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Negative Hesitation Fuzzy Sets and Their Application to Pattern Recognition

Youpeng YangSchool of Advanced Technology, Xi'an Jiaotong-Liverpool University, Suzhou, ChinaSanghyuk LeeSchool of Computing, New Uzbekistan University, Tashkent, UzbekistanHaolan ZhangSCDM Center, Zhejiang University, Ningbo, ChinaXiaowei HuangDepartment of Computer Science, University of Liverpool, Liverpool, U.KWitold PedryczDepartment of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada
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Аннотация

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 paper, a detailed clarification of NHFSs is proposed. Meanwhile, we introduced the way to construct membership, non-membership, and negative hesitation degrees by studying the overlap area between the projections of the element and classes in a two-dimensional space. This unified construction has concluded the relationship between NHFSs and Intuitionistic Fuzzy Sets (IFSs). 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 paper.

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