Algebra Seminar talk
Radomír Halaš (Palacký University Olomouc)
On aggregation functions on lattices
Aggregation represents a process of merging and combining several (usually numerical) data in a single output. The mathematical theory of aggregation is based on the notion of an aggregation function describing the process of merging. The talk is devoted to a study of aggregation functions on bounded lattices via clone theory approach. For any finite n-element lattice L we present a set of at most 2n + 2 aggregation functions on L from which the aggregation clone is generated. We also characterize all finite lattices L for which the aggregation clone is as small as possible, i.e. when it coincides with the clone of 0,1-polynomial functions on L. These lattices are shown to be completely determined by their tolerances.