Interval Neutrosophic Numbers Research Articles

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.

A computational trust model for social IoT based on interval neutrosophic numbers

Nowadays, the trend of evolution of connected devices, communication networks, and cloud services towards the internet of things (IoT) has facilitated the interaction between smart objects with minimal human mediation. Considering IoT, where smart objects can be clients and providers of services for each other, trust between objects is a significant concern for selecting the most appropriate service providers. Trust is an uncertain concept, and its uncertainty originates from different sources, including context conditions, social relationships, and the accuracy of quantitative evaluations. Modeling and considering uncertainty in trust management for the IoT is the principal objective of this research. To this aim, several sources of uncertainty are modeled in trust calculations where interval neutrosophic numbers are used for modeling imprecision, indeterminacy, and inconsistency of the trustworthiness data. In the proposed model, trust in the quality of the provided services (QoS trust), as well as trust in the honesty of the socially related entities providing trust-related information (i.e. social trust), and trust in the suitability of context conditions (i.e. context-trust) are considered to calculate the overall trust used for the decision-making process. The impact of each of these dimensions on the final calculated trust has been evaluated in different scenarios.

Cloud service recommendation for small and medium-sized enterprises: A context-aware group decision making approach

Recently, the enormous advantages of cloud services make them increasingly appealing to the small and medium-sized enterprises. The growing number of available services makes it challenging to select trustworthy services. Existing approaches focus on user preferences to guide personalized services recommendation for individual users, but lack of the research on trustworthy service recommendation for the small and medium-sized enterprises that represents a group user consisting of multiple individual users. For this type of enterprise, the cloud services recommendation must address the challenges from the diverse client context of individual users, the imprecise quality of experience in an uncertain cloud environment and the invalid or unsatisfactory recommendations. A client context-aware approach is proposed to recommend trustworthy cloud services for the small and medium-sized enterprises based on non-compensatory multi-criteria decision-making. In it, a type of client context is viewed as an independent evaluation criterion, and the interval neutrosophic numbers are employed to measure the fuzzy trustworthiness of cloud services. Based on the investigated outranking relations of interval neutrosophic numbers, a non-compensatory multi-criteria decision-making procedure via an improved ELECTRE III method is developed to rank candidate services. Experimental results demonstrate that this approach could efficiently produces the accurate ranking results of cloud services and effectively recommend the trustworthy service for small and medium-sized enterprises.

A study on a new method for solving interval neutrosophic linear programming problems

Neutrosophic set theory is a generalization of the intuitionistic fuzzy set which can be considered as a powerful tool to express the indeterminacy and inconsistent information that exist commonly in engineering applications and real meaningful science activities. In this paper an interval neutrosophic linear programming (INLP) model will be presented, where its parameters are represented by triangular interval neutrosophic numbers (TINNs) and call it INLP problem. Afterward, by using a ranking function we present a technique to convert the INLP problem into a crisp model and then solve it by standard methods

Multi-criteria decision making based on induced generalized interval neutrosophic Choquet integral.

In this paper, two new aggregation operators based on Choquet integral, namely the induced generalized interval neutrosophic Choquet integral average operator(IGINCIA) and the induced generalized interval neutrosophic Choquet integral geometric operator(IG-INCIG), are proposed for multi-criteria decision making problems (MCDM). Firstly, the criteria are dependent to each other and the evaluation information of the criteria are expressed by interval neutrosophic numbers. Moreover, two indices which are inspired by the geometrical structure are established to compare the interval neutrosophic numbers. Then, a MCDM method is proposed based on the proposed aggregation operators and ranking indices to cope with MCDM with interactive criteria. Lastly, an investment decision making problem is provided to illustrate the practicality and effectiveness of the proposed approach. The validity and advantages of the proposed method are analyzed by comparing with some existing approaches. By a numerical example in company investment to expand business though five alternatives with considering four criteria, the optimal decision is made.

A New Method for Solving Interval Neutrosophic Linear Programming Problems

Neutrosophic set theory is a generalization of the intuitionistic fuzzy set which can be considered as a powerful tool to express the indeterminacy and inconsistent information that exist commonly in engineering applications and real meaningful science activities. In this paper an interval neutrosophic linear programming (INLP) model will be presented, where its parameters are represented by triangular interval neutrosophic numbers (TINNs) and call it INLP problem. Afterward, by using a ranking function we present a technique to convert the INLP problem into a crisp model and then solve it by standard methods.

The Projection Model with Unknown Weight Information under Interval Neutrosophic Environment and Its Application to Software Quality-in-Use Evaluation

Interval neutrosophic sets (INSs) provide us with a more flexible and effective way to express incomplete, indeterminate, and inconsistent information. The purpose of this paper is to introduce the new multicriteria decision-making (MCDM) method based on the improved projection model under the interval neutrosophic environment. In this paper, we investigated the basic concepts and operational rules of interval neutrosophic numbers (INNs), then proposed the projection of two INNs and improved the entropy formula of the INNs. Furthermore, this paper took account into the decision maker’s attitude towards the indeterminacy and risk and proposed two different methods to determine the ideal solutions. Based on this, we presented an improved MCDM method based on the projection model under the interval neutrosophic environment. Finally, the practicability and reliability of the proposed method were explained by the example of software quality-in-use evaluation.

