Abstract
The main aim of this paper is to study aggregation functions on lattices via clone theory approach. Observing that the aggregation functions on lattices just correspond to 0, 1-monotone clones, as the main result we show that for any finite n-element lattice L there is a set of at most 2n+2 aggregation functions on L from which the respective clone is generated. Namely, the set of generating aggregation functions consists only of at most n unary functions, at most n binary functions, and lattice operations ∧, ∨, and all aggregation functions of L are composed of them by usual term composition. Moreover, our approach works also for infinite lattices (such as mostly considered bounded real intervals [a, b]), where in contrast to finite case infinite suprema (or, equivalently, a kind of limit process) have to be considered.
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