Efficient online generation of fuzzy measures via aggregation functions

Discrete fuzzy integrals (F-integrals) are fusion functions that leverage discrete fuzzy measures to capture interactions within the data. However, their scalability is often limited by the computational overhead of evaluating the measure across the entire measurable space. This paper introduces an efficient online approach for generating fuzzy measures using aggregation functions. The online methodology allows to calculate the F-integral alongside the fuzzy measure without increasing its asymptotic complexity and without requiring previous calculations. The role of the aggregation functions is to establish the properties of the generated measure. To this end, we define and study non-conjunctive aggregation functions, designed to prevent vanishing measures and ensure that the resulting measures retain meaningful and useful properties. In addition the methodology includes an optimizable component, enabling the learning of fuzzy measures and therefore the use of F-Integrals in learning environments. A complexity analysis confirms the method's efficiency, and experiments on supervised classification tasks demonstrate its practical utility.