A Topological Approach to the Study of Fuzzy Measures

Lattice uniformities on pseudo-D-lattices

“…These results extend similar ones estabilshed in [6] for lattice-ordered effect algebras, in [30] for orthomodular lattices, and in [10,22] for MV-algebras. Morevover they give, as a particular case, the order-isomorphism found in [23].…”

Lattice Uniformities on Effect Algebras

“…Also of importance is the role played in the study of modular functions on orthomodular lattices (see Weber, 1995) and of measures on MValgebras (see Barbieri and Weber, 1998;Graziano, 2000) by the lattice structure of filters which generate lattice uniformities making uniformly continuous the operations of these structures.…”

Decomposition of effect algebras and the Hammer–Sobczyk theorem

“…Indeed, we prove (see 4.3) that, if τ is an order continuous Hausdorff D-topology on L, then (L, τ ) is isomorphic and homeomorphic to the product of a connected and a totally disconnected D-lattice. As a consequence, we obtain in Section 5 a Hammer-Sobczyk type decomposition theorem for exhaustive modular measures on D-lattices (see 5.5), which extends results of [28] and [8].…”

“…This result has been generalized in [25] for group-valued measures on Boolean algebras (see also [13]). A Hammer-Sobczyk type decomposition theorem has been proved in [28] for modular functions on complemented lattices (in particular on orthomodular lattices) and in [8] for measures on MV-algebras.…”