The Cosine Measure of Single-Valued Neutrosophic Multisets for Multiple Attribute Decision-Making

Fuzzy multi-attribute decision making method based on new similarity measure under interval-valued neutrosophic sets

Interval-valued neutrosophic set (IVNS) plays an important role in dealing with imprecise judgment information. For a multi-attribute decision making problem, the information of alternatives under different attributes is given in the form of interval valued neutrosophic number(IVNN). The objective of the presented paper is to develop a multiple-attribute decision making (MADM) method under interval-valued neutrosophic sets(IVNSs) using the new similarity measurement. The similarity measurement of IVNSs has always been a research hotspot. A new similarity measurement of IVNSs is first proposed in this paper based on Chebyshev distance. The proposed method enriches the existing similarity measurement methods. It can be applied to not only IVNSs, but also single-valued neutrosophic sets(SVNSs). The influence of each attribute on the decision-making result can be described by the weight. How to formulate the weight scientifically is vital as well. In this paper, the objective weight is calculated by normalizing the grey correlation coefficient obtained by a score function which can be applied to IVNSs. The objective weight is then combined with the subjective one by considering an adjustment factor with the weighted summation method. The adjustment factor is determined by the importance of subjective weight. Finally, an example is used to illustrate the comparison results of the proposed algorithm and other three ones. The comparison shows that the proposed algorithm is effective and can identify the optimal scheme quickly.

Correlation coefficients of credibility interval-valued neutrosophic sets and their group decision-making method in single- and interval-valued hybrid neutrosophic multi-valued environment

Although a single-valued neutrosophic multi-valued set (SVNMVS) can reasonably and perfectly express group evaluation information and make up for the flaw of multi-valued/hesitant neutrosophic sets in group decision-making problems, its information expression and group decision-making methods still lack the ability to express and process single- and interval-valued hybrid neutrosophic multi-valued information. To overcome the drawbacks, this study needs to propose single- and interval-valued hybrid neutrosophic multi-valued sets (SIVHNMVSs), correlation coefficients of consistency interval-valued neutrosophic sets (CIVNSs), and their multi-attribute group decision-making (MAGDM) method in the setting of SIVHNMVSs. First, we propose SIVHNMVSs and a transformation method for converting SIVHNMVSs into CIVNSs based on the mean and consistency degree (the complement of standard deviation) of truth, falsity and indeterminacy sequences. Then, we present two correlation coefficients between CIVNSs based on the multiplication of both the correlation coefficient of interval-valued neutrosophic sets and the correlation coefficient of neutrosophic consistency sets and two weighted correlation coefficients of CIVNSs. Next, a MAGDM method is developed based on the proposed two weighted correlation coefficients of CIVNSs for performing MAGDM problems under the environment of SIVHNMVSs. At last, a selection case of landslide treatment schemes demonstrates the application of the proposed MAGDM method under the environment of SIVHNMVSs. By comparative analysis, our new method not only overcomes the drawbacks of the existing method, but also is more extensive and more useful than the existing method when tackling MAGDM problems in the setting of SIVHNMVSs.

Correlation Coefficients of Refined-Single Valued Neutrosophic Sets and Their Applications in Multiple Attribute Decision-Making

The paper presents the correlation coefficient of refined-single valued neutrosophic sets (Refined-SVNSs) based on the extension of the correlation of single valued neutrosophic sets (SVNSs), and then a decision making method is proposed by the use of the weighted correlation coefficient of Refined-SVNSs. Through the weighted correlation coefficient between the ideal alternative and each alternative, we can rank all alternatives and the best one of all alternatives can be easily identified as well. Finally, to prove this decision making method proposed in this paper is useful to deal with the actual application, we use an example to illustrate it.

Linguistic Neutrosophic Numbers Einstein Operator and Its Application in Decision Making

Linguistic neutrosophic numbers (LNNs) include single-value neutrosophic numbers and linguistic variable numbers, which have been proposed by Fang and Ye. In this paper, we define the linguistic neutrosophic number Einstein sum, linguistic neutrosophic number Einstein product, and linguistic neutrosophic number Einstein exponentiation operations based on the Einstein operation. Then, we analyze some of the relationships between these operations. For LNN aggregation problems, we put forward two kinds of LNN aggregation operators, one is the LNN Einstein weighted average operator and the other is the LNN Einstein geometry (LNNEWG) operator. Then we present a method for solving decision-making problems based on LNNEWA and LNNEWG operators in the linguistic neutrosophic environment. Finally, we apply an example to verify the feasibility of these two methods.

Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets

Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (<A>, <neutA>, <antiA>), where <A> is an entity (i.e. element, concept, idea, theory, logical proposition, etc.), <antiA> is the opposite of <A>, while <neutA> is the neutral (or indeterminate) between them, i.e., neither <A> nor <antiA> [...]

Neutrosophic Soft Expert Multiset and Their Application to Multiple Criteria Decision Making

In this paper, we have investigated neutrosophic soft expert multisets (NSEMs) in detail. The concept of NSEMs is introduced. Several operations have been defined for them and their important algebraic properties are studied. Finally, we define a NSEMs aggregation operator to construct an algorithm for a NSEM decision-making method that allows for a more efficient decision-making process.

Clustering Neutrosophic Data Sets and Neutrosophic Valued Metric Spaces

In this paper, we define the neutrosophic valued (and generalized or G) metric spaces for the first time. Besides, we newly determine a mathematical model for clustering the neutrosophic big data sets using G-metric. Furthermore, relative weighted neutrosophic-valued distance and weighted cohesion measure, is defined for neutrosophic big data set. We offer a very practical method for data analysis of neutrosophic big data although neutrosophic data type (neutrosophic big data) are in massive and detailed form when compared with other data types.