Abstract
This chapter focuses on a mathematical framework for handling information incompleteness, which is deeply related to machine learning. Recently, the handling of the information incompleteness in data sets is recognized to be very important research area for machine learning. We have already proposed a framework Rough Non − deterministic Information Analysis (RNIA). This is a rough sets based framework for handling not only definite (or complete) information but also indefinite (or incomplete) information. This RNIA handles lots of aspects in tables with the information incompleteness, i.e., rough sets based issues, data dependencies, question-answering, rule generation, estimation of actual values, etc. Each aspect is extended from tables with complete information to tables with incomplete information according to the modal concepts. We survey this RNIA, and we describe the perspective of RNIA with respect to machine learning.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Agrawal, R., Srikant, R.: Fast algorithms for mining association rules in large databases. In: Bocca, J.B., Jarke, M., Zaniolo, C. (eds.) VLDB 1994, pp. 487–499. Morgan Kaufmann (1994)
Agrawal, R., Mannila, H., Srikant, R., Toivonen, H., Verkamo, A.I.: Fast discovery of association rules. In: Advances in Knowledge Discovery and Data Mining, pp. 307–328. AAAI/MIT Press (1996)
Bazan, J., Nguyen, H.S., Nguyen, S.H., Synak, P., Wróblewski, J.: Rough set algorithms in classification problem. In: Rough Set Methods and Applications. STUDFUZZ, vol. 56, pp. 49–88. Springer (2000)
Blaszczynski, J., Greco, S., Słowiński, R.: Multi-criteria classification - a new scheme for application of dominance-based decision rules. European Journal of Operational Research 181(3), 1030–1044 (2007)
Ceglar, A., Roddick, J.F.: Association mining. ACM Computing Survey 38(2) (2006)
Chmielewski, M.R., Grzymała-Busse, J.W.: Global discretization of continuous attributes as preprocessing for machine learning. International Journal of Approximate Reasoning 15(4), 319–331 (1996)
Codd, E.F.: A relational model of data for large shared data banks. Communication of the ACM 13(6), 377–387 (1970)
Cornelis, C., Jensen, R., Martín, G.H., Ślęzak, D.: Attribute selection with fuzzy decision reducts. Information Sciences 180(2), 209–224 (2010)
Demri, S., Orłowska, E.: Incomplete Information: Structure, Inference, Complexity. Monographs in Theoretical Computer Science. An EATCS Series. Springer (2002)
Frank, A., Asuncion, A.: UCI Machine Learning Repository, School of Information and Computer Science, University of California, Irvine, CA (2010), http://mlearn.ics.uci.edu/MLRepository.html
Greco, S., Matarazzo, B., Słowiński, R.: Granular computing and data mining for ordered data: The dominance-based rough set approach. In: Meyers, R.A. (ed.) Encyclopedia of Complexity and Systems Science, pp. 4283–4305. Springer (2009)
Grzymała-Busse, J.W.: A new version of the rule induction system LERS. Fundamenta Informaticae 31(1), 27–39 (1997)
Grzymała-Busse, J.W., Werbrouck, P.: On the best search method in the lem1 and lem2 algorithms. In: Orłowska, E. (ed.) Incomplete Information: Rough Set Analysis. STUDFUZZ, vol. 13, pp. 75–91. Springer (1998)
Grzymała-Busse, J.W., Stefanowski, J.: Three discretization methods for rule induction. International Journal of Intelligent Systems 16(1), 29–38 (2001)
Grzymała-Busse, J.W.: Data with missing attribute values: Generalization of indiscernibility relation and rule induction. Transactions on Rough Sets 1, 78–95 (2004)
Huynh, V.N., Nakamori, Y., Ono, H., Lawry, J., Kreinovich, V., Nguyen, H.T. (eds.): Interval / Probabilistic Uncertainty and Non-Classical Logics. AISC, vol. 46. Springer (2008)
Huynh, V.N., Nakamori, Y., Hu, C., Kreinovich, V.: On decision making under interval uncertainty: A new justification of hurwicz optimism-pessimism approach and its use in group decision making. In: ISMVL 2009, pp. 214–220. IEEE Computer Society (2009)
