Fuzzy set (FS) theory is one of the most important tool to deasl with complicated and difficult information in real-world. Now FS has many extensions and hesitant fuzzy set (HFS) is one of them. Further generalization of FS is complex fuzzy set (CFS), which contains only the membership grade, whose range is unit disc instead of [0, 1]. The aim of this paper is to present the idea of complex hesitant fuzzy set (CHFS) and to introduce its basic properties. Basically, CHFS is the combination of CFS and HFS to deal with two dimension information in a single set. Further, the vector similarity measures (VSMs) such as Jaccard similarity measures (JSMs), Dice similarity measures (DSMs) and Cosine similarity measures (CSMs) for CHFSs are discussed. The special cases of the proposed measures are also discussed. Then, the notion of complex hesitant fuzzy hybrid vector similarity measures are utilized in the environment of pattern recognition and medical diagnosis. Further, based on these distance measures, a decision-making method has been presented for finding the best alternative under the set of the feasible one. Illustrative examples from the field of pattern recognition as well as medical diagnosis have been taken to validate the approach. Finally, the comparison between proposed approaches with existing approaches are also discussed to find the reliability and proficiency of the elaborated measures for complex hesitant fuzzy elements.
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