On comonotone k-maxitive aggregation functions

The aim of this paper is to study comonotone k-maxitive aggregation functions, i.e., aggregation functions fulfilling k-maxitivity for comonotone inputs. We characterize all comonotone k-maxitive aggregation functions and clarify the relation between comonotone k-maxitive aggregation functions and Sugeno integrals, level-dependent Sugeno integrals and Sugeno integrals w.r.t. k-maxitive fuzzy measure. The subset of the unit hypercube fully determining comonotone k-maxitive aggregation function is found and a construction method based on this set is proposed.