Approaches to strategic supplier selection under interval neutrosophic environment

In this article, we expand the dual generalized weighted BM (DGWBM) and the dual generalized weighted geometric BM (DGWGBM) operator with interval neutrosophic numbers (INNs) to propose the dual generalized interval neutrosophic number BM (DGINNBM) o

Distance-Based Similarity Measure Between Interval Neutrosophic Sets and Multi Criteria Decision Making Method

In this paper, the weighted similarity measure based on Hamming and Euclidean distances is extended to interval neutrosophic sets. It has been previously used for single valued neutrosophic sets. Then a multicriteria decision-making (MCDM) method is established, in which the criterion weights are known. In the problem the values of each alternative corresponding to the criteria are given with interval neutrosophic numbers. Finally, alternatives are ranked by using the weighted similarity measure between the ideal alternative and each alternative, and the best one is determined.

Interval neutrosophic preference relations and their application in virtual enterprise partner selection

How to select satisfactory partners is essential to virtual enterprise and has attracted lots of attention from practitioners and researchers. In many real situations, preference relation is an important structure in representing decision makers’ preference information during the partner selection process. As a special case of neutrosophic sets, interval neutrosophic set (INS) can be used to handle uncertain and inconsistent information in decision making. To show the application, this paper introduces the concept of interval neutrosophic preference relations (INPRs) using interval neutrosophic numbers to denote the true, indeterminacy and false judgments independently. Then, a multiplicative consistency concept for INPRs is proposed to guarantee the ranking accurately. After that, several multiplicative consistency-based nonlinear programming models to derive multiplicatively consistent INPRs and to determine missing values in incomplete INPRs are constructed, respectively. To broaden the application of INPRs, a consensus index based on the distance measure is defined. Meanwhile, an algorithm to group decision making based on INPRs is developed, which can be applied to address incomplete and inconsistent INPRs. Finally, the feasibility and practicability of the developed approach is manifested through an illustrative example, and comparison analysis is performed with several related previous methods about decision making with INSs.

Methods for Evaluating the Technological Innovation Capability for the High-Tech Enterprises With Generalized Interval Neutrosophic Number Bonferroni Mean Operators

As we all know, the Bonferroni mean (BM) operator has the advantage of considering interrelationships between parameters. In this paper, we combine the generalized weighted BM (GWBM) operator and generalized weighted Bonferroni geometric mean (GWGBM) operator with interval neutrosophic numbers (INNs) to develop the generalized interval neutrosophic number weight BM (GINNWBM) operator and generalized interval neutrosophic numbers weighted GBM (GINNWGBM) operator which consider the relationship among three aggregated arguments, then the MADM methods are developed with these operators. Finally, we use an example for evaluating the technological innovation capability for the high-tech enterprises to illustrate the proposed methods.

A new perspective on traffic control management using triangular interval type-2 fuzzy sets and interval neutrosophic sets

Controlling traffic flow on roads is an important traffic management task necessary to ensure a peaceful and safe environment for people. The number of cars on roads at any given time is always unknown. Type-2 fuzzy sets and neutrosophic sets play a vital role in dealing efficiently with such uncertainty. In this paper, a triangular interval type-2 Schweizer and Sklar weighted arithmetic (TIT2SSWA) operator and a triangular interval type-2 Schweizer and Sklar weighted geometric (TIT2SSWG) operator based on Schweizer and Sklar triangular norms have been studied, and the validity of these operators has been checked using a numerical example and extended to an interval neutrosophic environment by proposing interval neutrosophic Schweizer and Sklar weighted arithmetic (INSSWA) and interval neutrosophic Schweizer and Sklar weighted geometric (INSSWG) operators. Furthermore, their properties have been examined; some of the more important properties are examined in detail. Moreover, we proposed an improved score function for interval neutrosophic numbers (INNs) to control traffic flow that has been analyzed by identifying the junction that has more vehicles. This improved score function uses score values of triangular interval type-2 fuzzy numbers (TIT2FNs) and interval neutrosophic numbers.

Some Interval Neutrosophic Dombi Power Bonferroni Mean Operators and Their Application in Multi–Attribute Decision–Making

