Multiple attribute group decision-making method with single-valued neutrosophic interval number information

To describe decision makers’ judgments for an evaluated object more comprehensively in the decision-making process, this paper firstly defines the concept of a single-valued neutrosophic interval number (SVNIN), which is composed of both its interval number (interval judgment) and its single-valued neutrosophic number (SVNN) (confident degree). Then we present the basic operational laws of SVNINs and the score function of SVNIN based on the attitude index and confident level of decision makers to compare SVNINs. Next, we propose a single-valued neutrosophic interval number weighted arithmetic averaging (SVNINWAA) operator and a single-valued neutrosophic interval number weighted geometric averaging (SVNINWGA) operator to aggregate SVNIN information. Further, a multiple attribute group decision-making (MDGDM) method using the proposed SVNINWAA or SVNINWGA operator is established under an SVNIN environment. Finally, an illustrative example regarding the selection problem of global suppliers is presented to show the application and effectiveness of the developed method.     

Maximizing deviation method for neutrosophic multiple attribute decision making with incomplete weight information

This paper develops a method for solving the multiple attribute decision-making problems with the single-valued neutrosophic information or interval neutrosophic information. We first propose two discrimination functions referred to as score function and accuracy function for ranking the neutrosophic numbers. An optimization model to determine the attribute weights that are partly known is established based on the maximizing deviation method. For the special situations where the information about attribute weights is completely unknown, we propose another optimization model. A practical and useful formula which can be used to determine the attribute weights is obtained by solving a proposed nonlinear optimization problem. To aggregate the neutrosophic information corresponding to each alternative, we utilize the neutrosophic weighted averaging operators which are the single-valued neutrosophic weighted averaging operator and the interval neutrosophic weighted averaging operator. Thus, we can determine the order of alternatives and choose the most desirable one(s) based on the score function and accuracy function. Finally, some illustrative examples are presented to verify the proposed approach and to present its effectiveness and practicality.     

Possibility-induced simplified neutrosophic aggregation operators and their application to multi-criteria group decision-making

Abstract

Simplified neutrosophic set (SNS) is an appropriate tool used to express the incompleteness, indeterminacy and uncertainty of the evaluation objects in decision-making process. In this study, we define the concept of possibility SNS including two types of information such as the neutrosophic performance provided from the evaluation objects and its possibility degree using a value ranging from zero to one. Then by extending the existing neutrosophic information, aggregation models for SNSs that cannot be used effectively to fusion the two different information described above, we propose two novel neutrosophic aggregation operators considering possibility, which are named as a possibility-induced simplified neutrosophic weighted arithmetic averaging operator and possibility-induced simplified neutrosophic weighted geometric averaging operator, and discuss their properties. Moreover, we develop a useful method based on the proposed aggregation operators for solving a multi-criteria group decision-making problem with the possibility simplified neutrosophic information, in which the weights of decision-makers and decision criteria are calculated based on entropy measure. Finally, a practical example is utilised to show the practicality and effectiveness of the proposed method.     

Power Aggregation Operators of Simplified Neutrosophic Sets and Their Use in Multi-attribute Group Decision Making

The simplified neutrosophic set (SNS) is a useful generalization of the fuzzy set that is designed for some practical situations in which each element has different truth membership function, indeterminacy membership function and falsity membership function. In this paper, we develop a series of power aggregation operators called simplified neutrosophic number power weighted averaging (SNNPWA) operator, simplified neutrosophic number power weighted geometric (SNNPWG) operator, simplified neutrosophic number power ordered weighted averaging (SNNPOWA) operator and simplified neutrosophic number power ordered weighted geometric (SNNPOWG) operator. We present some useful properties of the operators and discuss the relationships among them. Moreover, an approach to multi-attribute group decision making (MAGDM) within the framework of SNSs is developed by the above aggregation operators. Finally, a practical application of the developed approach to deal with the problem of investment is given, and the result shows that our approach is reasonable and effective in dealing with uncertain decision making problems.      

Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment

The paper presents the correlation and correlation coefficient of single-valued neutrosophic sets (SVNSs) based on the extension of the correlation of intuitionistic fuzzy sets and demonstrates that the cosine similarity measure is a special case of the correlation coefficient in SVNS. Then a decision-making method is proposed by the use of the weighted correlation coefficient or the weighted cosine similarity measure of SVNSs, in which the evaluation information for alternatives with respect to criteria is carried out by truth-membership degree, indeterminacy-membership degree, and falsity-membership degree under single-valued neutrosophic environment. We utilize the weighted correlation coefficient or the weighted cosine similarity measure between each alternative and the ideal alternative to rank the alternatives and to determine the best one(s). Finally, an illustrative example demonstrates the application of the proposed decision-making method.     

A multi-criteria decision-making method based on single-valued trapezoidal neutrosophic preference relations with complete weight information

Single-valued trapezoidal neutrosophic numbers (SVTNNs) have a strong capacity to depict uncertain, inconsistent, and incomplete information about decision-making problems. Preference relations represent a practical tool for presenting decision makers’ preference information regarding various alternatives. The purpose of this paper is to propose single-valued trapezoidal neutrosophic preference relations (SVTNPRs) as a strategy for tackling multi-criteria decision-making problems. First, this paper briefly reviews basic concepts about neutrosophic sets and SVTNNs and defines a new comparison method and new operations for SVTNNs. Next, two aggregation operators, the single-valued trapezoidal neutrosophic weighted arithmetic average operator and the single-valued trapezoidal neutrosophic weighted geometric average operator, are proposed for applications in information fusion. Then, this paper discusses the definitions of completely consistent SVTNPRs and acceptably consistent SVTNPRs. Finally, we outline a decision-making method based on SVTNPRs to address green supplier selection problems, and we conduct a comparison study and discussion to illustrate the rationality and effectiveness of the decision-making method.

     

基于单值中智集的投资决策方案优选模型

为了优化投资决策方案优选模型,提出一个基于单值中智环境下的多属性决策问题的新方法。首先给出一个基于单值中智集的广义距离公式,然后通过语言变量确定了决策专家和属性指标的权重,接着构建了加权的综合决策矩阵,进一步得到各备选方案与正负理想方案的距离,利用相对贴近度系数对各备选方案就进行综合排序,得到最优决策方案。最后通过一个投资决策的实例,验证了该模型的有效性和实用性。     

Induced simplified neutrosophic correlated aggregation operators for multi-criteria group decision-making

Induced Choquet integral is a powerful tool to deal with imprecise or uncertain nature. This study proposes a combination process of the induced Choquet integral and neutrosophic information. We first give the operational properties of simplified neutrosophic numbers (SNNs). Then, we develop some new information aggregation operators, including an induced simplified neutrosophic correlated averaging (I-SNCA) operator and an induced simplified neutrosophic correlated geometric (I-SNCG) operator. These operators not only consider the importance of elements or their ordered positions, but also take into account the interactions phenomena among decision criteria or their ordered positions under multiple decision-makers. Moreover, we present a detailed analysis of I-SNCA and I-SNCG operators, including the properties of idempotency, commutativity and monotonicity, and study the relationships among the proposed operators and existing simplified neutrosophic aggregation operators. In order to handle the multi-criteria group decision-making (MCGDM) situations where the weights of criteria and decision-makers usually correlative and the criterion values are considered as SNNs, an approach is established based on I-SNCA operator. Finally, a numerical example is presented to demonstrate the proposed approach and to verify its effectiveness and practicality.     

Projection and bidirectional projection measures of single-valued neutrosophic sets and their decision-making method for mechanical design schemes

Abstract

Projection measure is one of important tools for handling decision-making problems. First, the paper proposes projection and bidirectional projection measures between single-valued neutrosophic sets, and then the comparison of numerical examples shows that the bidirectional projection measure is superior to the general projection measure in measuring closeness degree between two vectors. Next, we develop their decision-making method for selecting mechanical design schemes under a single-valued neutrosophic environment. Through the projection measure or bidirectional projection measure between each alternative and the ideal alternative with single-valued neutrosophic information, all the alternatives can be ranked and the best one can be selected as well. Finally, the proposed decision-making method is applied to the selection of design schemes of punching machine and its effectiveness and advantages are demonstrated by comparison with relative methods.     

