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Keywords:
aggregation functions; invariantness; homogeneity; quasi-homogeneity
aggregation functions; invariantness; homogeneity; quasi-homogeneity
Summary:
Homogeneity, as one type of invariantness, means that an aggregation function is invariant with respect to multiplication by a constant, and quasi-homogeneity, as a relaxed version, 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.
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