On some new geometrically motivated operators over intuitionistic fuzzy sets

We consider four new geometrically motivated operators acting in the interior of the interpretation triangle used to depict intuitionistic fuzzy sets. The first operators uses the points resulting from the classical "necessity" and "possibility" operators, in combination with the point ⟨0, 0⟩. The definition of the second operator employs the projections of the considered point onto the sides of the triangle, as viewed from the vertices ⟨0, 0⟩, ⟨0, 1⟩, and ⟨1, 0⟩. The remaining two operators combine two of these projections with the result of the modal operators of the internal point. We also consider operators obtained as linear combinations of some of these four operators.