Capacities with Values in Compact Hausdorff Lattices |
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Authors: | Oleh R Nykyforchyn |
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Institution: | (1) Precarpathian National University, Ivano-Frankivsk, Ukraine |
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Abstract: | For a compact Hausdorff topological lattice L the set M
L
X of L-valued normed regular capacities on a compact Hausdorff topological space X is investigated. It is shown that the set M
L
X carries a compact Hausdorff topology, and M
L
extends to a weakly τ-normal functor in the category of compacta. If L is an upper and lower Lawson semilattice, then M
L
is the functorial part of two semimonads. These semimonads coincide and are a monad if and only if L is distributive, i.e., is a Lawson lattice. The obtained results have a natural interpretation if capacities are regarded
as subjective estimates of likelihood of realization of events in conditions of uncertainty.
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Keywords: | capacity monad category of compacta Lawson lattice |
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