Probabilistic Averaging in Bounded Rℓ-Monoids |
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Authors: | Anatolij Dvurecenskij Jiri Rachunek |
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Institution: | (1) Mathematical Institute, Slovak Academy of Sciences, Stefanikova 49, SK-814 73 Bratislava, Slovakia;(2) Department of Algebra and Geometry, Faculty of Sciences, Palacky University, Tomkova 40, CZ-779 00 Olomouc, Czech Republic |
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Abstract: | Bounded Rℓ-monoids generalize
GMV-algebras and pseudo BL-algebras. Such monoids do not admit, in
general, any analogue of addition, in contrast to GMV-algebras.
Nevertheless we introduce the notion of a state (an analogue of a
probability measure). It coincides with that for GMV-algebras. We
show that the existence of states is crucially connected with the
existence of normal and maximal filters. In addition, some
topological properties of the extremal states and the hull-kernel
topology of filters are studied. |
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Keywords: | |
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