Interval Neutrosophic Numbers Research Articles

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.

Dombi Aggregation Operators of Neutrosophic Cubic Sets for Multiple Attribute Decision-Making

The neutrosophic cubic set can describe complex decision-making problems with its single-valued neutrosophic numbers and interval neutrosophic numbers simultaneously. The Dombi operations have the advantage of good flexibility with the operational parameter. In order to solve decision-making problems with flexible operational parameter under neutrosophic cubic environments, the paper extends the Dombi operations to neutrosophic cubic sets and proposes a neutrosophic cubic Dombi weighted arithmetic average (NCDWAA) operator and a neutrosophic cubic Dombi weighted geometric average (NCDWGA) operator. Then, we propose a multiple attribute decision-making (MADM) method based on the NCDWAA and NCDWGA operators. Finally, we provide two illustrative examples of MADM to demonstrate the application and effectiveness of the established method.

VIKOR Method for Interval Neutrosophic Multiple Attribute Group Decision-Making

In this paper, we will extend the VIKOR (VIsekriterijumska optimizacija i KOmpromisno Resenje) method to multiple attribute group decision-making (MAGDM) with interval neutrosophic numbers (INNs). Firstly, the basic concepts of INNs are briefly presented. The method first aggregates all individual decision-makers’ assessment information based on an interval neutrosophic weighted averaging (INWA) operator, and then employs the extended classical VIKOR method to solve MAGDM problems with INNs. The validity and stability of this method are verified by example analysis and sensitivity analysis, and its superiority is illustrated by a comparison with the existing methods.

Cosine Measures of Neutrosophic Cubic Sets for Multiple Attribute Decision-Making

The neutrosophic cubic set can contain much more information to express its interval neutrosophic numbers and single-valued neutrosophic numbers simultaneously in indeterminate environments.

Non-linear programming method for multi-criteria decision making problems under interval neutrosophic set environment

Interval neutrosophic sets (INSs) capturing the uncertainties by characterizing into the intervals of the truth, the indeterminacy, and the falsity membership degrees, is a more flexible way to explore the decision-making applications. In this paper, we develop a nonlinear programming (NP) model based on the technique for order preference by similarity to ideal solution (TOPSIS), to solve decision-making problems in which criterion values and their importance are given in the form of interval neutrosophic numbers (INNs). Based on the concept of closeness coefficient, we firstly construct a pair of the nonlinear fractional programming model and then transform it into the linear programming model. Furthermore, to determine the ranking of considered alternatives, likelihood-based comparison relations are constructed. Finally, an illustrative example demonstrates the applicability of the proposed method for dealing with decision making problems with incomplete knowledge.

Time-aware trustworthiness ranking prediction for cloud services using interval neutrosophic set and ELECTRE

The imprecise quality of service (QoS) evaluations from consumers may lead to the inappropriate prediction for the trustworthiness of cloud services in an uncertain cloud environment. The service ranking prediction is a promising idea to overcome this deficiency of values prediction approaches by probing the ordering relations between cloud services concealed in the imprecise evaluations. To address the challenges for trustworthy service selection resulting from fluctuating QoS, flexible service pricing and complicated potential risks, this paper proposes a time-aware approach to predict the trustworthiness ranking of cloud services, with the tradeoffs between performance-cost and potential risks in multiple periods. In this approach, the interval neutrosophic set (INS) theory is utilized to describe and assess the performance-costs and potential risks of cloud services: (1) the original evaluation data about cloud services are preprocessed into the trustworthiness interval neutrosophic numbers (INNs); (2) the new INS operators are proposed with the theoretical proofs to calculate the possibility degree and the ranking values of trustworthiness INNs, contributing to the identification of the neighboring users based on the Kendall rank correlation coefficient (KRCC). The problem of time-aware trustworthiness ranking prediction is formulated as a multi-criterion decision-making (MCDM) problem of creating a ranked services list using INS, and an improved ELECTRE method is developed to solve it. The proposed approach is verified by experiments based on an appropriate baseline for comparative analysis. The experimental results demonstrate that the proposed approach can achieve a better prediction quality than the existing approach. The results also show that our approach works effectively in the risk-sensitive and performance-cost-sensitive application scenarios and prevent the malignant price competition launched by low-quality services.

