Multicriteria Decision-Making Method Under a Single Valued Neutrosophic Environment

Multicriteria Decision-Making Method Under a Single Valued Neutrosophic Environment

Shapu Ren (Shaoxing University, Department of Electrical and Information Engineering, Shaoxing, China)
Copyright: © 2017 |Pages: 15
DOI: 10.4018/IJIIT.2017100102
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Abstract

A single valued neutrosophic set (SVNS) is a subclass of neutrosophic sets, which generalizes fuzzy sets, interval valued fuzzy set, and intuitionistic fuzzy set. It can be used to easily express incomplete, indeterminate and inconsistent information. This paper introduces the Dice similarity measure of single valued neutrosophic numbers (SVNNs) for ranking SVNNs and a single valued neutrosophic prioritized weighted geometric (SVNPWG) operator for aggregating single valued neutrosophic information. Based on the SVNPWG operator and the Dice similarity measure for SVNNs, a multicriteria decision-making method with different priority levels in the criteria is established in which the evaluation values of alternatives with respective to criteria are represented in the form of SVNNs. The ranking order of alternatives is performed through the Dice measure and the best one(s) can be determined as well. Finally, an illustrative example shows the application of the proposed method.
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Introduction

The neutrosophic set proposed by Smarandache (1999) is a powerful general formal framework, which generalizes fuzzy sets (Zadeh, 1965), intuitionistic fuzzy sets (Atanassov, 1986), interval valued fuzzy sets (Turksen, 1986), interval valued intuitionistic fuzzy sets (Atanassov & Gargov, 1989), and can be easier and better to express the incomplete, indeterminate and inconsistent information. However, intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets, which are generalized as fuzzy sets, can only handle incomplete information but not the indeterminate and inconsistent information which exists commonly in real situations, while the neutrosophic set can independently express truth-membership degree, indeterminacy-membership degree, and false-membership degree and deal with incomplete, indeterminate, and inconsistent information. Then, fuzzy multicriteria decision-making theory and methods are the important parts of decision-making applications (Liou & Chen, 2006; Ye, 2012). In real decision making, the evaluation information for alternatives given by decision makers is often incomplete, indeterminate and inconsistent information. Therefore, the neutrosophic set can effectively handle the decision-making problem with incomplete, indeterminate, and inconsistent information. However, the neutrosophic set was presented from philosophical point of view. Obviously, it was difficult to apply in the real applications. To obtain the real applications, Wang et al. (2005, 2010) proposed single valued neutrosophic sets (SVNSs) and interval neutrosophic sets (INSs) as the subclasses of neutrosophic sets and some operators of SVNSs and INSs. After that, Ye (2013) presented the correlation coefficient of SVNSs based on the extension of the correlation of intuitionistic fuzzy sets and proved that the cosine similarity measure is a special case of the correlation coefficient for SVNSs, and then applied it to single valued neutrosophic decision-making problems. Chi and Liu (2013) proposed a multiple attribute decision making method based on an extended TOPSIS method under interval neutrosophic environment. Moreover, Ye (2014a) defined the Hamming and Euclidean distances between INSs and developed the similarity measures between INSs based on the relationship between similarity measures and distances, and then a multicriteria decision-making method based on the similarity measures between INSs was established in interval neutrosophic setting, in which criterion values with respect to alternatives are expressed by the form of INSs. Furthermore, Ye (2014b) proposed a single valued neutrosophic cross-entropy measure and applied it to multicriteria decision making problems with single valued neutrosophic information.

Extracting information and converting it to ‘easy to interpret’knowledge is a very important but not a trivial task in Systems Engineering, in particular in the case of very complex and non-linear processes. Within this context, soft computing techniques can be utilized to offer their transparency and interpretability potential. Transparency plays a significant role as a measure of interpretability and distinguishability, i.e. the more interpretable information of a system under study, the better its understanding. Unlike popular clustering approaches such as fuzzy C-means, granular computing (GrC) groups data not only based on similar mathematical properties such as proximity but also it considers the raw data as conceptual entities that are captured in a compact and transparent manner. Therefore, such individual entities are merged into dense information granules whose similarity can be evaluated in a variety of ways depending on the application at hand. In GrC all operators act on the information granules and raw data, which can embed useful (for the data mining process) granular knowledge such as the proximity to other information granules, cardinality, density, function similarity, orientation, overlap, etc.

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