New classes of threshold aggregation functions based upon the Tsallis q-exponential

We introduce two new classes of single-parameter aggregation functions based upon the Tsallis q-exponential function of non-extensive statistical mechanics. These aggregation functions facilitate simple modeling of two different common human reasoning traits of “threshold” inference, where either: 1) at least one input must exceed a threshold in order to achieve a non-zero aggregation output, or 2) if any one of the inputs exceeds a different threshold, the aggregation output takes its maximum value. We illustrate the thresholding behavior of these functions on interval type-2 fuzzy set inputs.