Representation and construction of homogeneous and quasi-homogeneous $n$-ary aggregation functions

Homogeneity, as one type of invariantness, means that an aggregation function is invari-ant with respect to multiplication by a constant, and quasi-homogeneity, as a relaxed ver-sion, reflects the original output as well as the constant. In this paper, we characterize all homogeneous/quasi-homogeneous n-ary aggregation functions and present several methods to generate new homogeneous/quasi-homogeneous n-ary aggregation functions by aggregation of given ones.