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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Nykyforchyn, O.R. Capacities with Values in Compact Hausdorff Lattices. Appl Categor Struct 15, 243–257 (2007). https://doi.org/10.1007/s10485-007-9061-z
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DOI: https://doi.org/10.1007/s10485-007-9061-z