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This work studies the aggregation operators on the set of all possible membership degrees of typical hesitant fuzzy sets, which we refer to as H, as well as the action of H-automorphisms which are defined over the set of all finite non-empty subsets of the unitary interval. In order to do so, the partial order 6 H , based on a-normalization, is introduced, leading to a comparison based on selecting the greatest membership degrees of the related fuzzy sets. Additionally, the idea of interval representation is extended to the context of typical hesitant aggregation functions named as the H-representation. As main contribution, we consider the class of finite hesitant triangular norms, studying their properties and analyzing the H-conjugate functions over such operators.

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Orientation map 35 Singular points 36 3 7 a b s t r a c t 38 This paper reviews the fingerprint classification literature looking at the problem from a double perspec-39 tive. We first deal with feature extraction methods, including the different models considered for singular 40 point detection and for orientation map extraction. Then, we focus on the different learning models con-41 sidered to build the classifiers used to label new fingerprints. Taxonomies and classifications for the fea-42 ture extraction, singular point detection, orientation extraction and learning methods are presented. A 43 critical view of the existing literature have led us to present a discussion on the existing methods and 44 their drawbacks such as difficulty in their reimplementation, lack of details or major differences in their 45 evaluations procedures. On this account, an experimental analysis of the most relevant methods is car-46 ried out in the second part of this paper, and a new method based on their combination is presented.47

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