The power Bonferroni mean (PBM) operator is a hybrid structure and can take the advantage of a power average (PA) operator, which can reduce the impact of inappropriate data given by the prejudiced decision makers (DMs) and Bonferroni mean (BM) operator, which can take into account the correlation between two attributes. In recent years, many researchers have extended the PBM operator to handle fuzzy information. The Dombi operations of T-conorm (TCN) and T-norm (TN), proposed by Dombi, have the supremacy of outstanding flexibility with general parameters. However, in the existing literature, PBM and the Dombi operations have not been combined for the above advantages for interval-neutrosophic sets (INSs). In this article, we first define some operational laws for interval neutrosophic numbers (INNs) based on Dombi TN and TCN and discuss several desirable properties of these operational rules. Secondly, we extend the PBM operator based on Dombi operations to develop an interval-neutrosophic Dombi PBM (INDPBM) operator, an interval-neutrosophic weighted Dombi PBM (INWDPBM) operator, an interval-neutrosophic Dombi power geometric Bonferroni mean (INDPGBM) operator and an interval-neutrosophic weighted Dombi power geometric Bonferroni mean (INWDPGBM) operator, and discuss several properties of these aggregation operators. Then we develop a multi-attribute decision-making (MADM) method, based on these proposed aggregation operators, to deal with interval neutrosophic (IN) information. Lastly, an illustrative example is provided to show the usefulness and realism of the proposed MADM method. The developed aggregation operators are very practical for solving MADM problems, as it considers the interaction among two input arguments and removes the influence of awkward data in the decision-making process at the same time. The other advantage of the proposed aggregation operators is that they are flexible due to general parameter.

Interval neutrosophic stochastic multiple attribute decision-making method based on cumulative prospect theory and generalized Shapley function

Concerning the discrete stochastic multi-attribute decision making (SMADM) problems in which attribute values are interval neutrosophic numbers and the attribute weight is incompletely known, a novel SMADM method based on the cumulative prospect theory (CPT) and generalized Shapley function is prop osed. Firstly, the value prospect of each attribute under interval neutrosophic environment is calculated as well as subjective probability weights respectively, and the prospect function values are obtained according to the formulation of prospect function. Then, following the maximum deviation principle, the optimization model with respect to the incompletely known attribute weight information is constructed to obtain the optimal fuzzy measure, and the optimal weights of each attribute based on the formulation of generalized Shapley function are generated. Further, by aggregating the above prospect function values and the optimal weights, the values of the comprehensive prospect function are obtained and then alternatives are ranked. Finally, an illustrate example is presented to demonstrate the validity and feasibility of the proposed method.

Exponential Aggregation Operator of Interval Neutrosophic Numbers and Its Application in Typhoon Disaster Evaluation

Exponential Aggregation Operator of Interval Neutrosophic Numbers and Its Application in Typhoon Disaster Evaluation

Some hybrid weighted aggregation operators under neutrosophic set environment and their applications to multicriteria decision-making

A single-valued and an interval neutrosophic sets are two instances of the neutrosophic set(NS), which can efficiently deal with uncertain, imprecise and inconsistent information. In the present work, the work has been done under this environment to develop some novel hybrid aggregation operators based on arithmetic and geometric aggregation operators. The preferences related to the attributes are made in the form of single-valued and interval neutrosophic numbers. Their desirable properties such as idempotency, boundedness and monotonicity are also investigated. Furthermore, a decision-making approach presents to investigate the multi-criteria decision-making problem. The effectiveness of the approach is demonstrated through a case study and a comparison analysis with some other existing methods has been done to validate the results.

Multiple Attribute Decision-Making Method Using Similarity Measures of Neutrosophic Cubic Sets

In inconsistent and indeterminate settings, as a usual tool, the neutrosophic cubic set (NCS) containing single-valued neutrosophic numbers and interval neutrosophic numbers can be applied in decision-making to present its partial indeterminate and partial determinate information.

Multiple Attribute Decision-Making Method Using Similarity Measures of Neutrosophic Cubic Sets

In inconsistent and indeterminate settings, as a usual tool, the neutrosophic cubic set (NCS) containing single-valued neutrosophic numbers and interval neutrosophic numbers can be applied in decision-making to present its partial indeterminate and partial determinate information. However, a few researchers have studied neutrosophic cubic decision-making problems, where the similarity measure of NCSs is one of the useful measure methods. For this work, we propose the Dice, cotangent, and Jaccard measures between NCSs, and indicate their properties. Then, under an NCS environment, the similarity measures-based decision-making method of multiple attributes is developed. In the decision-making process, all the alternatives are ranked by the similarity measure of each alternative and the ideal solution to obtain the best one. Finally, two practical examples are applied to indicate the feasibility and effectiveness of the developed method.

Exponential Aggregation Operator of Interval Neutrosophic Numbers and Its Application in Typhoon Disaster Evaluation

In recent years, typhoon disasters have occurred frequently and the economic losses caused by them have received increasing attention. This study focuses on the evaluation of typhoon disasters based on the interval neutrosophic set theory. An interval neutrosophic set (INS) is a subclass of a neutrosophic set (NS). However, the existing exponential operations and their aggregation methods are primarily for the intuitionistic fuzzy set. So, this paper mainly focus on the research of the exponential operational laws of interval neutrosophic numbers (INNs) in which the bases are positive real numbers and the exponents are interval neutrosophic numbers. Several properties based on the exponential operational law are discussed in detail. Then, the interval neutrosophic weighted exponential aggregation (INWEA) operator is used to aggregate assessment information to obtain the comprehensive risk assessment. Finally, a multiple attribute decision making (MADM) approach based on the INWEA operator is introduced and applied to the evaluation of typhoon disasters in Fujian Province, China. Results show that the proposed new approach is feasible and effective in practical applications.