Heyting Wajsberg algebras as an abstract environment linking fuzzy and rough sets. (English) Zbl 1013.03073
Alpigini, James J. (ed.) et al., Rough sets and current trends in computing. 3rd international conference, RSCTC 2002, Malvern, PA, USA, October 14-16, 2002. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 2475, 77-84 (2002).
Summary: 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 Łukasiewicz 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 Łukasiewicz 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.
For the entire collection see [Zbl 1001.00048].
For the entire collection see [Zbl 1001.00048].
MSC:
| 03G25 | Other algebras related to logic |
| 03E72 | Theory of fuzzy sets, etc. |
| 68T37 | Reasoning under uncertainty in the context of artificial intelligence |
| 03B50 | Many-valued logic |