Inuiguchi, M., Yoshioka, Y., Kusunoki, Y.: Variable-precision dominance-based rough set approach and attribute reduction. International Journal of Approximate Reasoning 50(8), 1199–1214 (2009)
Komorowski, J., Pawlak, Z., Polkowski, L., Skowron, A.: Rough sets: a tutorial. In: Pal, S.K., Skowron, A. (eds.) Rough Fuzzy Hybridization: A New Method for Decision Making, pp. 3–98. Springer (1999)
Kryszkiewicz, M., Rybinski, H.: Computation of reducts of composed information systems. Fundamenta Informaticae 27(2-3), 183–195 (1996)
Kryszkiewicz, M.: Rough set approach to incomplete information systems. Information Sciences 112(1-4), 39–49 (1998)
Kryszkiewicz, M.: Rules in incomplete information systems. Information Sciences 113(3-4), 271–292 (1999)
Leung, Y., Fischer, M.M., Wu, W.Z., Mi, J.S.: A rough set approach for the discovery of classification rules in interval-valued information systems. International Journal of Approximate Reasoning 47(2), 233–246 (2008)
Lipski, W.: On semantic issues connected with incomplete information databases. ACM Transactions on Database Systems 4(3), 262–296 (1979)
Lipski, W.: On databases with incomplete information. Journal of the ACM 28(1), 41–70 (1981)
Murai, T., Resconi, G., Nakata, M., Sato, Y.: Operations of zooming in and out on possible worlds for semantic fields. In: Damiani, L.J.E., Howlett, R.J., Ichalkaranje, N. (eds.): Knowledge-Based Intelligent Information Engineering Systems and Allied Technologies. KES 2004, Frontiers in Artificial Intelligence and Applications, vol. 82, pp. 1083–1087. IOS Press (2002)
Nakamura, A.: A rough logic based on incomplete information and its application. International Journal of Approximate Reasoning 15(4), 367–378 (1996)
Nakamura, A., Tsumoto, S., Tanaka, H., Kobayashi, S.: Rough set theory and its applications. Journal of Japanese Society for Artificial Intelligence 11(2), 209–215 (1996)
Nakata, M., Sakai, H.: Rough-set-based approaches to data containing incomplete information: possibility-based cases. In: Nakamatsu, K., Abe, J.M. (eds.) Advances in Logic Based Intelligent Systems, Frontiers in Artificial Intelligence and Applications, vol. 132, pp. 234–241. IOS Press (2005)
Nakata, M., Sakai, H.: Lower and upper approximations in data tables containing possibilistic information. Transactions on Rough Sets 7, 170–189 (2007)
Nakata, M., Sakai, H.: Applying Rough Sets to Information Tables Containing Possibilistic Values. Transactions on Computational Science 2, 180–204 (2008)
Orłowska, E., Pawlak, Z.: Representation of nondeterministic information. Theoretical Computer Science 29(1-2), 27–39 (1984)
Orłowska, E. (ed.): Incomplete Information: Rough Set Analysis. STUDFUZZ, vol. 13. Springer (1998)
Orłowska, E.: Introduction: What you always wanted to know about rough sets. In: Orłowska, E. (ed.) Incomplete Information: Rough Set Analysis. STUDFUZZ, vol. 13, pp. 1–20. Springer (1998)
Orłowska, E.: A roadmap of information logics and information algebras inspired by rough sets. In: Plenary Workshop in Rough Sets, Fuzzy Sets, Data Mining and Granular Computing (2005)
Pawlak, Z.: Information systems theoretical foundations. Information Systems 6(3), 205–218 (1981)
Pawlak, Z.: Systemy Informacyjne: Podstawy teoretyczne. Wydawnictwa Naukowo-Techniczne Publishers (1983)
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers (1991)
Pawlak, Z.: Some Issues on Rough Sets. In: Peters, J.F., Skowron, A., Grzymała-Busse, J.W., Kostek, B.z., Świniarski, R.W., Szczuka, M.S. (eds.) Transactions on Rough Sets I. LNCS, vol. 3100, pp. 1–58. Springer, Heidelberg (2004)
Pedrycz, W., Skowron, A., Kreinovich, V. (eds.): Handbook of Granular Computing. Wiley (2008)