Cosine Measures of Neutrosophic Cubic Sets for Multiple Attribute Decision-Making

The neutrosophic cubic set can contain much more information to express its interval neutrosophic numbers and single-valued neutrosophic numbers simultaneously in indeterminate environments. Hence, it is a usual tool for expressing much more information in complex decision-making problems. Unfortunately, there has been no research on similarity measures of neutrosophic cubic sets so far. Since the similarity measure is an important mathematical tool in decision-making problems, this paper proposes three cosine measures between neutrosophic cubic sets based on the included angle cosine of two vectors, distance, and cosine functions, and investigates their properties. Then, we develop a cosine measures-based multiple attribute decision-making method under a neutrosophic cubic environment in which, from the cosine measure between each alternative (each evaluated neutrosophic cubic set) and the ideal alternative (the ideal neutrosophic cubic set), the ranking order of alternatives and the best option can be obtained, corresponding to the cosine measure values in the decision-making process. Finally, an illustrative example about the selection problem of investment alternatives is provided to illustrate the application and feasibility of the developed decision-making method.

Multi-objective Optimal Model of Two-sided Matching

Based on the interval neutrosophic numbers, a new multi-objective optimal model of two-sided matching is researched. Through integrating interval neutrosophic information of each subject, the relative closeness degree of uncertainty evaluation information and positive and negative ideal is calculated by the approximate method, which can be expected as the satisfaction of the matching subjects. According to these, a multi-objective optimal model of two-sided matching is constructed, and applied to the leisure industry technology demand and supply. Finally a numerical example is given to illustrate the feasibility and validity of the proposed method.

Exponential operations and aggregation operators of interval neutrosophic sets and their decision making methods

An interval neutrosophic set (INS) is a subclass of a neutrosophic set and a generalization of an interval-valued intuitionistic fuzzy set, and then the characteristics of INS are independently described by the interval numbers of its truth-membership, indeterminacy-membership, and falsity-membership degrees. However, the exponential parameters (weights) of all the existing exponential operational laws of INSs and the corresponding exponential aggregation operators are crisp values in interval neutrosophic decision making problems. As a supplement, this paper firstly introduces new exponential operational laws of INSs, where the bases are crisp values or interval numbers and the exponents are interval neutrosophic numbers (INNs), which are basic elements in INSs. Then, we propose an interval neutrosophic weighted exponential aggregation (INWEA) operator and a dual interval neutrosophic weighted exponential aggregation (DINWEA) operator based on these exponential operational laws and introduce comparative methods based on cosine measure functions for INNs and dual INNs. Further, we develop decision-making methods based on the INWEA and DINWEA operators. Finally, a practical example on the selecting problem of global suppliers is provided to illustrate the applicability and rationality of the proposed methods.

Interval Neutrosophic Multiple Attribute Decision-Making Method with Credibility Information

By considering credibility on every evaluation value of attributes in interval neutrosophic decision making, this paper proposes a credibility-induced interval neutrosophic weighted arithmetic averaging (CIINWAA) operator and a credibility-induced interval neutrosophic weighted geometric averaging (CIINWGA) operator, and investigates their properties. Then, we present a projection measure between interval neutrosophic numbers (INNs) and its ranking method for INNs. Furthermore, a decision-making method is established based on the CIINWAA and CIINWGA operators and the projection measure-based ranking method to handle multiple attribute decision-making problems with interval neutrosophic information and credibility information. Finally, an illustrative example and the comparative analysis are provided to demonstrate the application and effectiveness of the developed approach.

