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 1Lukasiewicz 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 1Lukasiewicz 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.
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CITATION STYLE
Cattaneo, G., & Ciucci, D. (2002). Heyting Wajsberg algebras as an abstract environment linking fuzzy and rough sets. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2475, pp. 77–84). Springer Verlag. https://doi.org/10.1007/3-540-45813-1_10
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