Aggregation Functions Transformed by 0 - 1 Valued Monotone Systems of Functions

In the paper Jin et al. [8] the authors introduced a generalized phi-transformation of aggregation functions. This is a kind of two-step aggregation. This transformation was further developed in Jin et al. [9] into a Generalized-Convex-Sum-Transformation. A special case of the proposed Generalized-Convex-Sum-Transformation is the well-known *-product, also known as the Darsow product of copulas. This approach covers also the discrete Choquet integral. In this paper we study the monotone systems of functions, particularly the case when functions in these systems are just two-valued.