Negative Hesitation Fuzzy Sets and Their Application to Pattern Recognition

The initial concept of negative hesitation fuzzy sets (NHFSs) has been introduced recently. NHFSs are applied to decision-making problems accompanied by soft set theory. In this article, a detailed clarification of NHFSs is proposed. Meanwhile, we introduced the way to construct membership, nonmembership, and negative hesitation degrees by studying the overlap area between the projections of the element and classes in a 2-D space. This unified construction has concluded the relationship between NHFSs and intuitionistic fuzzy sets. A corollary of cosine similarity satisfying the NHFSs is employed for the pattern recognition problems. Classification of both synthetic numerical examples and the EEG signals are evaluated for the effectiveness of NHFSs in this article.