Interval-valued Neutrosophic Sets Research Articles

An integrated Neutrosophic sets with MCDM methodology for location-allocation of relief centers

To aid those who have been affected by an earthquake, it is necessary to set up temporary relief facilities. The careful selection of suitable locations for these centers has a considerable impact on the procedures involved in the handling of urban emergencies. In this study, the decision model known as the VIKOR was used to determine the placement of relief centers in Cairo's district and the distribution of available space among them. The selection best location contains uncertainty, so the interval-valued neutrosophic sets were used to overwhelmed this vagueness. To begin, we will use VIKOR, which is the suggested clustering approach. The average method is used to compute the weights of selected criteria. Then the VIKOR technique is used to order and select the best location. The results of the implementation demonstrate that VIKOR, the clustering approach, is adequate in most situations. This strategy is suited for resolving such difficult site selection and allocation issues.

Interval Valued Pentapartitioned Neutrosophic Graphs with an Application to MCDM

The concept of interval valued pentapartitioned neutrosophic set is the extension of interval-valued neutrosophic set, quadripartitioned neutrosophic set, interval valued quadripartitioned neutrosophic set and pentapartitioned neutrosophic set. The powerful mathematical tool known as the interval valued pentapartitioned neutrosophic set divides indeterminacy into three separate components: unknown, contradiction, and ignorance. There are several applications for graph theory in everyday life, and it is a rapidly growing topic. The concept of an interval valued pentapartitioned neutrosophic set is used in graph theory. A decision-making method ( multicriteria, MCDM) is proposed by using the developed Interval valued Pentapartitioned Neutrosophic set with a numerical illustration. In this paper, as an extension of interval valued neutrosophic graph theory, we introduce the notions of Interval-Valued Pentapartitioned Neutrosophic Graph (IVPPN-graph) with degree, size, and order of an IVPPN-graph.

Construction of New Similarity Measures and Entropy for Interval-Valued Neutrosophic Sets with Applications

Construction of New Similarity Measures and Entropy for Interval-Valued Neutrosophic Sets with Applications

Single-Valued and Interval-Valued Neutrosophic Hidden Markov Model

Neutrosophic sets are employed to be handled indeterminacy in a real-life situation. Thus, neutrosophic approaches in the medical domain prove their excellence. The neutrosophic hidden Markov model is an inventiveness domain for uncertainty. The existing hidden Markov models are not able to consider the uncertainty information, but the neutrosophic hidden Markov model effectively finds the optimal path between the states where vagueness exists. The proposed study comprises the idea of single-value and interval-valued neutrosophic sets into the hidden Markov model and decoding the path using the Viterbi algorithm. It has been used to determine the sequence of motility primitives for an afforded time series. The method is to be handled without having a lower membership function for falsity, and because of this advantage, one can save time significantly during computation. The neutrosophic score helps to find the crisp value of the probability. Moreover, the proposed work highlights the main childhood obesity risk in lockdown situations.

Fuzzy multi-attribute decision making method based on new similarity measure under interval-valued neutrosophic sets

Interval-valued neutrosophic set (IVNS) plays an important role in dealing with imprecise judgment information. For a multi-attribute decision making problem, the information of alternatives under different attributes is given in the form of interval valued neutrosophic number(IVNN). The objective of the presented paper is to develop a multiple-attribute decision making (MADM) method under interval-valued neutrosophic sets(IVNSs) using the new similarity measurement. The similarity measurement of IVNSs has always been a research hotspot. A new similarity measurement of IVNSs is first proposed in this paper based on Chebyshev distance. The proposed method enriches the existing similarity measurement methods. It can be applied to not only IVNSs, but also single-valued neutrosophic sets(SVNSs). The influence of each attribute on the decision-making result can be described by the weight. How to formulate the weight scientifically is vital as well. In this paper, the objective weight is calculated by normalizing the grey correlation coefficient obtained by a score function which can be applied to IVNSs. The objective weight is then combined with the subjective one by considering an adjustment factor with the weighted summation method. The adjustment factor is determined by the importance of subjective weight. Finally, an example is used to illustrate the comparison results of the proposed algorithm and other three ones. The comparison shows that the proposed algorithm is effective and can identify the optimal scheme quickly.

Application Of Inclusion Measure In Interval Valued Neutrosophic Sets

In this paper, we discuss about Inclusion Measure for ranking the Interval Valued Neutrosophic Sets (IVNSs) by using some distance measure concepts. Inclusion Measure is an easy way to understand the ranking method between IVNSs. We finally illustrate a multi attribute decision making problem to reveal the strength and usefulness of Inclusion Measure.

