Interval Neutrosophic Sets Research Articles

A new approach for multiple attribute group decision-making based on interval neutrosophic sets

A new approach for multiple attribute group decision-making based on interval neutrosophic sets

Project Procurement Method Selection Using a Multi-Criteria Decision-Making Method with Interval Neutrosophic Sets

Project procurement method (PPM) selection influences the efficiency of project implementation. Owners are presented with different options for project delivery. However, selecting the appropriate PPM poses great challenges to owners, given the existence of ambiguous information. The interval neutrosophic set (INS) shows power to handle imprecise and ambiguous information. This paper aims to develop a PPM selection model under an interval neutrosophic environment for owners. The main contributions of this paper are as follows: (1) The similarity measure is innovatively introduced with interval neutrosophic information to handle the PPM selection problem. (2) The similarity measure based on minimum and maximum operators is applied to construct a decision-making model for PPM selection, through considering the truth, falsity, and indeterminacy memberships simultaneously. (3) This study establishes a PPM selection method with INS by applying similarity measures, that takes account into the determinacy, indeterminacy, and hesitation from the decision experts when giving an evaluation value. A case study on selecting PPM is made to show the applicability of the proposed approach. Finally, the results of the proposed method are compared with those of existing methods, which exhibit the superiority of the proposed PPM selection method.

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.

New multiparametric similarity measure and distance measure for interval neutrosophic set with IoT industry evaluation

New multiparametric similarity measure and distance measure for interval neutrosophic set with IoT industry evaluation

New Similarity and Entropy Measures of Interval Neutrosophic Sets with Applications in Multi-Attribute Decision-Making

New Similarity and Entropy Measures of Interval Neutrosophic Sets with Applications in Multi-Attribute Decision-Making

Multi-Attribute Decision-Making Based on Preference Perspective with Interval Neutrosophic Sets in Venture Capital

Multi-Attribute Decision-Making Based on Preference Perspective with Interval Neutrosophic Sets in Venture Capital

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

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

Approach to image segmentation based on interval neutrosophic set

As a generalization of the fuzzy set and intuitionistic fuzzy set, the neutrosophic set (NS) have been developed to represent uncertain, imprecise, incomplete and inconsistent information existing in the real world. Now the interval neutrosophic set (INS) which is an expansion of the neutrosophic set have been proposed exactly to address issues with a set of numbers in the real unit interval, not just one specific number. After definition of concepts and operations, INS is applied to image segmentation. Images are converted to the INS domain, which is described using three membership interval sets: T, I and F. Then, in order to increase the contrast between membership and evaluate the indeterminacy, a fuzzy intensification for each element in the interval set is made and a score function in the INS is defined. Finally, the proposed method is employed to perform image segmentation using the traditional k-means clustering. The experimental results on a variety of images demonstrate that the proposed approach can segment different sorts of images. Especially, it can segment 'clean' images and images with various levels of noise.

Some modified results of the subtraction and division operations on interval neutrosophic sets

ABSTRACTAn interval neutrosophic set (INS), characterised by the truth, indeterminacy and falsity membership functions, is a powerful structure for handling the uncertain, imprecise and incomplete information existing in the real world in a better way. Under this environment, an attempt is made to define the subtraction and division operations, by imposing some new constrained conditions, after removing the shortcomings of existing operations. The deficiencies of the existing operations are validated through some counterexamples. Further, various desirable properties related to these operations are investigated in detail. Finally, some numerical examples are provided to validate it.

Interval Neutrosophic Vague Sets

Recently, vague sets and neutrosophic sets have received great attention among the scholars and have been applied in many applications. But, the actual theoretical impacts of the combination of these two sets in dealing uncertainties are still not fully explored until now. In this paper, a new generalized mathematical model called interval neutrosophic vague sets is proposed, which is a combination of vague sets and interval neutrosophic sets and a generalization of interval neutrosophic vague sets. Some definitions of interval neutrosophic vague set such as union, complement and intersection are presented. Furthermore, the basic operations, the derivation of its properties and related example are included.

New Entropy Measures Based on Neutrosophic Set and Their Applications to Multi-Criteria Decision Making

Our aim in this work is to obtain two new entropy measures for single valued neutrosophic sets (SVNSs) and interval neutrosophic sets (INSs). Moreover, we give the essential properties of the proposed entropies. Finally, we introduce a numerical example to show that the entropy measures are more reliable and reasonable for representing the degree of uncertainty.

New Similarity and Entropy Measures of Interval Neutrosophic Sets with Applications in Multi-Attribute Decision-Making

Information measures play an important role in the interval neutrosophic sets (INS) theory. The main purpose of this paper is to study the similarity and entropy of INS and its application in multi-attribute decision-making. We propose a new inclusion relation between interval neutrosophic sets where the importance of the three membership functions may be different. Then, we propose the axiomatic definitions of the similarity measure and entropy of the interval neutrosophic set (INS) based on the new inclusion relation. Based on the Hamming distance, cosine function and cotangent function, some new similarity measures and entropies of INS are constructed. Finally, based on the new similarity and entropy, we propose a multi-attribute decision-making method and illustrate that these new similarities and entropies are reasonable and effective.

Multi-Attribute Decision-Making Based on Preference Perspective with Interval Neutrosophic Sets in Venture Capital

Fuzzy information in venture capital can be well expressed by neutrosophic numbers, and TODIM method is an effective tool for multi-attribute decision-making. The distance measure is an essential step in TODIM method. The keystone of this paper is to define several new distance measures, in particular the improved interval neutrosophic Euclidean distance, and these measures are applied in the TODIM method for multi-attribute decision-making. Firstly, the normalized generalized interval neutrosophic Hausdorff distance is defined and proved to be valid in this paper. Secondly, we define a weighted parameter interval neutrosophic distance and discuss whether different weight parameters affect the decision result based on TODIM method. Thirdly, considering the preference perspective of decision-makers in behavioral economics, we define the improved interval neutrosophic Euclidean distance with the known parameter of risk preference. Finally, an application example is given to compare the effects of different parameters on the result and discuss the feasibility of these two distance measures in TODIM method.