Polkowski, L., Skowron, A. (eds.): Rough Sets in Knowledge Discovery 1: Methodology and Applications. STUDFUZZ, vol. 18. Springer (1998)
Polkowski, L., Skowron, A. (eds.): Rough Sets in Knowledge Discovery 2: Applications, Case Studies and Software Systems. STUDFUZZ, vol. 19. Physica-Verlag (1998)
Quinlan, J.R.: Improved use of continuous attributes in C4.5. The Journal of Artificial Intelligence Research 4, 77–90 (1996)
Sakai, H.: On a Framework for logic programming with incomplete information. Fundamenta Informaticae 19(3/4), 223–234 (1993)
Sakai, H., Okuma, A.: An Algorithm for Finding Equivalence Relations from Tables with Non-Deterministic Information. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) RSFDGrC 1999. LNCS (LNAI), vol. 1711, pp. 64–73. Springer, Heidelberg (1999)
Sakai, H., Okuma, A.: An Algorithm for Checking Dependencies of Attributes in a Table with Non-Deterministic Information: A Rough Sets Based Approach. In: Mizoguchi, R., Slaney, J.K. (eds.) PRICAI 2000. LNCS(LNAI), vol. 1886, pp. 219–229. Springer, Heidelberg (2000)
Sakai, H., Okuma, A.: On a theorem prover for variational logic programs with functors setu and sets. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 8(1), 73–92 (2000)
Sakai, H.: Effective procedures for handling possible equivalence relations in non-deterministic information systems. Fundamenta Informaticae 48(4), 343–362 (2001)
Sakai, H.: Effective procedures for data dependencies in information systems. In: Inuiguchi, M., Tsumoto, S., Hirano, S. (eds.) Rough Set Theory and Granular Computing. STUDFUZZ, vol. 125, pp. 167–176. Springer (2003)
Sakai, H., Okuma, A.: Basic Algorithms and Tools for Rough Non-Deterministic Information Analysis. In: Peters, J.F., Skowron, A., Grzymała-Busse, J.W., Kostek, B.z., Świniarski, R.W., Szczuka, M.S. (eds.) Transactions on Rough Sets I. LNCS, vol. 3100, pp. 209–231. Springer, Heidelberg (2004)
Sakai, H.: Possible Equivalence Relations and their Application to Hypothesis Generation in Non-Deterministic Information Systems. In: Peters, J.F., Skowron, A., Dubois, D., Grzymała-Busse, J.W., Inuiguchi, M., Polkowski, L. (eds.) Transactions on Rough Sets II. LNCS, vol. 3135, pp. 82–106. Springer, Heidelberg (2004)
Sakai, H., Murai, T., Nakata, M.: On a Tool for Rough Non-Deterministic Information Analysis and its Perspective for Handling Numerical Data. In: Torra, V., Narukawa, Y., Miyamoto, S. (eds.) MDAI 2005. LNCS (LNAI), vol. 3558, pp. 203–214. Springer, Heidelberg (2005)
Sakai, H., Nakata, M.: Discernibility Functions and Minimal Rules in Non-Deterministic Information Systems. In: Ślęzak, D., Wang, G., Szczuka, M.S., Düntsch, I., Yao, Y. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 254–264. Springer, Heidelberg (2005)
Sakai, H.: On a Rough Sets Based Data Mining Tool in Prolog: An Overview. In: Umeda, M., Wolf, A., Bartenstein, O., Geske, U., Seipel, D., Takata, O. (eds.) INAP 2005. LNCS (LNAI), vol. 4369, pp. 48–65. Springer, Heidelberg (2006)
Sakai, H., Nakata, M.: An application of discernibility functions to generating minimal rules in non-deterministic information systems. Journal of Advanced Computational Intelligence and Intelligent Informatics 10(5), 695–702 (2006)
Sakai, H., Nakata, M.: On Possible Rules and Apriori Algorithm in Non-Deterministic Information Systems. In: Greco, S., Hata, Y., Hirano, S., Inuiguchi, M., Miyamoto, S., Nguyen, H.S., Słowiński, R. (eds.) RSCTC 2006. LNCS (LNAI), vol. 4259, pp. 264–273. Springer, Heidelberg (2006)
Sakai, H., Ishibashi, R., Koba, K., Nakata, M.: Rules and Apriori Algorithm in Non-Deterministic Information Systems. In: Peters, J.F., Skowron, A., Rybiński, H. (eds.) Transactions on Rough Sets IX. LNCS, vol. 5390, pp. 328–350. Springer, Heidelberg (2008)
Sakai, H., Koba, K., Nakata, M.: Rough sets based rule generation from data with categorical and numerical values. Journal of Advanced Computational Intelligence and Intelligent Informatics 12(5), 426–434 (2008)
