Fuzzy filters and fuzzy prime filters of bounded Rl-monoids and pseudo BL-algebras

  • Authors:
  • Jiří Rachnek;Dana Šalounová

  • Affiliations:
  • Department of Algebra and Geometry, Faculty of Sciences, Palacký University, Tomkova 40, 779 00 Olomouc, Czech Republic;VŠB-Technical University Ostrava, Sokolská 33, 701 21 Ostrava, Czech Republic

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2008

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Abstract

The logical foundations of processes handling uncertainty in information use some classes of algebras as algebraic semantics. The sets of provable formulas in corresponding inference systems from the point of view of uncertain information can be described by fuzzy filters of those algebraic semantics. Bounded residuated lattice ordered monoids (R@?-monoids) are a common generalization of pseudo BL-algebras (and consequently of pseudo MV-algebras) and Heyting algebras, i.e. algebras behind fuzzy and intuitionistic reasoning. In the paper, we introduce and investigate fuzzy filters of bounded R@?-monoids and fuzzy prime filters of pseudo BL-algebras.