As a generalization of bivariate overlap functions, which measure the degree of overlapping (intersection for non-crisp sets) of n different classes, in this paper we introduce the concept of general overlap functions. We characterize the class of general overlap functions and include some construction methods by means of different aggregation and bivariate overlap functions. Finally, we apply general overlap functions to define a new matching degree in a classification problem. We deduce that the global behavior of these functions is slightly better than some other methods in the literature.

The work has been supported by the Research Services of the Universidad Publica de Navarra, the research projects TIN2016-77356-P (AEI/FEDER, UE) and TIN2015-66471-P from the Government of Spain and by the Brazilian National Counsel of Technological and Scientific Development CNPq (Proc. 233950/2014-1, 306970/2013-9, 307781/2016-0) and by Caixa and Fundación Caja Navarra of Spain.