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.     

Multi-criteria decision-making method based on single-valued neutrosophic linguistic Maclaurin symmetric mean operators

This paper investigates a wide range of generalized Maclaurin symmetric mean (MSM) aggregation operators, such as the generalized arithmetic MSM and the generalized geometric MSM, whose predominant characteristic is capturing the interrelationships among multi-input arguments. The single-valued neutrosophic linguistic set plays an essential role in decision making, which can serve as an extension of either a linguistic term set or a single-valued neutrosophic set. This study centers on multi-criteria decision-making (MCDM) issues in which criteria are weighed differently and criteria values are expressed as single-valued neutrosophic linguistic numbers. Based on this foundation, we extend a series of MSM aggregation techniques under single-valued neutrosophic linguistic environments and propose procedures for solving MCDM problems. We also explore the influence of parameters on aggregation results. Finally, we provide a practical example and conduct a comparison analysis between the proposed approach and other existing methods in order to verify the proposed approach and demonstrate its validity.

     

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.

     

Novel neutrosophic Dombi Bonferroni mean operators with mobile cloud computing industry evaluation

In the age of mobile cloud computing, we are confronted by mobility, diversity of network access types, frequent network disconnection and poor reliability, and security with complex structures. Mobile cloud computing industry decision making is crucially important for countries or societies to enhance the effectiveness and validity of leadership, which can greatly expedite industrialized and large‐scale development. In the case of mobile cloud computing industry decision evaluation, the indispensable issue arises serious inexactness, fuzziness, and ambiguity. Single‐valued neutrosophic set, disposing the indeterminacy portrayed by truth membership T, indeterminacy membership I, and falsity membership F, is a more viable and effective means to seize indeterminacy. The main purpose of the current paper is to investigate the novel operations on single‐valued neutrosophic number (SVNN) based on Dombi Bonferroni mean (DBM) and Dombi geometric Bonferroni mean (DGBM) operator, which have the enormous advantage of high flexibility with adjustable parameters. Moreover, we employ the DBM operator to present single‐valued neutrosophic DBM (SVNDBM) operator, single‐valued neutrosophic weighted DBM (SVNWDBM) operator, single‐valued neutrosophic DGBM (SVNDGBM), operator and single‐valued neutrosophic weighted DGBM (SVNWDGBM) operator for disposing with the aggregation of SVNNs and develop two multiple attribute decision making methods based on SVNWDBM and SVNWDGBM. The validity of algorithms are illustrated by a mobile cloud computing industry decision making issue, along with the sensitivity analysis of diverse parameters on the ranking. Finally, a comparison of the developed with the existing single‐valued neutrosophic decision making methods has been executed for displaying their effectiveness.     

Some new operations on single-valued neutrosophic matrices and their applications in multi-criteria group decision making

The single-valued neutrosophic set plays a crucial role to handle indeterminant and inconsistent information during decision making process. In recent research, a development in neutrosophic theory is emerged, called single-valued neutrosophic matrices, are used to address uncertainties. The beauty of single-valued neutrosophic matrices is that the utilizing of several fruitful operations in decision making. In this paper, some novel operations on neutrosophic matrices of are introduced, that is, type-1 product \((\tilde \odot )\), type-2 product \((\tilde \otimes )\) and minus \((\tilde \ominus )\) between two single-valued neutrosophic matrices. Also, we introduced complement, transpose, upper and lower α ?level matrices of single-valued neutrosophic matrices and discussed related properties. Furthermore, we propose a multi-criteria group decision making method based on these new operations, and give an application of the proposed method in a real life problem. Finally, we compare proposed method in this paper with proposed methods previously.     

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.     

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.     

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.     

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.     

单值中智信息熵及其多属性决策方法

针对评估信息为单值中智数的多属性决策问题,建立了基于单值中智熵的多属性决策方法。首先,针对现有单值中智熵定义的不足,引入了新的单值中智熵的公理化定义;其次,基于三角函数,设计了一种衡量单值中智数不确定性的信息熵公式,并证明其满足单值中智熵的四个公理化条件;然后,运用提出的熵公式,并结合Lagrange乘数法和贴近度,构建了一种新的单值中智多属性决策方法;最后,将提出的决策方法运用于数据产品服务商的选择问题验证该方法的合理性与有效性。     

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.     

