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

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Rough Sets and Current Trends in Computing (RSCTC 2002)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2475))

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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.

This work has been supported by MIURCOFIN project “Formal Languages and Automata: Theory and Application”.

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References

  1. Chellas, B.F..: Modal Logic, An Introduction. Cambridge University Press, Cambridge (1988)

    Google Scholar 

  2. Cattaneo, G. Ciucci, D.: BZW algebras for an abstract approach to roughness and fuzziness. Accepted to IPMU 2002 (2002)

    Google Scholar 

  3. Cattaneo, G., Dalla Chiara, M.L., Giuntini, R.: Some algebraic structures for many-valued logics. Tatra Mountains Mathematical Publication 15 (1998) 173–196

    MATH  MathSciNet  Google Scholar 

  4. Cattaneo, G., Giuntini, R., Pilla, R.: BZMVdM and Stonian MV algebras (applications to fuzzy sets and rough approximations). Fuzzy Sets Syst. 108 (1999) 201–222

    Article  MATH  MathSciNet  Google Scholar 

  5. Cattaneo, G., Nisticó, G.: Brouwer-Zadeh posets and three valued Łukasiewicz posets. Fuzzy Sets Syst. 33 (1989) 165–190

    Article  MATH  Google Scholar 

  6. Chang, C.C.: Algebraic analysis of many valued logics. Trans. Amer. Math. Soc. 88 (1958) 467–490

    Article  MATH  MathSciNet  Google Scholar 

  7. Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer, Dordrecht (1998)

    MATH  Google Scholar 

  8. Klement, E. P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Academic, Dordrecht (2000)

    MATH  Google Scholar 

  9. Monteiro, A.A..: Sur les algébres de Heyting symétriques. Portugaliae Mathematica 39 (1980) 1–237

    MathSciNet  Google Scholar 

  10. Pagliani, P.: Rough set theory and logic-algebraic structures. In Orlowska, E., ed.: Incomplete Information: Rough Set Analysis. Physica-Verlag, Heidelberg (1998) 109–190

    Google Scholar 

  11. Rasiowa, H. Sikorski, R.: The Mathematics of Metamathematics. Third edn. Polish Scientific Publishers, Warsaw (1970)

    Google Scholar 

  12. Rescher, N.: Many-valued logic. Mc Graw-Hill, New York (1969)

    MATH  Google Scholar 

  13. Surma S.: Logical Works. Polish Academy of Sciences, Wroclaw (1977)

    Google Scholar 

  14. Turunen, E.: Mathematics Behind Fuzzy Logic. Physica-Verlag, Heidelberg (1999)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Dipartimento Di Informatica, Sistemistica e Comunicazione, Universitá di Milano - Bicocca, Via Bicocca degli Arcimboldi 8, I-20126, Milano, Italia

    Gianpiero Cattaneo & Davide Ciucci

Authors
  1. Gianpiero Cattaneo
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  2. Davide Ciucci
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Editor information

Editors and Affiliations

  1. Penn State Great Valley School of Professional Graduate Studies, 30 East Swedesford Road, Malvern, PA, 19355, USA

    James J. Alpigini

  2. Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, MB, R3T 5V6, Canada

    James F. Peters

  3. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

  4. Department of Systems and Information Engineering, Maebashi Institute of Technology, 460-1 Kamisadori-Cho, Maebashi-City, 371-0816, Japan

    Ning Zhong

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© 2002 Springer-Verlag Berlin Heidelberg

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Cattaneo, G., Ciucci, D. (2002). Heyting Wajsberg Algebras as an Abstract Environment Linking Fuzzy and Rough Sets. In: Alpigini, J.J., Peters, J.F., Skowron, A., Zhong, N. (eds) Rough Sets and Current Trends in Computing. RSCTC 2002. Lecture Notes in Computer Science(), vol 2475. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45813-1_10

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  • DOI: https://doi.org/10.1007/3-540-45813-1_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44274-5

  • Online ISBN: 978-3-540-45813-5

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