A general class of triangular norm-based aggregation operators: quasi-linear T–S operators

AbstractThis paper generalizes the well-known exponential and linear convex T–S aggregation operators into a wider class of compensatory aggregation operators, built as the composition of an arbitrary quasi-linear mean with a t-norm and a t-conorm, which are called quasi-linear T–S operators. These new operators are compared with other existing ones, and their main properties, such as the existence of neutral or annihilator elements, are studied. In particular, the self-duality property is investigated, and a characterization of an important family of self-dual quasi-linear T–S operators is provided