On exactness, definability and vagueness in partial approximation spaces

• Autorzy: Ciucci D. , Mihálydeák T. , Csajbók Z. E.
• Języki publikacji: EN

Abstrakty

EN

In this paper, lower/upper, boundary, and negative regions of set approximations, the fundamental concepts of classical rough set theory, have been considered as primitive ones. Assuming that they are independent of each other, a generalized framework for their investigations is outlined. Its main building blocks are base sets and definable sets. Lower/upper approximations, boundaries and negative sets are all considered as definable sets and their mutual interactions are studied. Lastly exact/rough sets are discussed. In generalized framework, four groups of formulae are defined for representing different variants of rough sets. They emphasize distinct features of roughness, and so it may be of highly importance which one is used in practical applications. Some possible choices appeared in authors’ publications are mentioned.

Słowa kluczowe

EN

partial approximation framework; vagueness; exactness; rough sets; definability

• Wydawca: Wydawnictwo Uniwersytetu Warmińsko-Mazurskiego w Olsztynie
• Czasopismo: Technical Sciences / University of Warmia and Mazury in Olsztyn
• Rocznik: 2015
• Tom: nr 18(3)
• Strony: 203--212
• Opis fizyczny: Bibliogr. 33 poz., tab.

Twórcy

autor

Ciucci D.

• Department of Informatics, Systems and Communication University of Milano-Bicocca (Italia)

autor

Mihálydeák T.

• Department of Computer Science, Faculty of Informatics, University of Debrecen (Hungary)

autor

Csajbók Z. E.

• Department of Health Informatics, Faculty of Health, University of Debrecen (Hungary)