Adaptive Autonomous Robot Navigation by Neutrosophic WASPAS Extensions

In this research, a novel adaptive frontier-assessment-based environment exploration strategy for search and rescue (SAR) robots is presented. Two neutrosophic WASPAS multi-criteria decision-making (MCDM) method extensions that provide the tools for addressing the inaccurate input data characteristics are applied to measure the utilities of the candidate frontiers. Namely, the WASPAS method built under the interval-valued neutrosophic set environment (WASPAS-IVNS) and the WASPAS method built under the m-generalised q-neutrosophic set environment (WASPAS-mGqNS). The indeterminacy component of the neutrosophic set can be considered as the axis of symmetry, and neutrosophic truth and falsity membership functions are asymmetric. As these three components of the neutrosophic set are independent, one can model the input data characteristics applied in the candidate frontier assessment process, while also taking into consideration uncertain or inaccurate input data obtained by the autonomous robot sensors. The performed experiments indicate that the proposed adaptive environment exploration strategy provides better results when compared to the baseline greedy environment exploration strategies.

A multi-distance interval-valued neutrosophic approach for social failure detection in sustainable municipal waste management

Developing sustainable municipal waste management systems requires an in-depth analysis and synthesis of economic, environmental, and social sustainable development indicators. However, despite its profound impact on organizational performance, social sustainability has received little attention in previous studies compared to economic and environmental sustainability. Although a few studies have been conducted to analyze and measure the impact of social sustainability indicators, most of these endeavors fail to consider many indicators that must be evaluated under uncertain and incomplete information. This study proposes a new decision model that implements Interval-Valued Neutrosophic Sets (IVNS) within a multi-distance measure defined with respect to an ideal reference solution. IVNS allows decision-makers to reliably express their opinions using truth, indeterminacy, and falsity membership functions. A linguistic framework is developed to categorize indicators based on their performance and suggest potential solutions when detecting indicators with relatively weak performances. Social sustainability failures in the municipal waste management system of Istanbul are investigated to show the applicability and efficacy of the proposed approach. We identify salary satisfaction and health insurance as the most significant social indicators determining the success of the system, while freedom of association and citizen participation are categorized as the worst-performing ones. The stability of the proposed methodology is illustrated by performing a comparative analysis with Single-Valued Neutrosophic Sets and Interval-Valued Fuzzy Pythagorean Sets.

Interval Valued Neutrosophic Sets and Multi-Criteria Decision Making for Sustainable Mobile Healthcare Promotion

The use of health mobile websites or apps on smartphones like mobile-phones has made it possible for users to have quick, inexpensive access to the services of licensed medical professionals. As a result, mobile health care has the potential to lessen the burden on the healthcare system by lowering costs, decreasing wait times, and maximizing the effectiveness of available resources. In order to foster the long-term growth of healthcare infrastructure. This paper introduce the interval valued neutrosophic sets (IVNSs) to overcome the uncertainty. The IVNSs is combined with the MCDM methodology such as TOPSIS method. The TOPSIS technique is used to order the options. In addition to assisting with the selection of the best mobile health care option, this methodology may be used to close the performance gap between competing products and meet customer expectations. There were four distinct categories of mobile health care products investigated.

Multi-criteria Decision Making based on EDAS Approach for Business Risk Assessment in Electricity Retail Companies

This paper introduce a multi- criteria decision making (MCDM) perfect to assess business risk in electricity retail company to decrease risk loss and mange risks of business. The evaluation of business risk in electricity company included many conflicting criteria such as risk of political, risk of economic, and risk of market. So, this paper presented an Evaluation based on distance from average solution (EDAS) MCDM method to compute the weights of these criteria and rank the alternatives. Distances between each option and the mean answer on each criteria form the basis of EDAS. It expedites the decision-making process by streamlining the computation of distances to the deal solution. But in this evaluation, there are many imperfect and unclear data. So, the neutrosophic sets is presented to overcome this vague information. The interval valued neutrosophic sets (IVNSs) is a type of neutrosophic sets is presented in this work.

