A graded meaning of formulas in approximation spaces

Fundamenta Informaticae

Volumn 60, Issue 1-4, 2004, Pages 159-172

  Gomolińska, Anna ^a  

^a UNIVERSITY OF BIALYSTOK   (Poland)

Author keywords

Approximation space; Graded meaning of formulas; Granulation of information; Pawlak information systems

Indexed keywords

APPROXIMATION THEORY; FUZZY SETS; KNOWLEDGE REPRESENTATION; MATHEMATICAL MODELS; MEMBERSHIP FUNCTIONS; THEOREM PROVING;

APPROXIMATION SPACE; GRADED MEANING OF FORMULAS; GRANULATION OF INFORMATION; PAWLAK INFORMATION SYSTEMS;

DATA PROCESSING;

EID: 3042533767     PISSN: 01692968     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (35)

1. Chakraborty, M. K.: Use of fuzzy set theory in introducing graded consequence in multiple-valued logic, Fuzzy Logic in Knowledge-Based Systems, Decision and Control (M. M. Gupta, T. Yamakawa, Eds.), Elsevier Science Publishers B. V. (North-Holland), 1988, 247-257.
2. Chakraborty, M. K.: Graded consequence: Further studies, Journal of Applied Non-Classical Logics, 5(2), 1995, 127-137.
3. Chakraborty, M. K., Banerjee, M.: Rough consequence, Bull. Polish Acad. Sci. Math., 41(4), 1993, 299-304.
4. Chakraborty, M. K., Basu, S.: Approximate reasoning methods in vagueness: Graded and rough consequences, vol. 29/95 of ICS Research Report, Institute of Computer Science, Warsaw University of Technology, Warsaw, 1995.
5. Chakraborty, M. K., Basu, S.: Graded consequence and some metalogical notions generalized, Fundamenta Informaticae, 32(3-4), 1997/1998, 299-311.
6. Drwal, G., Mrózek, A.: System RClass - Software implementation of a rough classifier, Proc. 7th Int. Symposium on Intelligent Information Systems (IIS'1998), Malbork, Poland, 1998, June 15-19 (M. A. Kłopotek, M. Michalewicz, Z. W. Raś, Eds.), Computer Science Institute of Polish Acad. Sci., Warsaw, 1998, 392-395.
7. Gomolińska, A.: A comparative study of some generalized rough approximations, Fundamenta Informaticae, 51 (1-2), 2002, 103-119.
8. Gomolińska, A.: A graded meaning of formulas and their sets in generalized approximation spaces, Proc. Int. Workshop on Concurrency, Specification and Programming (CS&P '2003), Czarna, Poland, 2003, September 25-27 (L. Czaja, Ed.), Warsaw University, 2003, ISBN 83-88374-71-0, 157-170.
9. Inuiguchi, M., Tanino, T.: On rough sets under generalized equivalence relations, Bull. Int. Rough Set Society, 5(1-2), 2001, 167-171, ISSN 1346-0013.
10. Komorowski, J., Pawlak, Z., Polkowski, L., Skowron, A.: Rough sets: A tutorial, Rough-Fuzzy Hybridization: A New Trend in Decision Making (S. K. Pal, A. Skowron, Eds.), Springer-Verlag, Singapore, 1999, 3-98.
11. Leśniewski, S.: Foundations of the general set theory 1 (in Polish), Works of the Polish Scientific Circle, 2, 1916, (see also Stanisław Leśniewski Collected Works (S. J. Surma et al., Eds.), Kluwer Acad. Publ., Dordrecht, 128-173, 1992).
12. Leśniewski, S.: Foundations of the general set theory 1 (in Polish), Works of the Polish Scientific Circle, 2, 1916, (see also Stanisław Leśniewski Collected Works (S. J. Surma et al., Eds.), Kluwer Acad. Publ., Dordrecht, 128-173, 1992).
13. Lin, T. Y.: Granular computing: Fuzzy logic and rough sets, Computing with Words in Information/Intelligent Systems (L. A. Zadeh, J. Kacprzyk, Eds.), vol. 1, Physica-Verlag, Heidelberg, 1999, 183-200.
14. Łukasiewicz, J.: Die logischen Grundlagen der Wahrscheinlichkeitsrechnung, Jan Łukasiewicz - Selected Works (L. Borkowski, Ed.), North Holland Publ., Polish Scientific Publ., Amsterdam London Warsaw, 1970, 16-63, (originally published in Kraków, 1913).
