Abstract
Minimal rule generation in Non-deterministicInformation Systems (NISs), which follows rough sets based rule generation in DeterministicInformation Systems (DISs), is presented. According to certainrules and possiblerules in NISs, minimalcertain rules and minimalpossible rules are defined. Discernibilityfunctions are also introduced into NISs for generating minimal certain rules. Like minimal rule generation in DISs, the condition part of a minimal certain rule is given as a solution of an introduced discernibility function. As for generating minimal possible rules, there may be lots of discernibility functions to be solved. So, an algorithm based on an order of attributes is proposed. A tool, which generates minimal certain and minimal possible rules, has also been implemented.
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References
Pawlak, Z.: Rough Sets. Kluwer Academic Publishers, Dordrecht (1991)
Pawlak, Z.: Some Issues on Rough Sets. Transactions on Rough Sets 1, 1–58 (2004)
Komorowski, J., Pawlak, Z., Polkowski, L., Skowron, A.: Rough Sets: a tutorial. Rough Fuzzy Hybridization, pp. 3–98. Springer, Heidelberg (1999)
Rough Set Software. In: Bulletin of Int’l., Rough Set Society, vol. 2, pp. 15–46(1998)
Orłowska, E. (ed.): Incomplete Information: Rough Set Analysis. Physica, Heidelberg (1998)
Lipski, W.: On Semantic Issues Connected with Incomplete Information Data Base. ACM Trans. DBS 4, 269–296 (1979)
Grzymala-Busse, J., Werbrouck, P.: On the Best Search Method in the LEM1 and LEM2 Algorithms. In: Incomplete Information: Rough Set Analysis, pp. 75–91. Phisica, Heidelberg (1998)
Grzymala-Busse, J.: Data with Missing Attribute Values: Generalization of Indiscernibility Relation and Rule Induction. Transactions on Rough Sets 1, 78–95 (2004)
Kryszkiewicz, M.: Rules in Incomplete Information Systems. Information Sciences 113, 271–292 (1999)
Sakai, H., Okuma, A.: Basic Algorithms and Tools for Rough Non-deterministic Information Analysis. Transactions on Rough Sets 1, 209–231 (2004)
Sakai, H.: A Framework of Rough Sets based Rule Generation in Non-deterministic Information Systems. In: Zhong, N., Raś, Z.W., Tsumoto, S., Suzuki, E. (eds.) ISMIS 2003. LNCS (LNAI), vol. 2871, pp. 143–151. Springer, Heidelberg (2003)
Skowron, A., Rauszer, C.: The Discernibility Matrices and Functions in Information Systems. In: Intelligent Decision Support - Handbook of Advances and Applications of the Rough Set Theory, pp. 331–362. Kluwer Academic Publishers, Dordrecht (1992)
Kryszkiewicz, M., Rybinski, H.: Computation of Reducts of Composed Information Systems. Fundamenta Informaticae 27, 183–195 (1996)
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Sakai, H., Nakata, M. (2005). Discernibility Functions and Minimal Rules in Non-deterministic Information Systems. In: Ślęzak, D., Wang, G., Szczuka, M., Düntsch, I., Yao, Y. (eds) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. RSFDGrC 2005. Lecture Notes in Computer Science(), vol 3641. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11548669_27
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DOI: https://doi.org/10.1007/11548669_27
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