Car Sharing Station Choice by using Interval Valued Neutrosophic WASPAS Method

Adding car-sharing to existing public transit options is a great idea. However, finding the right location for a car-sharing station is difficult. The car-sharing station choice has many conflicting criteria, so the multi-criteria decision-making idea is used to deal with various conflict criteria. The process of choosing a suitable car-sharing station is containing vague and imprecise information. So, the neutrosophic set (NS) is used to overcome this problem. This paper introduced a framework consisting of the weighted aggregated sum product assessment (WASPAS) method with the NS. The WASPAS is an MCDM method. The WASPAS is used to compute the importance of criteria and the importance of alternatives. The WASPAS is a hybrid with interval-valued neutrosophic sets (IVNS). The suggested framework is applied to select car-sharing stations. This paper can help decision-makers in selecting the location to install a car sharing station.

Interval-Valued Neutrosophic Deductive Systems of Hilbert Algebras

Interval-valued neutrosophic sets (IVNSs) are a notion that was initially developed by Wang et al.19 The idea of IVNSs to deductive systems (DSs) in Hilbert algebras is presented in this study. It is shown how intervalvalued neutrosophic deductive systems (IVNDSs) relate to their level cuts. In addition, certain related features are examined as well as the homomorphic inverse image of IVNDSs in Hilbert algebras.

Multi-Criteria Data Analysis with Interval-Valued Neutrosophic Sets to Decrease Plastic Pollution rivers

Whether for human consumption, agricultural production, or industrial processes, groundwater, and rivers, in particular, are crucial. The river is a major water source; therefore, we must do all we can to keep it clean. Inconsistencies in data, algorithms and expert judgments have contributed to the growing recognition of ambiguity analysis' significance. However, it is not common practice to include vulnerability assessment in MCA based Interval-Valued Neutrosophic Sets (IVNSs). To better understand what causes MCA uncertainty, this research examines the factors that contribute to it. Probabilistic techniques, indicator-based methods, and neutrosophic logic are examined as examples of broad approaches to analysis methods in MCA. The practicality, financial and ecological consequences, unexpected social and environmental implications, possible scale of change, and confirmation of the impact of plastic reduction strategies were investigated using an MCA technique.

Interval-Valued Neutrosophic Ideals of Hilbert Algebras

The concept of interval-valued neutrosophic sets (IVNSs) was first introduced by Wang et al. (Wang, H.; Smarandache, F.; Zhang, Y. Q.; Sunderraman, R. Interval neutrosophic sets and logic: Theory and applications in computing. Hexis, Phoenix, Ariz, USA, 2005.). In this paper, the concept of IVNSs to ideals of Hilbert algebras is introduced. The homomorphic inverse image of interval-valued neutrosophic ideals (IVN ideals) in Hilbert algebras is also studied and some related properties are investigated.

Interval Valued Neutrosophic VIKOR Method for Assessment Green Suppliers in Supply Chain

In order to remain competitive, businesses must now invest in developing environmentally responsible green suppliers. The purpose of this article is to determine which vendors should be incorporated into green supplier growth programs in order to enhance their ecological sustainability, as well as the suppliers' current greenenvironmental efficiency. Factor evaluation was used to examine the reliability of the parameters used to assess green suppliers' efficiency and overall quality. To determine which provider offers the greatest ecological performance, the suggested technique uses a hybrid interval-valued neutrosophic set (IVNS) and VIKOR structure to assign relative importance to each criterion. To manage ambiguity while choosing choices, we combine the neutrosophic method with the VIKOR technique. We used 10 criteria and ten vendors in this research to demonstrate the usefulness and effectiveness of the suggested framework. The suggested methodology is applied in the application.

Some Notions on Interval-Valued Neutrosophic Sets

In this study, we give some new notions such as intersection, union and complement on interval-valued neutrosophic sets and introduce basic properties related these notions.

Correlation coefficients of credibility interval-valued neutrosophic sets and their group decision-making method in single- and interval-valued hybrid neutrosophic multi-valued environment

