A constructive framework to define fusion functions with floating domains in arbitrary closed real intervals

Fusion functions and their most important subclass, aggregation functions, have been successfully applied in fuzzy modeling. However, there are practical problems, such as classification via Convolutional Neural Networks (CNNs), where the data to be aggregated are not modeling membership degrees in the unit interval. In this scenario, systems could benefit from the application of operators defined in domains different from [0,1], although, presenting similar behavior of some aggregation functions whose subclasses are currently defined only in the fuzzy context (e.g., overlap functions and t-norms). So, the main objective of this paper is to present a general framework to characterize classes of fusion functions with floating domains, called (a,b)-fusion functions, defined on any closed real interval [a,b], based on classes of core fusion functions defined on [0,1]. The fundamental aspect of this framework is that the properties of a core fusion function are preserved in the context of the analogous (a,b)-fusion function. Construction methods are presented, and some properties are studied. We also introduce a framework to define fusion functions in which the inputs come from an interval [a,b] but the output is mapped on a possibly different interval [c,d]. Finally, we present an illustrative example in image classification via CNNs.(C) 2022 Elsevier Inc. All rights reserved.