Entropy and co-entropy of partitions and coverings with applications to roughness theory

Studies in Fuzziness and Soft Computing

Volumn 224, Issue , 2008, Pages 55-77

  Cattaneo, Gianpiero ^a   Ciucci, Davide ^a   Bianucci, Daniela ^a  

^a UNIVERSITY OF MILANO BICOCCA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 37749009467     PISSN: 14349922     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-540-76973-6_4     Document Type: Article

References (20)

1. Cattaneo, G.: Abstract approximation spaces for rough theories. In: Polkowski, L., Skowron, A. (eds.) Rough Sets in Knowledge Discovery 1, pp. 59-98. Physica-Verlag, Heidelberg (1998)
2. Pawlak, Z.: Rough sets. Int. J. Inform. Comput. Sci. 11, 341-356 (1982)
3. Cattaneo, G., Ciucci, D.: Investigation about Time Monotonicity of Similarity and Preclusive Rough Approximations in Incomplete Information Systems. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymabla-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 38-48. Springer, Heidelberg (2004)
4. Pawlak, Z.: Rough sets: A new approach to vagueness. In: Zadeh, L.A., Kacprzyc, J. (eds.) Fuzzy Logic for the Management of Uncertainty, pp. 105-118. J. Wiley and Sons, New York (1992)
5. Taylor, A.: General Theory of Functions and Integration. Dover Publications, New York (1985)
6. Khinchin, A.I.: Mathematical Foundations of Information Theory. Dover Publications, New York (1957) (translation of two papers appeared in Russian in Uspekhi Matematicheskikh Nauk 3, 3-20 (1953) and 1, 17-75 (1965)
7. Hartley, R.V.L.: Transmission of information. The Bell System Technical Journal 7, 535-563 (1928)
8. Ash, R.B.: Information Theory. Dover Publications, New York (1990) (originally published by John Wiley & Sons, New York, 1965)
9. Reza, F.M.: An Introduction to Information theory. Dover Publications, New York (1994) (originally published by Mc Graw-Hill, New York, 1961)
10. Shannon, C.E.: A mathematical theory of communication. The Bell System Technical Journal 27, 379-423, 623-656 (1948)
11. Bianucci, D., Cattaneo, G., Ciucci, D.: Entropies and co-entropies of coverings with application to incomplete information systems. Fundamenta Informaticae 75, 77-105 (2007)
12. Wierman, M.: Measuring uncertainty in rough set theory. International Journal of General Systems 28, 283-297 (1999)
13. Liang, J., Shi, Z.: The information entropy, rough entropy and knowledge granulation in rough set theory. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 12, 37-46 (2004)
14. Beaubouef, T., Petry, F.E., Arora, G.: Information-theoretic measures of uncertainty for rough sets and rough relational databases. Journal of Information Sciences 109, 185-195 (1998)
15. Pawlak, Z.: Rough sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)
16. Pawlak, Z.: Information systems - theoretical foundations. Information Systems 6, 205-218 (1981)
17. Komorowski, J., Pawlak, Z., Polkowski, L., Skowron, A.: Rough sets: A tutorial. In: Pal, S., Skowron, A. (eds.) Rough Fuzzy Hybridization, pp. 3-98. Springer, Singapore (1999)
18. Birkhoff, G.: Lattice Theory. American Mathematical Society, Providence, Rhode Island. American Mathematical Society Colloquium Publication, 3rd edn., vol. XXV (1967)
19. Liang, J., Xu, Z.: Uncertainty measure of randomness of knowledge and rough sets in incomplete information systems. Proc. of the 3rd World Congress on Intelligent Control and Automata 4, 2526-2529 (2000)
20. Bianucci, D., Cattaneo, G.: Monotonic behavior of entropies and co-entropies for coverings with respect to different quasi-orderings. LNCS (LNAI), vol. 4585, pp. 584-593. Springer, Heidelberg (to appear, 2007)