Interval neutrosophic numbers Choquet integral operator for multi-criteria decision making

In this paper, the Choquet integral and the interval neutrosophic set theory are combined to make multi-criteria decision for problems under neutrosophic fuzzy environment. Firstly, a ranking index is proposed according to its geometrical structure, and an approach for comparing two interval neutrosophic numbers is given. Then, a ≤L implied operation-invariant total order which satisfies order-preserving condition is proposed.

Multi-criteria decision-making method based on a cross-entropy with interval neutrosophic sets

ABSTRACTIn this paper, two optimisation models are established to determine the criterion weights in multi-criteria decision-making situations where knowledge regarding the weight information is incomplete and the criterion values are interval neutrosophic numbers. The proposed approach combines interval neutrosophic sets and TOPSIS, and the closeness coefficients are expressed as interval numbers. Furthermore, the relative likelihood-based comparison relations are constructed to determine the ranking of alternatives. A fuzzy cross-entropy approach is proposed to calculate the discrimination measure between alternatives and the absolute ideal solutions, after a transformation operator has been developed to convert interval neutrosophic numbers into simplified neutrosophic numbers. Finally, an illustrative example is provided, and a comparative analysis is conducted between the approach developed in this paper and other existing methods, to verify the feasibility and effectiveness of the proposed approach.

Interval neutrosophic numbers Choquet integral operator for multi-criteria decision making

In this paper, the Choquet integral and the interval neutrosophic set theory are combined to make multi-criteria decision for problems under neutrosophic fuzzy environment. Firstly, a ranking index is proposed according to its geometrical structure, and an approach for comparing two interval neutrosophic numbers is given. Then, a ≤L implied operation-invariant total order which satisfies order-preserving condition is proposed. Secondly, an interval neutrosophic number Choquet integral (INNCI) operator is established and a detailed discussion on its aggregation properties is presented. In addition, the procedure of multi-criteria decision making based on INNCI operator is given. Finally, a practical example for selecting the third party logistics providers is provided to illustrate the feasibility of the developed approach.

Interval neutrosophic prioritized OWA operator and its application to multiple attribute decision making

On the basis of prioritized aggregated operator and prioritized ordered weighted average (POWA) operator, in this paper, the authors further present interval neutrosophic prioritized ordered weighted aggregation (INPOWA) operator with respect to interval neutrosophic numbers (INNs). Firstly, the definition, operational laws, characteristics, expectation and comparative method of INNs are introduced. Then, the INPOWA operator is developed, and some properties of the operator are analyzed. Furthermore, based on the INPOWA operator and the comparative formula of the INNs, an approach to decision making with INNs is established. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

An outranking approach for multi-criteria decision-making problems with interval-valued neutrosophic sets

In this paper, a novel outranking approach for multi-criteria decision-making (MCDM) problems is proposed to address situations where there is a set of numbers in the real unit interval and not just a specific number with a neutrosophic set. Firstly, the operations of interval neutrosophic sets and their related properties are introduced. Then some outranking relations for interval neutrosophic numbers (INNs) are defined based on ELECTRE IV, and the properties of the outranking relations are further discussed in detail. Additionally, based on the outranking relations of INNs, a ranking approach is developed in order to solve MCDM problems. Finally, two practical examples are provided to illustrate the practicality and effectiveness of the proposed approach. Moreover, a comparison analysis based on the same examples is also conducted.

Multiple attribute decision-making method based on the possibility degree ranking method and ordered weighted aggregation operators of interval neutrosophic numbers

The paper proposes the possibility degree ranking method for interval neutrosophic numbers INNs from the probability viewpoint since the ranking of INNs is very important for the interval neutrosophic decision-making problems. Then, we develop an interval neutrosophic number ordered weighted averaging INNOWA operator and an interval neutrosophic number ordered weighted geometric INNOWG operator and investigate their properties, and then establish a decision-making method based on the possibility degree ranking method and the INNOWA and INNOWG operators to handle multiple attribute decision-making problems with interval neutrosophic information. Finally, an illustrative example of investment alternatives is given to demonstrate the application and effectiveness of the developed approach.