Neutrosophic Cubic Einstein Geometric Aggregation Operators with Application to Multi-Criteria Decision Making Method

Neutrosophic cubic sets (NCs) are amore generalized version of neutrosophic sets(Ns) and interval neutrosophic sets (INs). Neutrosophic cubic setsare better placed to express consistent, indeterminate and inconsistent information, which provides a better platform to deal with incomplete, inconsistent and vague data. Aggregation operators play a key role in daily life, and in relation to science and engineering problems. In this paper we defined the algebraic and Einstein sum, multiplication and scalar multiplication, score and accuracy functions. Using these operations we defined geometric aggregation operators and Einstein geometric aggregation operators. First, we defined the algebraic and Einstein operators of addition, multiplication and scalar multiplication. We defined score and accuracy function to compare neutrosophic cubic values. Then we definedthe neutrosophic cubic weighted geometric operator (NCWG), neutrosophic cubic ordered weighted geometric operator (NCOWG), neutrosophic cubic Einstein weighted geometric operator (NCEWG), and neutrosophic cubic Einstein ordered weighted geometric operator (NCEOWG) over neutrosophic cubic sets. A multi-criteria decision making method is developed as an application to these operators. This method is then applied to a daily life problem.

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.

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.

New Multiparametric Similarity Measure and Distance Measure for Interval Neutrosophic Set With IoT Industry Evaluation

In the epoch of the Internet of Things (IoT), we have confronted five challenges (Connectivity, Value, Security, Telepresence, and Intelligence) with complex structures. The IoT industry decision making is critically important for countries or societies to enhance the effectiveness and validity of leadership, which can greatly accelerate the industrialized and large-scale development. In the case of IoT industry decision evaluation, the essential problem arises serious incompleteness, impreciseness, subjectivity, and incertitude. Interval neutrosophic set, disposing of the indeterminacy portrayed by truth membership T, indeterminacy membership I, and falsity membership F with interval form, is a more viable and effective means to seize indeterminacy. The main purpose of this paper is to investigate the multiparametric distance measure and similarity measure. Meanwhile, some interesting properties of distance measure and similarity measure are proved. Then, the objective weights of diverse attributes are ascertained by the deviation-based method. Moreover, we explore the combination weight, which reveals both the objective preference and subjective preference. The validity of the algorithm is illustrated by an IoT industry decision-making issue, along with the effect of diverse parameters on the ranking. Finally, a comparison of the developed with the existing interval neutrosophic decision-making methods have been executed in the light of the counter-intuitive phenomena and unauthentic issue for displaying their effectiveness.

Linguistic Approaches to Interval Complex Neutrosophic Sets in Decision Making

One of the most efficient tools for modeling uncertainty in decision-making problems is the neutrosophic set (NS) and its extensions, such as complex NS (CNS), interval NS (INS), and interval complex NS (ICNS). Linguistic variables have been long recognized as a useful tool in decision-making problems for solving the problem of crisp neutrosophic membership degree. In this paper, we aim to introduce new concepts: single-valued linguistic complex neutrosophic set (SVLCNS-2) and interval linguistic complex neutrosophic set (ILCNS-2) that are more applicable and adjustable to real-world implementation than those of their previous counterparts. Some set-theoretic operations and the operational rules of SVLCNS-2 and ILCNS-2 are designed. Then, gather classifications of the candidate versus criteria, gather the significance weights, gather the weighted rankings of candidates versus criteria and a score function to arrange the candidates are determined. New TOPSIS decision-making procedures in SVLCNS-2 and ICNS-2 are presented and applied to lecturer selection in the case study of the University of Economics and Business, Vietnam National University. The applications demonstrate the usefulness and efficiency of the proposal.

Trapezoidal neutrosophic aggregation operators and its application in multiple attribute decision making process

The aim of this paper is to introduce interval trapezoidal neutrosophic set which is a combination of trapezoidal fuzzy numbers and interval neutrosophic set. The paper presents some operational rules, the score and accuracy functions of interval trapezoidal neutrosophic numbers. Then, some aggregating operators under interval trapezoidal neutrosophic information which are called interval trapezoidal neutrosophic number weighted arithmetic averaging (ITNNWAA) operator and interval trapezoidal neutrosophic number weighted geometric averaging (ITNNWGA) operator, are proposed, and their properties are investigated in detail. Furthermore, based on these operators a multi-attribute decision making method is developed. Finally, a numerical example is presented to illustrate the application and effectiveness of the proposed method.

Block-based tri-channel hybrid segmentation of images for foreground extraction

Image segmentation is crucial in image analysis, object representation, visualization and other image processing tasks. An image can be distinguished in terms of the foreground and the background. A new hybrid segmentation of images for foreground extraction is proposed, based on Interval Neutrosophic Set (INS) and Sparse Field Active Contour. In this method, an image is represented in three channels using a Gaussian filter bank and each channel is split into blocks to which the INS is applied. The resultant neutrosophic image for three channels undergoes isodata thresholding to obtain the tri-channel edge image, which is segmented using the Sparse Field Active Contour. The proposed method is evaluated by conducting three different experiments in natural image datasets like the Semantic Dataset100, Weizmann_Seg_DB_1obj, BSR and standard MATLAB test images. Finally, it is compared to other existing segmentation methods, which shows promising achievement in terms of their evaluation metrics like overlap-based metrics, pair-counting-based method and distance measures.