论文信息 - Heyting Wajsberg Algebras as an Abstract Environment Linking Fuzzy and Rough Sets

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 ?ukasiewicz 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 ?ukasiewicz 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.

Gianpiero Cattaneo | Davide Ciucci | G. Cattaneo | D. Ciucci

[1] D Ciucci,et al. BZW algebras for an abstract approach to roughness and fuzziness , 2002 .

[2] R. Sikorski,et al. The mathematics of metamathematics , 1963 .

[3] Gianpiero Cattaneo,et al. Some algebraicstructures for many-valued logics , 1998 .

[4] Petr Hájek,et al. Metamathematics of Fuzzy Logic , 1998, Trends in Logic.

[5] Gianpiero Cattaneo,et al. Brouwer-Zadeh posets and three-valued Ł ukasiewicz posets , 1989 .

[6] Brian F. Chellas. Modal Logic: Normal systems of modal logic , 1980 .

[7] N. Rescher. Many Valued Logic , 1969 .

[8] C. Chang,et al. Algebraic analysis of many valued logics , 1958 .

[9] J. Kacprzyk,et al. Incomplete Information: Rough Set Analysis , 1997 .

[10] P. Pagliani. Rough Set Theory and Logic-Algebraic Structures , 1998 .

[11] Francesc Esteva,et al. Review of Triangular norms by E. P. Klement, R. Mesiar and E. Pap. Kluwer Academic Publishers , 2003 .

[12] Gianpiero Cattaneo,et al. BZMVdM algebras and stonian MV-algebras (applications to fuzzy sets and rough approximations) , 1999, Fuzzy Sets Syst..

[13] A. Monteiro. Sur les algèbres de Heyting symétriques , 1980 .

[14] E. Turunen. Mathematics Behind Fuzzy Logic , 1999 .