Some similarity measures for MADM under a complex neutrosophic set environment

Abstract Selection of a suitable alternative among the possible options is a difficult activity for decision-makers. Because of the indeterminate information and the complexity in periodic form of decision problems, it is difficult to express attributes in terms of crisp sets, fuzzy sets, and neutrosophic sets. However, complex neutrosophic set (CNS)—an important mathematical tool—can tackle uncertainty and indeterminate situations that are in periodic form. CNS generalizes the neutrosophic set whose truth membership function (complex-valued), indeterminacy membership function (complex-valued), and falsity membership functions (complex-valued) are the accumulations of truth amplitude term (real-valued) with phase term, indeterminate amplitude term (real-valued) with phase term, and false amplitude term (real-valued) with phase term, respectively. This chapter presents three similarity measures between CNSs. We propose complex neutrosophic cosine, Jaccard, and Dice similarity measures, and prove some important results of the proposed measures. We also propose weighted complex neutrosophic cosine, Jaccard, and Dice similarity measures, and prove some basic properties of the proposed weighted measures. We define a tangent function for determining unknown attributes weights under CNS environment. We develop cosine, Jaccard, and Dice similarity-based measures as three new strategies for multi-attribute decision-making problems. A numerical example of stream selection of students after secondary examination is given to demonstrate the proposed strategies.