Q-Aggregates: The smallest universal nonlinear connective operators

A novel class of highly adaptive nonlinear digital aggregation connectives called Q-aggregates is described in this paper. The Q-aggregate approach relies on a unique control parameter lambda to characterize the three conventional fuzzy intersection, union, and averaging aggregation operators. In addition to this universal coverage property of the proposed model, a distinguishing and extremely interesting characteristic of the Q-aggregate connective is that even for a fixed value of the control parameter lambda, a given operator can behave as "more than one" family of the conventional connectives depending on the input values. We present the Q-aggregate in application to a real-valued signal processing task, with an optimization algorithm, so that the parameters of the operators can be tuned automatically. The Q-aggregate operator is tested on electrocardiogram (EKG) data. The experiments show that the proposed model can be used to map input signals to their corresponding target signals through learning.