Roughness in residuated lattices

Communications in Computer and Information Science

Volumn 297 CCIS, Issue PART 1, 2012, Pages 596-603

  Rachůnek, Jiří ^a   Šalounová, Dana ^b  

^a PALACKÝ UNIVERSITY   (Czech Republic)

^b VSB TECHNICAL UNIVERSITY OF OSTRAVA   (Czech Republic)

Author keywords

commutative bounded integral residuated lattice; congruence; filter; Rough set

Indexed keywords

APPROXIMATION SPACES; CONGRUENCE; FILTER; REASONING UNDER UNCERTAINTY; RESIDUATED LATTICES; ROUGH SET;

ALGEBRA; ARTIFICIAL INTELLIGENCE; DATA PROCESSING; FUZZY LOGIC; KNOWLEDGE BASED SYSTEMS;

INFORMATION MANAGEMENT;

EID: 84868029349     PISSN: 18650929     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-642-31709-5_60     Document Type: Conference Paper

References (34)

1. Biswas, R., Nanda, S.: Rough groups and rough subgroups. Bulletin of the Polish Academy of Sciences Mathematics 42, 251-254 (1994)
2. Cattaneo, G., Ciucci, D.: Algebraic Structures for Rough Sets. In: Peters, J.F., Skowron, A., Dubois, D., Grzyma-la-Busse, J.W., Inuiguchi, M., Polkowski, L. (eds.) Transactions on Rough Sets II. LNCS, vol. 3135, pp. 208-252. Springer, Heidelberg (2004)
3. Ciucci, D.: On the axioms of residuated structures independence dependencies and rough approximations. Fundam. Inform. 69, 359-387 (2006)
4. Ciucci, D.: A Unifying Abstract Approach for Rough Models. In: Wang, G., Li, T., Grzymala-Busse, J.W., Miao, D., Skowron, A., Yao, Y. (eds.) RSKT 2008. LNCS (LNAI), vol. 5009, pp. 371-378. Springer, Heidelberg (2008)
5. Cignoli, R.L.O., D'Ottaviano, I.M.L., Mundici, D.: Algebraic Foundation of Manyvalued Reasoning. Kluwer Acad. Publ., Dordrecht (2000)
6. Ciungu, L.C.: Bosbach and Riecan states on residuated lattices. J. Appl. Funct. Anal. 3, 175-188 (2008)
7. Davvaz, B.: Roughness in rings. Inf. Sci. 164, 147-163 (2004)
8. Davvaz, B.: Roughness based on fuzzy ideals. Inf. Sci. 176, 2417-2437 (2006)
9. Dvurecenskij, A., Rachunek, J.: Probabilistic averaging in bounded commutative residuated -monoids. Discret. Math. 306, 1317-1326 (2006)
10. Estaji, A.A., Khodaii, S., Bahrami, S.: On rough set and fuzzy sublattice. Inf. Sci., doi:10.1016/j.ins.2011.04.043
11. Esteva, F., Godo, L.: Monoidal t-norm based logic: towards a logic for leftcontinuous t-norms. Fuzzy Sets Syst. 124, 271-288 (2001)
12. Galatos, N., Jipsen, P., Kowalski, T., Ono, H.: Residuated lattices: An Algebraic Glimpse at Substructural Logics. Elsevier Sudies in Logic and Foundations. Elsevier, New York (2007)
13. H́ajek, P.: Metamathematics of Fuzzy Logic. Kluwer, Amsterdam (1998)
14. Jipsen, P., Tsinakis, C.: A survey of residuated lattices. In: Martinez, J. (ed.) Ordered Algebraic Structures, pp. 19-56. Kluwer Acad. Publ., Dordrecht (2002)
15. Kondo, M.: Algebraic Approach to Generalized Rough Sets. In: Śl -ezak, D., Wang, G., Szczuka,M.S., Düntsch, I., Yao, Y., et al. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 132-140. Springer, Heidelberg (2005)
16. Kuroki, N.: Rough ideals in semigroups. Inf. Sci. 100, 139-163 (1997)
17. Leoreanu-Fotea, V., Davvaz, B.: Roughness in n-ary hypergroups. Inf. Sci. 178, 4114-4124 (2008)
18. Li, T.J., Leung, Y., Zhang,W.X.: Generalized fuzzy rough approximation operators based on fuzzy coverings. Int. J. Approx. Reasoning 48, 836-856 (2008)
19. Li, X., Liu, S.: Matroidal approaches to rough sets via closure operators. Int. J. Approx. Reasoning 53, 513-527 (2012)
20. Liu, G.L., Zhu, W.: The algebraic structures of generalized rough set theory. Inf. Sci. 178, 4105-4113 (2008)
21. Mundici, D.: Interpretation of AF C -algebras in sentential calculus. J. Funct. Analys. 65, 15-63 (1986)
22. Pawlak, Z.: Rough sets. Int. J. Inf. Comput. Sci. 11, 341-356 (1982)
23. Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. System Theory, Knowledge Engineering and Problem Solving, vol. 9. Kluwer Academic Publishers, Dordrecht (1991)
24. Pawlak, Z., Skowron, A.: Rudiments of rough sets. Inf. Sci. 177, 3-27 (2007)
25. Pawlak, Z., Skowron, A.: Rough sets: some extensions. Inf. Sci. 177, 28-40 (2007)
26. Pawlak, Z., Skowron, A.: Rough sets and Boolean reasoning. Inf. Sci. 177, 41-73 (2007)
27. Pei, D.: On definable concepts of rough set models. Inf. Sci. 177, 4230-4239 (2007)
28. Radzikowska, A.M., Kerre, E.E.: Fuzzy Rough Sets Based on Residuated Lattices. In: Peters, J.F., Skowron, A., Dubois, D., Grzyma-la-Busse, J.W., Inuiguchi, M., Polkowski, L. (eds.) Transactions on Rough Sets II. LNCS, vol. 3135, pp. 278-296. Springer, Heidelberg (2004)
29. Rasouli, S., Davvaz, B.: Roughness in MV-algebras. Inf. Sci. 180, 737-747 (2010)
30. She, Y.H., Wang, G.J.: An approximatic approach of fuzzy rough sets based on residuated lattices. Comput. Math. Appl. 58, 189-201 (2009)
31. Xiao, Q.M., Zhang, Z.L.: Rough prime ideals and rough fuzzy prime ideals in semigroups. Inf. Sci. 176, 725-733 (2006)
32. Yang, L., Xu, L.: Algebraic aspects of generalized approximation spaces. Int. J. Approx. Reasoning 51, 151-161 (2009)
33. Zhu, P.: Covering rough sets based on neighborhoods: An approach without using neighborhoods. Int. J. Approx. Reasoning 52, 461-472 (2011)
34. Zhu, W.: Relationship between generalized rough set based on binary relation and covering. Inf. Sci. 179, 210-225 (2009)