On aggregation functions on lattices
by
Radomír Halaš (Palacký University Olomouc)
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.
(back
to Algebra Seminar)