Aggregation functions for typical hesitant fuzzy elements and the action of automorphisms

This work studies the aggregation operators on the set of all possible membership degrees of typical hesitant fuzzy sets, which we refer to as image, as well as the action of image-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 image, based on α-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 image-representation. As main contribution, we consider the class of finite hesitant triangular norms, studying their properties and analyzing the image-conjugate functions over such operators.