In this paper, we propose a new class of type-2 fuzzy sets: Hedge Algebraic Type-2 Fuzzy Sets - HaT2FS. The particular feature of HaT2FS is that the membership grades of each element are linguistic truth values of hedge algebras. We consider some important aspects of this class of type-2 fuzzy sets: operations on linguistic truth values including linguistic aggregation, meet and join; HaT2FSs representation by hedge union of k-level embedded HaT2FSs; and intersection, union and complement operations on HaT2FSs.

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