New Classes of Threshold Aggregation Functions Based Upon the Tsallis q-Exponential With Applications to Perceptual Computing

Abstract

We introduce two new classes of single-parameter aggregation functions based upon the Tsallis q-exponential (QE) function of nonextensive statistical mechanics. These aggregation functions (denoted QE aggregation) facilitate simple modeling of the common human reasoning trait of “threshold” inference, where either 1) at least one input must exceed a threshold in order to achieve a nonzero 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 inputs using an example known in the literature as the Investment Judgment Advisor. We believe that the new QE class of aggregation operators will prove useful in extending the range of options available for the design of perceptual computing systems.