Some 2-tuple linguistic neutrosophic number Muirhead mean operators and their applications to multiple attribute decision making

In this paper, we expand the Muirhead mean (MM) operator and dual MM (DMM) operator with 2-tuple linguistic neutrosophic numbers (2TLNNs) to propose the 2-tuple linguistic neutrosophic numbers MM (2TLNNMM) operator, 2-tuple linguistic neutrosophic numbers weighted MM (2TLNNWMM) operator, 2-tuple linguistic neutrosophic numbers DMM (2TLNNDMM) operator and 2-tuple linguistic neutrosophic numbers weighted DMM (2TLNNWDMM) operator. Then, the MADM methods are proposed with these two operators. Finally, an example for green supplier selection is used to show the proposed methods.     

TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment

A single-valued neutrosophic set is a special case of neutrosophic set. It has been proposed as a generalization of crisp sets, fuzzy sets, and intuitionistic fuzzy sets in order to deal with incomplete information. In this paper, a new approach for multi-attribute group decision-making problems is proposed by extending the technique for order preference by similarity to ideal solution to single-valued neutrosophic environment. Ratings of alternative with respect to each attribute are considered as single-valued neutrosophic set that reflect the decision makers’ opinion based on the provided information. Neutrosophic set characterized by three independent degrees namely truth-membership degree (T), indeterminacy-membership degree (I), and falsity-membership degree (F) is more capable to catch up incomplete information. Single-valued neutrosophic set-based weighted averaging operator is used to aggregate all the individual decision maker’s opinion into one common opinion for rating the importance of criteria and alternatives. Finally, an illustrative example is provided in order to demonstrate its applicability and effectiveness of the proposed approach.     

Neutrosophic structured element

This paper presents a new concept in neutrosophic sets (NS) called neutrosophic structured element (NSE). Based on this concept, we define the operational laws, score function, and some aggregation operators of NS. Finally, as an application of this concept, we propose a decision-making method for a multi-attribute decision making (MADM) problem under NSE information. The results indicate that this concept is a useful tool for dealing with neutrosophic decision problems.     

Multiple attribute decision-making method based on single-valued neutrosophic normalized weighted Bonferroni mean

In this paper, we proposed a single-valued neutrosophic normalized weighted Bonferroni mean (SVNNWBM) operator on the basis of Bonferroni mean, the weighted Bonferroni mean (WBM), and the normalized WBM. Firstly, the definition, operational laws, characteristics, and comparing method of single-valued neutrosophic numbers (SVNNs) are introduced. Then, the SVNNWBM operator is developed, and some properties and special cases of this operator are analyzed. Furthermore, an approach is developed to solve the multiple attribute decision-making problems with SVNNs based on the SVNNWBM operator. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.     

概率多值中智集的关联系数及其应用

为了研究不同概率多值中智集的相关关系,提出了概率多值中智集的关联系数。提出了概率多值中智集的期望关联系数、精确度关联系数和信息完全度关联系数,以便测量不同概率多值中智集在平均程度、精确程度和信息完全度之间的相关关系。为了测量不同概率多值中智集的整体相关关系,基于三种关联系数和加权平均算子的思想定义了包含参数的概率多值中智集的综合关联系数,并且给出了关联系数的性质。考虑到权重的重要性,提出了概率多值中智集的一系列加权关联系数。基于概率多值中智集的加权关联系数构建一种可以有效地确定参数且适用于属性权重已知的多属性决策模型,并通过具体案例和对比分析验证该模型的有效性和合理性。     

Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems

As a variation of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to represent uncertain, imprecise, incomplete and inconsistent information that exists in the real world. Simplified neutrosophic sets (SNSs) have been proposed for the main purpose of addressing issues with a set of specific numbers. However, there are certain problems regarding the existing operations of SNSs, as well as their aggregation operators and the comparison methods. Therefore, this paper defines the novel operations of simplified neutrosophic numbers (SNNs) and develops a comparison method based on the related research of intuitionistic fuzzy numbers. On the basis of these operations and the comparison method, some SNN aggregation operators are proposed. Additionally, an approach for multi-criteria group decision-making (MCGDM) problems is explored by applying these aggregation operators. Finally, an example to illustrate the applicability of the proposed method is provided and a comparison with some other methods is made.     

