Vector Similarity Measures of Simplified Neutrosophic Sets and Their Application in Multicriteria Decision Making

Neutrosophic set is a powerful general formal framework, which generalizes the concept of the classic set, fuzzy set, interval valued fuzzy set, intuitionistic fuzzy set, and interval-valued intuitionistic fuzzy set from philosophical point of view. However, it will be difficult to apply in real science and engineering areas, while a simplified neutrosophic set (SNS) is a subclass of a neutrosophic set and includes the concepts of a single valued neutrosophic set (SVNS) and an interval neutrosophic set (INS), which can be used in real science and engineering applications with the incomplete, indeterminate and inconsistent information which exists commonly in real situations. Therefore, the main purposes of the paper are to present three vector similarity measures between SNSs as a generalization of the Jaccard, Dice, and cosine similarity measures in vector space and to apply them to the multicriteria decision-making problem with simplified neutrosophic information. Through the similarity measure between each alternative and the ideal alternative, the ranking order of all alternatives can be determined and the best alternative can be easily selected as well. Finally, an illustrative example demonstrates the application of the proposed measure methods in the simplified neutrosophic multicriteria decision making.