Threshold constructions of aggregation functions

In this paper, the properties of a new construction method of aggregation functions from two given ones, called threshold construction, are examined. This class of nonsymmetric functions provides a generalization of t-norms and t-conorms by partitioning the unit interval with respect to only one variable. Fuzzy modeling provides a framework in which relationship of the input and the output can be modeled by splitting the input into fuzzy regions for which we can describe the output in different ways. In several applications the roles of the inputs are not symmetric, which indicates the uuse of the examined construction.