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Probabilistic Averaging in Bounded Rℓ-Monoids

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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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Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Stefanikova 49, SK-814 73 Bratislava, Slovakia

    Anatolij Dvurecenskij

  2. Department of Algebra and Geometry, Faculty of Sciences, Palacky University, Tomkova 40, CZ-779 00 Olomouc, Czech Republic

    Jiri Rachunek

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  1. Anatolij Dvurecenskij
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  2. Jiri Rachunek
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Correspondence to Anatolij Dvurecenskij or Jiri Rachunek.

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Dvurecenskij, A., Rachunek, J. Probabilistic Averaging in Bounded Rℓ-Monoids . Semigroup Forum 72, 191–206 (2006). https://doi.org/10.1007/s00233-005-0545-6

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  • DOI: https://doi.org/10.1007/s00233-005-0545-6

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