Sakai, H., Hayashi, K., Nakata, M., Ślęzak, D.: The Lower System, the Upper System and Rules with Stability Factor in Non-Deterministic Information Systems. In: Sakai, H., Chakraborty, M.K., Hassanien, A.E., Ślęzak, D., Zhu, W. (eds.) RSFDGrC 2009. LNCS(LNAI), vol. 5908, pp. 313–320. Springer, Heidelberg (2009)
Sakai, H., Hayashi, K., Kimura, H., Nakata, M.: An Aspect of Decision Making in Rough Non-Deterministic Information Analysis. In: Nakamatsu, K., Phillips-Wren, G., Jain, L.C., Howlett, R.J. (eds.) New Advances in Intelligent Decision Technologies. SCI, vol. 199, pp. 527–536. Springer, Heidelberg (2009)
Sakai, H., Nakata, M., Ślęzak, D.: Rule Generation in Lipski’s Incomplete Information Databases. In: Szczuka, M., Kryszkiewicz, M., Ramanna, S., Jensen, R., Hu, Q. (eds.) RSCTC 2010. LNCS(LNAI), vol. 6086, pp. 376–385. Springer, Heidelberg (2010)
Sakai, H., Okuma, H., Nakata, M., Ślęzak, D.: Stable rule extraction and decision making in rough non-deterministic information analysis. International Journal of Hybrid Intelligent Systems 8(1), 41–57 (2011)
Skowron, A., Rauszer, C.: The discernibility matrices and functions in information systems. In: Słowiński, R. (ed.) Intelligent Decision Support - Handbook of Advances and Applications of the Rough Set Theory, pp. 331–362. Kluwer Academic Publishers (1992)
Ślęzak, D.: Rough sets and functional dependencies in data: Foundations of association reducts. Transactions on Computational Science 5, 182–205 (2009)
Ślęzak, D., Sakai, H.: Automatic Extraction of Decision Rules from Non-Deterministic Data Systems: Theoretical Foundations and SQL-Based Implementation. In: Ślęzak, D., Kim, T.-h., Zhang, Y., Ma, J., Chung, K.-i. (eds.) DTA 2009. CCIS, vol. 64, pp. 151–162. Springer, Heidelberg (2009)
Stefanowski, J., Tsoukiàs, A.: On the Extension of Rough Sets Under Incomplete Information. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) RSFDGrC 1999. LNCS (LNAI), vol. 1711, pp. 73–82. Springer, Heidelberg (1999)
Stefanowski, J., Tsoukiàs, A.: Incomplete information tables and rough classification. Computational Intelligence 17(3), 545–566 (2001)
Tsumoto, S.: Knowledge discovery in clinical databases and evaluation of discovered knowledge in outpatient clinic. Information Sciences 124(1-4), 125–137 (2000)
Yang, X., Yu, D., Yang, J., Wei, L.: Dominance-based rough set approach to incomplete interval-valued information system. Data & Knowledge Engineering 68(11), 1331–1347 (2009)
Yao, Y(Y.Y.), Liau, C.-J., Zhong, N.: Granular Computing Based on Rough Sets, Quotient Space Theory, and Belief Functions. In: Zhong, N., Raś, Z.W., Tsumoto, S., Suzuki, E. (eds.) ISMIS 2003. LNCS (LNAI), vol. 2871, pp. 152–159. Springer, Heidelberg (2003)
Zadeh, L.A.: Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets and Systems 90(2), 111–127 (1997)
Ziarko, W.: Variable precision rough set model. Journal of Computer and System Sciences 46(1), 39–59 (1993)
Backpropagation, http://en.wikipedia.org/wiki/Backpropagation
Confidence Interval, http://en.wikipedia.org/wiki/Confidence_interval
ILP, http://en.wikipedia.org/wiki/Inductive_logic_programming
Rough Set Software, Bulletin of Int’l Rough Set Society 2(1), 15–46 (1998)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Sakai, H., Okuma, H., Nakata, M. (2013). Rough Non-deterministic Information Analysis: Foundations and Its Perspective in Machine Learning. In: Ramanna, S., Jain, L., Howlett, R. (eds) Emerging Paradigms in Machine Learning. Smart Innovation, Systems and Technologies, vol 13. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28699-5_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-28699-5_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28698-8
Online ISBN: 978-3-642-28699-5
eBook Packages: EngineeringEngineering (R0)