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Heyting Wajsberg Algebras as an Abstract Environment Linking Fuzzy and Rough Sets

  • Gianpiero Cattaneo
  • Davide Ciucci
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2475)

Abstract

Heyting Wajsberg (HW) algebras are introduced as algebraic models of a logic equipped with two implication connectives, the Heyting one linked to the intuitionistic logic and the Wajsberg one linked to the Lukasiewicz approach to many-valued logic. On the basis of an HW algebra it is possible to obtain a de Morgan Brouwer-Zadeh (BZ) distributive lattice with respect to the partial order induced from the Lukasiewicz implication. Modal-like operators are also defined generating a rough approximation space. It is shown that standard Pawlak approach to rough sets is a model of this structure.

Keywords

Heyting algebra Wajsberg algebra fuzzy sets rough approximation space rough sets 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Gianpiero Cattaneo
    • 1
  • Davide Ciucci
    • 1
  1. 1.Dipartimento Di Informatica, Sistemistica e ComunicazioneUniversitá di Milano - BicoccaMilanoItalia

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