Although a single-valued neutrosophic multi-valued set (SVNMVS) can reasonably and perfectly express group evaluation information and make up for the flaw of multi-valued/hesitant neutrosophic sets in group decision-making problems, its information expression and group decision-making methods still lack the ability to express and process single- and interval-valued hybrid neutrosophic multi-valued information. To overcome the drawbacks, this study needs to propose single- and interval-valued hybrid neutrosophic multi-valued sets (SIVHNMVSs), correlation coefficients of consistency interval-valued neutrosophic sets (CIVNSs), and their multi-attribute group decision-making (MAGDM) method in the setting of SIVHNMVSs. First, we propose SIVHNMVSs and a transformation method for converting SIVHNMVSs into CIVNSs based on the mean and consistency degree (the complement of standard deviation) of truth, falsity and indeterminacy sequences. Then, we present two correlation coefficients between CIVNSs based on the multiplication of both the correlation coefficient of interval-valued neutrosophic sets and the correlation coefficient of neutrosophic consistency sets and two weighted correlation coefficients of CIVNSs. Next, a MAGDM method is developed based on the proposed two weighted correlation coefficients of CIVNSs for performing MAGDM problems under the environment of SIVHNMVSs. At last, a selection case of landslide treatment schemes demonstrates the application of the proposed MAGDM method under the environment of SIVHNMVSs. By comparative analysis, our new method not only overcomes the drawbacks of the existing method, but also is more extensive and more useful than the existing method when tackling MAGDM problems in the setting of SIVHNMVSs.

Fusion of interval-valued neutrosophic sets and financial assessment for optimal renewable energy portfolios with uncertainties

Renewable energy has been actively researched and developed in many countries to replace the conventional energy resources that come from fossil fuels. As social and environmental awareness of the renewable energy has grown, it is essential to address both quantitative factors and qualitative factors in determination of the optimal renewable energy portfolio. This paper proposes a novel approach to integrate a financial model and a fuzzy model to analyze both quantitative and qualitative factors. The financial model is utilized to calculate the quantitative factors, thereby assisting experts make judgments more accurately in the fuzzy model. The fuzzy model is utilized to evaluate the qualitative factors based on the expert judgements. Moreover, this paper proposes multi-segment judgment model that analyzes the evaluation of different groups, including government, investor and user groups. The results show that each group has different priority order. For example, the highest-priority factor of Government, Investor and User is environmental (with a score of 0.665), economic (with a score of 0.854), and technological criteria (with a score of 0.771), respectively. The results also indicated that small-scale onshore wind energy, large-scale onshore wind energy and solar energy is the best option for Government, Investor and User, respectively.

A fault detection method for FADS system based on interval-valued neutrosophic sets, belief rule base, and D-S evidence reasoning

Fault detection, with the characteristics of strong uncertainty and randomness, has always been one of the research hotspots in the field of aerospace. Considering that devices will inevitably encounter various unknown interference in the process of use, which greatly limits the performance of many traditional fault detection methods. Therefore, the main aim of this paper is to address this problem from the perspective of uncertainty and randomness of measurement signal. In information engineering, interval-valued neutrosophic sets (IVNSs), belief rule base (BRB), and Dempster-Shafer (D-S) evidence reasoning are always characterized by the strong ability in revealing uncertainty, but each has its drawbacks. As a result, the three theories are firstly combined in this paper to form a powerful fault detection algorithm. Besides, a series of innovations are proposed to improve the method, including a new score function based on p-norm for IVNSs and a new approach of calculating the similarity between IVNSs, which are both proved by authoritative prerequisites. To illustrate the effectiveness of the proposed method, flush air data sensing (FADS), a technologically advanced airborne sensor, is adopted in this paper. The aerodynamic model of FADS is analyzed in detail using knowledge of aerodynamics under subsonic and supersonic conditions, meanwhile, the high-precision model is established based on the aerodynamic database obtained from CFD software. For further confirming the validity and feasibility, a comparison with the methods based on parity equation, χ2 distribution, and information fusion method ordered weighted averaging (OWA) with three sets of weight vectors are conducted.

Distance, similarity and entropy measures of dynamic interval-valued neutrosophic soft sets and their application in decision making

In this paper, we introduce the notion of dynamic interval-valued neutrosophic soft sets (DIVNSSs) by embedding the time factor to interval-valued neutrosophic soft sets (IVNSSs). We also present some related set theoretic operations, such as complement, union, intersection, and-product, and or-product. Then, we propose the information measures of DIVNSSs, including the distance, similarity, and entropy measures. And we develop three corresponding decision making methods. In the decision making process, we employ a nonlinear programming model to weight every single time objectively, considering that the importance degrees of every single time are quite different. Further, we put forward a dynamic interval-valued neutrosophic soft aggregation rule to combine the parameter weights evaluated by all experts under every single time. Moreover, we give a numerical example to display the application of the proposed methods in decision making. Finally, we present a sensitivity analysis of the parameter time-degree and a comparative analysis with the methods of IVNSSs and interval-valued neutrosophic sets (IVNSs). The results show the effectiveness and superiority of the proposed method in solving the problem with dynamic inconsistent information.