Abstract
In the paper, we draw a perspective of the computer-assisted theory exploration within rough set theory. We examine two well-known approaches to the topic, drawing some paradigms for a machine math-assistant to be feasible tool any researcher can use to verify his own results. Some features of a Mizar language chosen for the verification task are also presented.
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Keywords
- Approximation Space
- Jordan Curve Theorem
- Indiscernibility Relation
- Mizar Mathematical Library
- Contact Algebra
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References
Bryniarski, E.: Formal conception of rough sets. Fundamenta Informaticae 27(2-3), 109–136 (1996)
Düntsch, I., Winter, M.: Construction of Boolean contact algebras. AI Communications 13, 235–246 (2004)
Gomolińska, A.: A comparative study of some generalized rough approximations. Fundamenta Informaticae 51(1-2), 103–119 (2002)
Grabowski, A.: On the computer-assisted reasoning about rough sets. In: Dunin-Kȩplicz, B., et al. (eds.) Monitoring, Security, and Rescue Techniques in Multiagent Systems. Advances in Soft Computing, pp. 215–226. Springer, Heidelberg (2005)
Grabowski, A., Schwarzweller, C.: Rough Concept Analysis – theory development in the Mizar system. In: Asperti, A., Bancerek, G., Trybulec, A. (eds.) MKM 2004. LNCS, vol. 3119, pp. 130–144. Springer, Heidelberg (2004)
Iwiński, T.B.: Algebraic approach to rough sets. Bull. Pol. Acad. Sci. Math. 35, 673–683 (1987)
Järvinen, J.: Approximations and rough sets based on tolerances. In: Ziarko, W., Yao, Y. (eds.) RSCTC 2000. LNCS (LNAI), vol. 2005, pp. 182–189. Springer, Heidelberg (2001)
Järvinen, J.: Ordered set of rough sets. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 49–58. Springer, Heidelberg (2004)
Pawlak, Z.: Rough Sets. International Journal of Information and Computer Science 11, 341–356 (1982)
Pomykała, J.A.: About tolerance and similarity relations in information systems. In: Alpigini, J.J., Peters, J.F., Skowron, A., Zhong, N. (eds.) RSCTC 2002. LNCS (LNAI), vol. 2475, pp. 175–182. Springer, Heidelberg (2002)
Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundamenta Informaticae 27(2-3), 245–253 (1996)
Yao, Y.Y.: Two views of the theory of rough sets in finite universes. International Journal of Approximation Reasoning 15(4), 291–317 (1996)
Ziarko, W.: Variable precision rough set model. Journal of Computer and System Sciences 46(1), 39–59 (1993)
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Grabowski, A., Jastrzȩbska, M. (2007). Rough Set Theory from a Math-Assistant Perspective. In: Kryszkiewicz, M., Peters, J.F., Rybinski, H., Skowron, A. (eds) Rough Sets and Intelligent Systems Paradigms. RSEISP 2007. Lecture Notes in Computer Science(), vol 4585. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73451-2_17
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DOI: https://doi.org/10.1007/978-3-540-73451-2_17
Publisher Name: Springer, Berlin, Heidelberg
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