Bibliografia

• ATANASSOV K.T. 1986. Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1): 87-96.
• ATANASSOV K.T. 1999. Intuitionistic fuzzy sets. Theory and Applications. Studies in Fuzziness and Soft Computing, 35. Physica Verlag Heidelberg.
• ATANASSOV K.T. 2012. On Intuitionistic Fuzzy Sets Theory. Studies in Fuzziness and Soft Computing, 283. Springer-Verlag Berlin Heidelberg.
• BANERJEE M., CHAKRABORTY M. 2004. Algebras from rough sets. In: Rough-Neuro Computing: Techniques for Computing with Words. Eds. S. Pal, L. Polkowski, A. Skowron. Springer-Verlag, Berlin, pp. 157-184.
• CATTANEO G., CIUCCI D. 2006. Basic intuitionistic principles in fuzzy set theories and its extensions (A terminological debate on Atanassov IFS). Fuzzy Sets and Systems, 157(24): 3198-3219
• BONIKOWSKI Z., BRYNIARSKI E., WYBRANIEC-SKARDOWSKA U. 1998. Extensions and intentions in the rough set theory. Information Sciences, 107(1-4): 149-167.
• CHAKRABORTY M. 2011. On fuzzy sets and rough sets from the perspective of indiscernibility. In: Logic and its Applications. Eds. M. Banerjee, A. Seth. 4th Indian Conference (ICLA 2011), Delhi, India, January 5-11, 2011, Proceedings, Springer-Verlag, LNCS-LNAI, 6521: 22-37.
• CIUCCI D. 2011. Orthopairs: A Simple and Widely Used Way to Model Uncertainty. Fundamenta Informaticae, 108: 287-304.
• CIUCCI D. 2014. Orthopairs in the 1960s: Historical Remarks and New Ideas. In: Rough Sets and Current Trends in Computing. Eds. C. Cornelis, M. Kryszkiewicz, D. Ślęzak, E.M. Ruiz, R. Bello, L. Shang. 9th International Conference, RSCTC 2014, Granada and Madrid, Spain, July 9-13, 2014. Proceedings, Springer, LNCS-LNAI, 8536: 1-12.
• CIUCCI D., DUBOIS D., LAWRY J. 2014a. Borderline vs. unknown: comparing three-valued representations of imperfect information. International Journal of Approximate Reasoning, 55: 1866-1889.
• CIUCCI D., MIHÁLYDEÁK T., CSAJBÓK Z.E. 2014b. On definability and approximations in partial approximation spaces. In: Rough Sets and Knowledge Technology. Eds. D. Miao, W. Pedrycz, D. Ślęzak, G. Peters, Q. Hu, R. Wang. 9th International Conference, RSKT 2014, Shanghai, China, October 24-26, 2014. Proceedings, Springer, LNCS-LNAI, 8818: 15-26.
• CSAJBÓK Z.E. 2013. Approximation of sets based on partial covering. In: Transactions on Rough Sets XVI. Eds.: J.F. Peters, A. Skowron, S. Ramanna, Z. Suraj, X. Wang. Springer-Verlag, Berlin, Heidelberg, LNCS, 7736: 144-220.
• CSAJBÓK Z., MIHÁLYDEÁK T. 2011. General Tool-Based Approximation Framework Based on Partial Approximation of Sets. In: Rough Sets, Fuzzy Sets. Ds. Eds.: S.O. Kuznetsov, D. Ślęzak, D.H. Hepting, B.G. Mirkin. Data Mining and Granular Computing 13th International Conference, RSFDGrC 2011 Moscow, Russia, June 25-27, 2011 Proceedings, Springer, LNCS-LNAI, 6743: 52-59.
• CSAJBÓK Z., MIHÁLYDEÁK T. 2012a. Partial approximative set theory: A generalization of the rough set theory. International Journal of Computer Information Systems and Industrial Management Applications, 4: 437-444.
• CSAJBÓK Z., MIHÁLYDEÁK T. 2012b. A general set theoretic approximation framework. In: Proceedings of IPMU 2012. Eds.: S. Greco, B. Bouchon-Meunier, G. Coletti, M. Fedrizzi, B. Matarazzo, R.R Yager. Catania, Italy, July 9-13, 2012, Part I. Springer-Verlag, Berlin Heidelberg, CCIS, 297: 604-612.
• CSAJBÓK Z., MIHÁLYDEÁK T. 2013. Fuzziness in Partial Approximation Framework. In: Annals of Computer Science and Information Systems. Vol. 1. Eds. M. Ganzha, L. A. Maciaszek, M. Paprzycki. Proceedings of the 2013 Federated Conference on Computer Science and Information Systems Kraków, Poland, September 8-11, 2013. FedCSIS 2013. IEEE Computer Society Press, pp. 35-41.
• DUBOIS D., PRADE H. 1987. Rough fuzzy sets and fuzzy rough sets. Fuzzy Sets and Systems, 23: 3-18.
• DUBOIS D., PRADE H. 1990. Rough fuzzy sets and fuzzy rough sets. International Journal of General Systems, 17(2-3): 191-209.
• DUBOIS D., PRADE H. 1992. Putting rough sets and fuzzy sets together. In: Intelligent Decision Support - Handbook of Applications and Advances of the Rough Set Theory. D. Ed. R. Slowinski. Kluwer Academic Publishers, Dordrecht, pp. 203-232.
• MIHÁLYDEÁK T. 2013. Partial first-order logic relying on optimistic, pessimistic and average partial membership functions. In: 8th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2013). Eds. G. Pasi, J. Montero, D. Ciucci. University of Milano-Bicocca, Milan, Italy, September 11-13, 2013. Proceedings, Atlantis Press, Advances in Intelligent Systems Research, 32: 334-339.
• MOUSAVI A., JABEDAR-MARALANI P. 2001. Relative sets and rough sets. International Journal of Applied Mathematics and Computer Science, Special issue on rough sets and their application, 11(3): 637-654.
• MOUSAVI A., JABEDAR-MARALANI P. 2002. Double-faced rough sets and rough communication. Information Sciences, 148: 41-53
• PAWLAK Z. 1982. Rough sets. International Journal of Computer and Information Sciences. 11(5): 341-356.
• PAWLAK Z. 1991. Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht.
• PAWLAK Z., SKOWRON A. 2007a. Rudiments of rough sets. Information Sciences, 177(1): 3-27.
• PAWLAK Z., SKOWRON A. 2007b. Rough sets: Some extensions. Information Sciences, 177: 28-40.
• PRIEST G. 2002. Paraconsistent Logic. Handbook of Philosophical Logic. Vol. 6. Eds. D. Gabbay, F. Guenthner. Second Edition. Dordrecht: Kluwer Academic Publishers, pp. 287-393.
• PRIEST G., TANAKA K., WEBER Z. 2013. Paraconsistent Logic. In: The Stanford Encyclopedia of Philosophy. Ed. E.N. Zalta. Fall 2013 Edition, on line: http://plato.stanford.edu/archives/ fall2013/entries/logic-paraconsistent/.
• PRIEST G., ROUTLEY R., NORMAN J. 1989. Paraconsistent Logic: Essays on the Inconsistent. Munchen: Philosophia Verlag.
• YAO Y.Y. 2003. On generalizing rough set theory. In: Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. Eds. G. Wang, Q. Liu, Y. Yao, A. Skowron. 9th International Conference, RSFDGrC 2003, Chongqing, China, May 26-29, 2003, Proceedings. Springer-Verlag, Berlin Heidelberg, LNCS- LNAI, 2639: 44-51.
• YAO Y.Y., YAO B. 2012. Covering based rough set approximations. Information Sciences, 200: 91-107.
• YAO Y.Y., ZHANG J.P. 2000. Interpreting fuzzy membership functions in the theory of rough sets. In: Rough Sets and Current Trends in Computing. Eds. W. Ziarko, Y.Y. Yao. Springer, LNCS, 2005: 82-89.
• ZHU W. 2007. Generalized rough sets based on relations. Information Sciences, 177: 4997-5011