15. Nguyen, S. H., Skowron, A., Stepaniuk, J.: Granular computing. A rough set approach, J. Comput. Intelligence, 17(3), 2001, 514-544.
16. Pawlak, Z.: Rough sets, Int. J. Computer and Information Sciences, 11, 1982, 341-356.
17. Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning about Data, Kluwer Acad. Publ., Dordrecht, 1991.
18. Pawlak, Z., Skowron, A.: Rough membership functions, Fuzzy Logic for the Management of Uncertainty (L. A. Zadeh, J. Kacprzyk, Eds.), John Wiley & Sons, New York, 1994, 251-271.
19. Polkowski, L., Skowron, A.: Rough mereology: A new paradigm for approximate reasoning, Int. J. Approximated Reasoning, 15(4), 1996, 333-365.
20. Polkowski, L., Skowron, A.: Rough mereological approach - A survey, Bull. Int. Rough Set Society, 2(1), 1998, 1-13.
21. Polkowski, L., Skowron, A., Eds.: Rough Sets in Knowledge Discovery, vol. 1-2, Physica-Verlag, Heidelberg, 1998.
22. Polkowski, L., Skowron, A.: Towards adaptive calculus of granules, Computing with Words in Information/Intelligent Systems (L. A. Zadeh, J. Kacprzyk, Eds.), vol. 1, Physica-Verlag, Heidelberg, 1999, 201-228.
23. Polkowski, L., Skowron, A.: Rough mereology in information systems. A case study: Qualitative spatial reasoning, Rough Set Methods and Applications: New Developments in Knowledge Discovery in Information Systems (L. Polkowski, S. Tsumoto, T. Y. Lin, Eds.), Physica-Verlag, Heidelberg New York, 2001.
24. Pomykała, J. A.: Approximation operations in approximation space, Bull. Polish Acad. Sci. Math., 35(9-10), 1987, 653-662.
25. Skowron, A., Stepaniuk, J.: Tolerance approximation spaces, Fundaments Informaticae, 27, 1996, 245-253.
26. Słowiński, R., Vanderpooten, D.: Similarity Relation as a Basis for Rough Approximations, vol. 53/95 of ICS Research Report, Institute of Computer Science, Warsaw University of Technology, Warsaw, 1995, (see also Advances in Machine Intelligence and Soft Computing (P. P. Wang, Ed.), vol. 4, Duke University Press, 1997, 17-33).
27. Słowiński, R., Vanderpooten, D.: Similarity Relation as a Basis for Rough Approximations, vol. 53/95 of ICS Research Report, Institute of Computer Science, Warsaw University of Technology, Warsaw, 1995, (see also Advances in Machine Intelligence and Soft Computing (P. P. Wang, Ed.), vol. 4, Duke University Press, 1997, 17-33).
28. Słowiński, R., Vanderpooten, D.: A generalized definition of rough approximations based on similarity, IEEE Transactions on Data and Knowledge Engineering, 12, 2000, 331-336.
29. Stefanowski, J., Tsoukiàs, A.: Decision rules and valued tolerance, Proc. 2nd Int. Conf. on Rough Sets and Current Trends in Computing (RSCTC'2000), Banff, Canada, 2000, October 16-19 (W. Ziarko, Y. Yao, Eds.), Lecture Notes in Artificial Intelligence, 2005, Springer-Verlag, Berlin, 2001, 180-187.
30. Stefanowski, J., Tsoukiàs, A.: Incomplete information tables and rough classification, Int. J. Comput. Intelligence, 17(3), 2001, 545-566.
31. Stepaniuk, J.: Knowledge discovery by application of rough set models, Rough Set Methods and Applications: New Developments in Knowledge Discovery in Information Systems (L. Polkowski, S. Tsumoto, T. Y. Lin, Eds.), Physica-Verlag, Heidelberg New York, 2001, 137-233.
32. Wybraniec-Skardowska, U.: On a generalization of approximation space. Bull. Polish Acad. Sci. Math., 37(1-6), 1989, 51-62.
33. Zadeh, L. A.: Outline of a new approach to the analysis of complex system and decision processes, IEEE Trans. on Systems, Man, and Cybernetics, 3, 1973, 28-44.
34. Zakowski, W.: Approximations in the space (U, II), Demonstratio Mathematica, 16, 1983, 761-769.
35. Ziarko, W.: Variable precision rough set model, J. Computer and System Sciences, 46(1), 1993, 39-59.