q. The four most important factors for courier services in India are reliability, turnaround time, payment options, and tracking capabilities. Expert judgments and criteria will determine the most appropriate options. Furthermore, several proposed and current models are compared to demonstrate their reliability and utility. A fascinating and intriguing conclusion can be drawn from the study.

Choice Optimal Fuel Alternative in Thermal Power Station Using Neutrosophic Set and MCDM Methodology

In a power plant, the fuel choice directly impacts the efficiency, cost, and ecological impact of generating electricity. For power plants to produce electricity effectively and affordably to fulfill the needs of consumers in homes, companies, and communities, they need a fuel supply that is constant, dependable, and inexpensive. In this study, we used the concept of multi-criteria decision-making (MCDM) to deal with the various criteria of fuel alternatives. We used the EDAS method as an MCDM methodology to rank the fuel alternatives and select the best one. The EDAS method is employed with the interval-valued neutrosophic sets (IVNSs) to deal with the uncertainty information in the evaluation process. We compute the weights of the criteria of thermodynamic parameters. We used ten thermodynamic parameters such as temperature, mass, energy, etc. Then, the principal results show that temperature is the best criterion, and the work interaction is the worst criterion in all criteria. The EDAS method ranked twenty alternatives. The results show that alternative 20 are the best and alternative 14 is the worst of all alternatives. We employed the sensitivity analysis to show the rank of alternatives under ten cases. The results show the 20 alternative is the best in all cases. The results are stable.

Cosine trigonometric rules applied to average and geometric aggregating operators using extension q-rung interval-valued neutrosophic set approach.

We introduce the concept of cosine trigonometric q-rung Diophantine neutrosophic interval-valued set (CosTq-rung DioNSIVS). The fact that CosTq-rung DioNSIVS combines q-rung neutrosophic interval-valued set, q-rung neutrosophic set and neutrosophic interval-valued set is one of its distinguishing characteristics. A new idea of CosTq-rung DioNSIVWA, CosTq-rung DioNSIVWG, GCosTq-rung DioNSIVWA and GCosTq-rung DioNSIVWG is proposed in this study. We also look at the idempotency, boundedness, commutativity, and monotonicity of the CosTq-rung DioNSIVS based on algebraic operations. We considered new kinds of two distances in the proposed models, besides Euclidean and Hamming distances. The CosTq-rung DioNSIVS method was used to analyze the cosine trigonometric aggregation procedures. The study's concluding results include several fascinating and captivating discoveries.

MADM framework based on interval-valued neutrosophic aczel-alsina power average operator and application to translation teaching quality evaluation of college English

The huge demand for translation talents has prompted the universities to focus on improving the quality of translation teaching. As a necessary means to improve the quality of teaching, translation teaching quality evaluation plays a role in guiding, regulating and managing translation teaching, which is an important part of translation teaching. The translation teaching quality evaluation of college English is viewed as the multiple attribute decision making (MADM). The interval-valued neutrosophic sets (IVNSs) are used as an effective tool for characterizing uncertain information during the translation teaching quality evaluation of college English. In this paper, interval-valued neutrosophic number (IVNN) Aczel-Alsina power average (IVNNAAPA) operator is proposed based on the classical Aczel-Alsina operator and power average (PA) operator. Then, IVNNAAPA operator is employed to cope with MADM problem. Finally, the numerical decision example for translation teaching quality evaluation of college English is employed to illustrate the produced method and some comparative models are used to prove the effectiveness of the IVNNAAPA method.

