On the structure of rough approximations

Fundamenta Informaticae

Volumn 53, Issue 2, 2002, Pages 135-153

  Järvinen, Jouni ^a  

^a TURKU CENTRE FOR COMPUTER SCIENCE   (Finland)

Author keywords

[No Author keywords available]

Indexed keywords

MAPPING; MATHEMATICAL OPERATORS; ROUGH SET THEORY;

ROUGH APPROXIMATIONS;

APPROXIMATION THEORY;

EID: 0036874722     PISSN: 01692968     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. G. Birkhoff, Lattice Theory, 3rd ed., Colloquium Publications XXV (American Mathematical Society, Providence, R. I., 1967).
2. G. Cattaneo, Abstract Approximation Spaces for Rough Theories, In: L. Polkowski, A. Skowron (eds.), Rough Sets in Knowledge Discovery I (Physica, Heidelberg, 1998) 59-98.
3. B.A. Davey, H.A. Priestley, Introduction to Lattices and Order (Cambridge University Press, Cambridge, 1990).
4. I. Düntsch, E. Ortowska, H. Wang, Algebras of Approximating Regions, Fundamenta Informaticae 46 (2001) 71-82.
5. M. Gehrke, E. Walker, On the Structure of Rough Sets, Bulletin of the Polish Academy of Sciences, Mathematics 40 (1992) 235-245.
6. T.B. Iwiński Algebraic Approach to Rough Sets, Bulletin of the Polish Academy of Sciences, Mathematics 35 (1987) 673-683.
7. J. Järvinen, Knowledge Representation and Rough Sets, TUCS Dissertations 14 (Turku Centre for Computer Science, Turku, 1999).
8. J. Järvinen, Approximations and Rough Sets Based on Tolerances, in: W. Ziarko, Y. Yao (eds.), Proceedings of The Second International Conference on Rough Sets and Current Trends in Computing (RSCTC 2000), Lecture Notes in Artificial Intelligence 2005 (Springer, Berlin, 2001) 182-189.
9. J. Järvinen, On the Structure of Rough Approximations (Extended Abstract), in: J.J. Alpigini, J.F. Peters, A. Skowron, N. Zhong (eds.), Proceedings of The Third International Conference on Rough Sets and Current Trends in Computing (RSCTC 2002), Lecture Notes in Artificial Intelligence 2475 (Springer, Berlin, 2002) 123-130.
10. B. Jónsson, A. Tarski, Boolean Algebras with Operators. Part I, American Journal of Mathematics 73 (1951) 891-939.
11. J. Kortelainen, A Topological Approach to Fuzzy Sets, Ph.D. Dissertation, Lappeenranta University of Technology, Acta Universitatis Lappeenrantaensis 90 (1999).
12. E.J. Lemmon, Algebraic Semantics for Modal Logics. Part I, Journal of Symbolic Logic 31 (1966) 46-65.
13. J.C.C. McKinsey, A. Tarski, The Algebra of Topology, Annals of Mathematics 45 (1944) 141-191.
14. E. Orłowska, Introduction: What You Always Wanted to Know About Rough Sets, in: E. Ortowska (ed.), Incomplete Information: Rough Set Analysis (Physica, Heidelberg, 1998) 1-20.
15. Z. Pawlak, Rough Sets, International Journal of Computer and Information Sciences 5 (1982) 341-356.
16. J.A Pomykała, About Tolerance and Similarity Relations in Information Systems, in: J.J. Alpigini, J.F. Peters, A. Skowron, N. Zhong (eds.), Proceedings of The Third International Conference on Rough Sets and Current Trends in Computing (RSCTC 2002), Lecture Notes in Artificial Intelligence 2475 (Springer, Berlin, 2002) 175-182.
17. A. Skowron, J. Stepaniuk, Tolerance Approximation Spaces, Fundamenta Informaticae 27 (1996) 245-253.
18. R. Slowinski, D. Vanderpooten, A Generalized Definition of Rough Approximations Based on Similarity, IEEE Transactions on Knowledge and Data Engineering 12 (2000) 331-336.
19. Y.Y. Yao, T.Y. Lin, Generalization of Rough Sets using Modal Logics, Intelligent Automation and Soft Computing, An International Journal 2 (1996) 103-120.
20. Y.Y. Yao, On Generalizing Pawlak Approximation Operators, in: L. Polkowski, A. Skowron (eds.), Proceedings of The First International Conference on Rough Sets and Current Trends in Computing (RSCTC 1998), Lecture Notes in Artificial Intelligence 1424 (Springer, Berlin, 1998) 298-307.