Single Valued Neutrosophic Similarity Measures for Multiple Attribute Decision-Making

Abstract

Similarity measures play an important role in data mining, pattern recognition, decision making, machine learning, image process etc. Then, single valued neutrosophic sets (SVNSs) can describe and handle the indeterminate and inconsistent information, which fuzzy sets and intuitionistic fuzzy sets cannot describe and deal with. Therefore, the paper proposes new similarity measures between SVNSs based on the minimum and maxi-mum operators. Then a multiple attribute decision-making method based on the weighted similarity measure of SVNSs is established in which attribute values for alternatives are represented by the form of single valued neutrosophic values (SVNVs) and the attribute weights and the weights of the three independent elements (i.e., truth membership degree, indeterminacy-membership degree, and falsity-membership degree) in a SVNV are considered in the decision-making method. In the decision making, we utilize the single-valued neutrosophic weighted similarity measure between the ideal alternative and an alternative to rank the alternatives corresponding to the measure values and to select the most desirable one(s). Finally, two practical examples are provided to demonstrate the applications and effectiveness of the single valued neutrosophic multiple attribute decision-making method.