Charging Type Selection for Electric Buses Using Interval-Valued Neutrosophic Decision Support Model

Using electricity to fuel buses has always been known as a green option for the public bus operations considering the recent regulations on environmental and climate concerns. Emission-free public transportation modes such as electric buses improve local air quality and reduce noise pollution and also contribute to achieving sustainability goals by developing a sustainable transportation system. Many projects have been carried out using different charging strategies for electric buses around the world. However, selecting the most appropriate charging strategy for the electric buses in the public transportation is a challenging and multidimensional decision-making problem for transportation management sector. Therefore, this article proposes a decision support model based on the interval-valued neutrosophic set which uses Shannon's entropy and mixed aggregation by comprehensive normalization technique to choose the most appropriate charging type for urban electric buses among alternatives such as opportunity, depot, inductive, and no shift. This article presents a real-life case study in Turkey to illustrate the applicability and advantages of the proposed model. Extensive sensitivity analysis and comparative analysis tests are conducted to show the robustness of the proposed methodology. The results show that depot charging is the most suitable charging strategy for Istanbul's bus operator system.

Uncertainty and decision-making with multi-polar interval-valued neutrosophic hypersoft set: A distance, similarity measure and machine learning approach

The issue of decision-making (DM) is intricate due to the environment's ambiguous, imprecise, and uncertain nature, particularly when multiple attributes are involved and further subdivided. To address such complex problems, the concept of the hypersoft set has been employed. This article shows how to combine the multi-polar interval-valued neutrosophic set with the hypersoft set. This can help you solve DM problems that have more than one attribute. Additionally, we define similarity measures for multipolar interval-valued neutrosophic hypersoft sets (mPIVNHSs). We discuss the proposed extensions' definitions and mathematical operations and present an algorithm to solve DM problems related to everyday life using the proposed operators under mPIVNHSs. A machine learning method called K-Nearest Neighbor (KNN) is also employed to calculate ranking in the selection of sites for a new store. By utilizing the potential of data point similarity, K-Nearest Neighbors (KNN) and similarity measurements have practical value in daily life. KNN mimics the human propensity to draw from related experiences, resulting in applications like customized suggestions. Parallel to this, similarity metrics statistically evaluate resemblance to support tasks like personalized advice across fields like biology and social networks. Finally, we conclude the present study by comparing it with the existing studies, and future directions are also given.

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.

Neutrosophic multiplicative preference relations based on consensus analysis and additive consistency in group decision making: A goal programming approach

Multiplicative preference relations can be expanded into Neutrosophic multiplicative preference relations (NMPR) and Interval Neutrosophic Multiplicative Preference Relations (INMPR). They are appropriate for capturing the experts' assessments' uncertainty, ambiguity, and indeterminacy. This work aims to provide a consistency and consensus-based approach for dealing with group decision-making using NMPRs and INMPRs, as well as many goal programming models to manage the consistency and consensus of NMPRs and INMPRs. To define and measure acceptable consistency for NMPRs and INMPRs, the study first offers a consistency index. Several consistency-based programming approaches are designed to address the inconsistency and provide an appropriate consistent NMPR and INMPR for an NMPR and INMPR that are not consistent enough. We provide a consistency-based approach to NMPR and INMPR decision-making. Then, considering the consensus in GDM, a consensus index is suggested for determining the level of agreement between specific NMPRs and INMPRs. Thereafter, a group NMPR and INMPR are created by combining individual NMPRs and INMPRs using an aggregation operator that ensures the consistency of the group NMPRs and INMPRs. With a collection of NMPRs and INMPRs, a consistency- and consensus-based GDM approach is built on single-valued neutrosophic sets (SVNS) and interval-valued neutrosophic sets (IVNS). Finally, two real-world numerical examples are shown, along with a comparison. The proposed method checked the individual consistency level and the group consensus, which is less than the existing method. The ranking of the alternatives was given, which was more convincing than the existing methods. It is also clear that it is much simpler than the previous methods.

Toward Energy Transformation: Intelligent Decision-Making Model Based on Uncertainty Neutrosophic Theory

There has been an increasing tendency for the generation of energy from diverse renewable resources because of the application of contemporary pollution mitigation and justification regulations. Precisely a consequence, choosing the best renewable energy source might be considered a challenging issue given the complexity of the future conditions in any society. Environmental, economic, social, and technical aspects are merely some of the factors that are taken into consideration while evaluating renewable energy sources (RnESs). The suitable RES selection problem, which relies on ambiguous and imprecise data, is also influenced by a variety of circumstances. Hence, this study constructs multi-stages intelligent decision-making model (MsIDMM) based on multi-criteria decision making (MCDM) with support with neutrosophic theory especially, interval valued neutrosophic sets to rank the sources of renewable energy. Ultimately, combinative distance-based assessment (CODAS) method under interval-valued neutrosophic sets is used to rank the sources of renewable energy.

