Heyting Wajsberg Algebras as an Abstract Environment Linking Fuzzy and Rough Sets
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.
KeywordsHeyting algebra Wajsberg algebra fuzzy sets rough approximation space rough sets
Unable to display preview. Download preview PDF.
- Chellas, B.F..: Modal Logic, An Introduction. Cambridge University Press, Cambridge (1988)Google Scholar
- Cattaneo, G. Ciucci, D.: BZW algebras for an abstract approach to roughness and fuzziness. Accepted to IPMU 2002 (2002)Google Scholar
- Pagliani, P.: Rough set theory and logic-algebraic structures. In Orlowska, E., ed.: Incomplete Information: Rough Set Analysis. Physica-Verlag, Heidelberg (1998) 109–190Google Scholar
- Rasiowa, H. Sikorski, R.: The Mathematics of Metamathematics. Third edn. Polish Scientific Publishers, Warsaw (1970)Google Scholar
- Surma S.: Logical Works. Polish Academy of Sciences, Wroclaw (1977)Google Scholar