Weakly Prioritized Measure Aggregation in Prioritized Multicriteria Decision Making

This paper mainly investigates a special kind of multicriteria decision–making problem, in which all the criteria can be divided into several hierarchies and the criteria in the higher hierarchy have priorities over those in the lower hierarchy. It implies that the loss of the higher priority criterion can't be compensated by the gain of the lower prioritized criteria. As we know, fuzzy measures can well represent the interactions between criteria. In this situation, we develop a new fuzzy measure called weakly ordered prioritized measure (WOPM) to express the priority rule among the weakly ordered prioritized criteria. On the basis of the WOPM, we use discrete Choquet integral to construct a new WOPM‐guided aggregation (WOPMGA) operator. To understand the priority property of this aggregation operator deeply, we get all the criteria's Shapley values and make an analysis of all criteria's Shapley values with different parameter values. Through analysis, we can find that the WOPMGA operator has the properties of boundedness, idempotency and monotonicity. Finally, we give several practical examples to illustrate the effectiveness of this aggregation operator.     

Generalized prioritized aggregation operators

This paper deals with multicriteria decision‐making problems in which the criteria are partitioned into q categories, and a prioritization relationship exists over categories. We aggregate the criteria in the same priority category by a weighted OWA (ordered weighted averaging) operator and introduce two averaging operators, a generalized prioritized averaging operator and a generalized prioritized OWA operator. In the case with one criterion in each priority category, the two operators reduce to the prioritized averaging operator and the prioritized OWA operator as proposed by Yager. © 2012 Wiley Periodicals, Inc.     

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.     

Correlation coefficient of single-valued neutrosophic hesitant fuzzy sets and its applications in decision making

As a combination of the hesitant fuzzy set (HFS) and the single-valued neutrosophic set (SVNS), the single-valued neutrosophic hesitant fuzzy set (SVNHFS) is an important concept to handle uncertain and vague information existing in real life, which consists of three membership functions including hesitancy, as the truth-hesitancy membership function, the indeterminacy-hesitancy membership function and the falsity-hesitancy membership function, and encompasses the fuzzy set, intuitionistic fuzzy set (IFS), HFS, dual hesitant fuzzy set (DHFS) and SVNS. Correlation and correlation coefficient have been applied widely in many research domains and practical fields. This paper, motivated by the idea of correlation coefficients derived for HFSs, IFSs, DHFSs and SVNSs, focuses on the correlation and correlation coefficient of SVNHFSs and investigates their some basic properties in detail. By using the weighted correlation coefficient information between each alternative and the optimal alternative, a decision-making method is established to handling the single-valued neutrosophic hesitant fuzzy information. Finally, an effective example is used to demonstrate the validity and applicability of the proposed approach in decision making, and the relationship between the each existing method and the developed method is given as a comparison study.

     

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.     

Prioritized aggregation operators based on the priority degrees in multicriteria decision-making

We consider the multicriteria decision-making (MCDM) problems where there exists a prioritization relationship over the criteria. We introduce the concept of the priority degree. Then we give three kinds of prioritized aggregation operators based on the priority degrees: the prioritized averaging operator with the priority degrees, the prioritized scoring operator with the priority degrees, and the prioritized ordered weighted averaging operator with the priority degrees. Some desired properties of these prioritized aggregation operators are also investigated. The priority degree plays an important role in the prioritized MCDM problems. We also investigate how to select a proper priority degree according to the giving decision information. By using an illustrative example, we show that the prioritized aggregation operators based on the priority degrees provide the decision-makers more choices and they are more flexible in the process of decision-making.     

考虑优先级的广义犹豫模糊信息集成方法

研究了在属性之间存在优先级的情况下的广义犹豫模糊信息集成问题。考虑到属性优先级以及属性元素的统一程度的双重影响,首先给出了犹豫模糊信息下的熵值求法,并在其基础上提出了优先级混合赋权方法。之后,在该优先级混合赋权方法的基础上提出了广义犹豫模糊优先级混合几何(GHFPHG)算子,并给出了该类算子的优良特性。最后,利用案例验证了本文所提方法的实用性和有效性。     

Scaled prioritized aggregation operators and their applications to decision making

As an extension of the prioritized aggregation operators by Yager (Int J Approx Reason 48:263–274, 2008), this paper uses the priority labels to express the prioritized relationship between criteria and presents some scaled prioritized aggregation operators, including the scaled prioritized score operator and the scaled prioritized averaging operator. Moreover, we consider the priority under uncertain environment and develop the uncertain prioritized aggregation operators, including the uncertain prioritized scoring operator and the uncertain prioritized averaging operator. We investigate the properties of these operators and build the models to derive the weights by maximizing square deviations from a possible range to distinguish the candidate alternatives mostly. Furthermore, approaches to multi-attribute decision making based on the proposed operators are given, which have benefits over the TOPSIS method (Behzadian, Expert Syst Appl 39:13051–13069, 2012) and the methods based on the OWA operator (Zhou and Chen, Fuzzy Sets Syst 168:18–34, 2011) when prioritized relationship between criteria is considered. Finally, examples are illustrated to show the feasibility and validity of the new approaches to the application of decision making.