Supply chain performance: a novel integrated decision-making model

PurposeKnowledge 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.Design/methodology/approachIntegrating 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.FindingsThe 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.Originality/valueThis 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.

Combining grey relation analysis with MCGDM to evaluate the higher education management quality with interval-valued neutrosophic sets

With the continuous deepening of higher education management reform, university leaders have realized that the merger of universities, annual expansion of enrollment, and expansion of educational scale have broadened the development space for universities. At the same time, many management problems have also emerged, and education management problems are particularly prominent, such as some decisions, plans, instructions, etc. of the school level education management department not being well implemented in various departments, and the channels for the school level education management department to understand the true situation of each department are not smooth. Therefore, deepening reform provides a good opportunity for universities to strengthen management and streamline relationships. Teaching and scientific research must be upgraded, and the quality of teaching management must be improved. Establishing an education management quality evaluation system and emphasizing the quality of education management work are the key. The higher education management quality evaluation is affirmed as multi-criteria group decision-making (MCGDM). Interval-valued neutrosophic sets (IVNSs) have been widely used and researched in MCGDM. The interval-valued neutrosophic sets (IVNSs) could depict the uncertain information within the higher education management quality evaluation. The purpose of this article is to proposed a new improved grey relation analysis (GRA) method based on prospect theory (PT-GRA) to solve the MCGDM under IVNSs. At the end of this paper, an example for higher education management quality evaluation is illustrated through the built method and the comparison. Thus, the main contribution of this study is: (1) the PT-GRA method is used to deal with the MCGDM problems under IVNSs; (2) the weight information is obtained through entropy method; (3) an empirical example for higher education management quality evaluation has been given. (4) some comparative algorithms are given to show the rationality of PT-GRA method with IVNSs.

Comprehensive evaluation of sustainable consumption towards green growth based on an interval valued Neutrosophic TOPSIS approach.

Sustainable consumption is crucial in reducing the growing pressure of environmental crises. This study proposes the Technique of Order Preference by Similarity to the Ideal Solution (TOPSIS) approach to evaluate sustainable consumption toward green growth. The proposed approach assesses criteria weights in Interval Valued Neutrosophic Sets (IVNSs) using the Method of Maximizing Deviation. The proposed method evaluates sustainable consumption for ten selected developed and developing countries, including Canada, France, Japan, China, Indonesia, Korea, Malaysia, Singapore, Thailand, and Vietnam. The evaluation process encompasses four main criteria with eight sub-criteria, namely environment (population density, CO2), energy (total natural resource rents, renewable electricity), economics (value added of agriculture, forestry, and fishing, GDP per capita), and health (fertility rate, mortality rate). The countries are ranked based on the relative closeness coefficient. The results reveal that two economic sub-criteria are pivotal in the sustainable consumption rankings. Canada emerges as the country with the highest degree of green growth, attributed to its extensive land area and potential for renewable energy. Based on the findings, this study proposes some policy implications for Vietnam, including balancing fertility and mortality rates and regulating economic growth and resource exploitation.

Properties of interval-valued quadripartitioned neutrosophic graphs with real-life application

The interval-valued quadripartitioned neutrosophic set is represented by the partition of the interval-valued neutrosophic set’s indeterminacy function into contradiction and ignorance parts. This article introduces the properties of interval quadripartitioned single valued neutrosophic graph. The properties like complementary, self-complementary, strong and complete interval-valued quadripartitioned neutrosophic graphs are investigated. The finest illustration of locating a climate conducive to apricot cultivation in Ladakh is provided by the notion that has been offered. The model gives us details on the location that should be chosen for apricot farming. Using the proposed concepts, we highlight potential applications of the usual apricot plant that thrives in extremely cold climates and is appropriate for higher production. The adopted approach makes a superior fit to consider the problems in application viewpoint.