Frank prioritized Bonferroni mean operator with single-valued neutrosophic sets and its application in selecting third-party logistics providers

The selection of third-party logistics (TPL) providers can greatly influence the development of a company, and it has therefore become a hot topic for research. The process of selecting TPL providers is complicated because it includes fuzzy information that can be depicted by single-valued neutrosophic numbers (SVNNs). This paper establishes a new method for selecting TPL providers under single-valued neutrosophic environments. This method simultaneously takes into account the interrelationships among criteria and the different priority levels of criteria. To construct the method, we first introduce Frank operations of SVNNs, considering that extant operations for SVNNs lack flexibility and robustness. Then, we develop the single-valued neutrosophic Frank normalized prioritized Bonferroni mean (SVNFNPBM) operator utilizing the proposed Frank operations. The SVNFNPBM operator considers the interrelationships among criteria and their distinct priority levels by combining the Bonferroni mean and the prioritized average operators. Subsequently, we construct a method for selecting TPL providers based on the proposed operator. Finally, we describe a numerical example of selecting a TPL provider and conduct a comparative analysis to verify the applicability and feasibility of the proposed method.

     

Fault Diagnoses of Hydraulic Turbine Using the Dimension Root Similarity Measure of Single-valued Neutrosophic Sets

This paper proposes a dimension root distance and its similarity measure of single-valued neutrosophic sets (SVNSs), and then develops the fault diagnosis method of hydraulic turbine by using the dimension root similarity measure of SVNSs. By the similarity measures between the fault diagnosis patterns and a testing sample with single-valued neutrosophic information and the relation indices, we can determine the main fault type and the ranking order of various vibration faults for predicting some possible fault trend. Then, the comparison of the fault diagnoses of hydraulic turbine based of the proposed dimension root similarity measure and the existing cotangent similarity measure of SVNSs is provided to demonstrate the effectiveness and rationality of the proposed fault diagnosis method. The fault diagnosis results of hydraulic turbine show that the proposed fault diagnosis method not only gives the main fault types of hydraulic turbine, but also provides useful information for multifault analyses and future possible fault trends. The developed fault diagnosis method is effective and reasonable in the fault diagnosis of hydraulic turbine under single-valued neutrosophic environment.     

The generalized hybrid weighted average operator based on interval neutrosophic hesitant set and its application to multiple attribute decision making

The Neutrosophic set and Hesitant set are the important and effective tools to describe the uncertain information. In this paper, we combine the interval neutrosophic sets and interval-valued hesitant fuzzy sets, and propose the concept of the interval neutrosophic hesitant fuzzy set (INHFS) in order to use the advantages of them. Then, we present the operations and comparison method of INHFS, and develop some new aggregation operators for the interval neutrosophic hesitant fuzzy information, including interval neutrosophic hesitant fuzzy generalized weighted operator, interval neutrosophic hesitant fuzzy generalized ordered weighted operator, and interval neutrosophic hesitant fuzzy generalized hybrid weighted operator, and discuss some properties. Furthermore, we propose the decision-making method for multiple attribute group decision making with interval neutrosophic hesitant fuzzy information, and give the detail decision steps. Finally, we give an illustrate example to show the process of decision making.     

一种基于信息测度的多属性决策方法

单值中智集（SVN）可以用来表示现实情况中存在的不确定性和不一致信息。信息测度在支持向量网络理论中占有重要地位,近年来受到越来越多的关注。本文提出一种基于单值中智信息测度的多属性决策方法。首先介绍信息度量的3个公理化定义,其中包括熵、相似性测度和交叉熵。然后,基于余弦函数构造信息测度公式,进一步讨论熵、相似测度和交叉熵之间的关系及其相互转换。在此基础上,提出一种基于信息测度公式的单值中智集多属性决策方法。最后,给出城市污染评价的数值实例,论证该方法的适用性和有效性。