Neutrosophic MCDM Methodology for Evaluation Onshore Wind for Electricity Generation and Sustainability Ecological

The conviction in the necessity of renewable energy has been prompted by both the constantly increasing need for power production and the ecological issues of recent years. When it comes to generating power in a sustainable manner, wind is among the most essential renewable energy sources. This research attempts to present a structural technique for assessing the performance of operational onshore wind facilities with respect to the three dimensions of sustainability. The energy production, environmental effect, and practicability of onshore wind facilities are all dependent on accurate assessments. Wind resources, site accessibility, environmental impact, permitting and regulatory requirements, turbine technology, maintenance and operation, interconnection and transmission, and other criteria and factors are discussed in this research paper. Renewable energy, cost-effectiveness, dependability, and job creation are only a few of the advantages of onshore wind facilities that are mentioned. This study used the interval-valued neutrosophic set with the Weighted Sum Model (WSM) method to compute the weights of criteria and rank the alternatives. We got the wind speed and direction as the best criterion. The potential energy production of a wind plant is heavily dependent on the local wind speed and direction.

IVNN-Taxonomy method for teaching effect evaluation of “micro-ideological and political” model in medical colleges and universities

How to make good use of new network technology and design the classroom teaching of a course needs to be based on the teaching object, teaching content, and the teacher’s mastery of the technology and teaching platform. In teaching design, scholars also put forward different teaching links based on their own teaching experience. The cooperative learning links should be designed in college teaching. To build a positive and interdependent organizational structure and an equal and democratic learning atmosphere will help students to stimulate their learning motivation and sense of responsibility. The fuzzy evaluation of the teaching effect of the “micro-ideological and political” model in medical colleges and universities is viewed as the multiple attribute group decision making (MAGDM) issue. In such paper, Taxonomy method is designed for solving the MAGDM under interval-valued neutrosophic sets (IVNSs). First, the score function of IVNSs and Criteria Importance Though Intercrieria Correlation (CRITIC) method is used to derive the attribute weights. Second, then, the interval-valued neutrosophic numbers Taxonomy (IVNN-Taxonomy) method is built to deal with MAGDM problem. Finally, a numerical example for teaching effect evaluation of the “micro-ideological and political” model in medical colleges and universities is given to illustrate the built method.

An interval-valued neutrosophic based MAIRCA method for sustainable material selection

A plethora of Multi-Criteria Decision-Making (MCDM) methods is available for selecting an optimal material for a design problem with quantitative measurements. However, little research has been conducted on material selection methods in an interval neutrosophic environment to address uncertainty. In this research paper, a unique framework is presented that combines Interval-Valued Neutrosophic Sets (IVNSs) with the entropy–MultiAtributive Ideal-Real Comparative Analysis (MAIRCA) framework with the aim of simultaneously handling the objective criteria with crisp inputs and subjective criteria with ambiguous or uncertain information. To demonstrate the applicability of the proposed approach, a wing-spar of a Human-Powered Aircraft (HPA) is considered. At first, a panel of three subject experts makes judgments on the alternatives or criteria linguistically through IVNSs. Next, the skill level of each expert involved in the decision-making process is assessed using a novel weighting approach with linguistic information. After obtaining the objective criteria weights using the entropy weighting method, the performance of candidate materials for the HPA spar is evaluated using the MAIRCA method. The results indicate that S-glass70%-Epoxy Continuous Fibers, Ti-2Fe-3Al-10V and Al-7075 T6 are the top-ranked alternatives for spar application. The strong correlation of the proposed approach with other extant MCDM techniques demonstrates the reliability of the results obtained. In addition, the efficacy and practicality of the material selection tool is also validated with an outranking method in a simplified neutrosophic environment.