In data mining, many real-life data sets are not only incomplete, but also encompass various kinds of knowledge and are shared by many users. Different users may prefer different kinds of knowledge. Nowadays how to mine rules meeting users’ requirements from incomplete data sets has become one of the important research issues of data mining. In this paper, we investigate decision rules induction methods in incomplete decision tables by considering attribute order. The users’ requirements are described by an attribute order. Then a hierarchical algorithm of decision rules mining based on the attribute order is proposed, and its properties and complexity are examined. An example is given to illustrate the algorithm. Simulation experimental results show that compared with the algorithm MLEM2, the proposed algorithm is valid and effective.
HirokaneM. and KonishiH., et al., Extraction of minimal decision algorithm using rough sets and genetic algorithm, Systems and Computers in Japan38(4) (2007), 39–51.
2.
HongT.P. and LinC.E., et al. Learning cross-level certain and possible rules by rough sets, Expert Systems with Applications34(3) (2008), 1698–1706.
3.
FengQ.R., MiaoD.Q. and ChengY., Hierarchical decision rules mining, Expert Systems with Applications37(3) (2010), 2081–2091.
4.
PawlakZ., Rough sets, International Journal of Computer and Information Sciences11 (1982), 341–356.
5.
Grzymala-BusseJ.W. and HuM., A comparison of several approaches to missing attribute values in data mining. In: Proc of the Second International Conference on Rough Sets and Current Trends in Computing (RSCTC’2000), Springer-Verlag, 2001, pp. 340–347.
6.
WangG.Y., GuanL.H. and HuF., Rough set extensions in incomplete information systems, Frontiers of Electrical and Electronic Engineering in China3(4) (2008), 399–405.
7.
WangG.Y., Domain-oriented data-driven data mining based on rough sets, Proc of International Forum on Theory of GrC from Rough Set Perspective (IFTGrCRSP’2006), 2006, pp. 46–46.
8.
KryszkiewiczM., Rough set approach to incomplete information systems, Information Sciences112(1-4) (1998), 39–49.
9.
StefanowskiJ. and TsoukiasA., Incomplete information tables and rough classification, Computational Intelligence17(3) (2001), 545–566.
10.
Grzymala-BusseJ.W., Characteristic relation for incomplete data: A generalization of the indiscernibility relation. In: Proc of the fourth International conference on Rough Sets and Current Trends in Computing (RSCTC’2004), TsumotoS., et al. (eds.). Lecture Notes in Artificial Intelligence, vol. 3066Springer-Verlag, 2004, pp. 244–253.
11.
StefanowskiJ. and TsoukiasA., Valued tolerance and decision rules. In ZiarkoW and YaoY (Eds.), Rough Sets and Current Trends in Computing , Springer-Verlag, 2001, pp. 212–219.
12.
WangG.Y., GuanL.H., WuW.Z. and HuF., Data-driven valued tolerance relation based on the extended rough set, Fundamenta Informaticae132 (2014), 349–363.
13.
GuanL.H. and WangG.Y., Generalized approximations defined by non-equivalence relations, Information Sciences193(1) (2012), 163–179.
14.
SalamaA.S., Topological solution of missing attribute values problem in incomplete information tables, Information Sciences180(5) (2010), 631–639.
15.
CousoI. and DuboisF., Rough sets, Coverings and Incomplete Information, Fundamenta Informaticae108(3-4) (2011), 223–347.
16.
NakataM. and SakaiH., Twofold rough sets in incomplete information, International Journal of General Systems42(6) (2013), 546–571.
17.
Grzymala-BusseJ.W., Data with Missing Attribute Values: Generalization of Indiscernibility Relation and Rule Induction. In PetersJF, et al. (Eds.): Transactions on Rough Sets I, Springer-Verlag, 2004, pp. 78–95.
18.
Grzymala-BusseJ.W. and WangA.Y., Modified algorithms LEM1 and LEM2 for rule induction from data with missing attribute values, Proceedings of the Fifth International Workshop on Rough Sets and Soft Computing (RSSC’1997) at the Third Joint Conference on Information Sciences (JCIS’1997), 1997, pp. 69–72.
19.
Grzymala-BusseJ.W., On the unknown attribute values in learning from examples In: Proc of the ISMIS-91, 6th International Symposium on Methodologies for Intelligent Systems, Lecture Notes in Artificial Intelligence, vol. 542, Springer-Verlag, 1991, pp. 368–377.
20.
KryszkiewiczM., Rules in incomplete information systems, Information Sciences113(3-4) (1999), 271–292.
21.
Grzymala-BusseJ.W., LERS –A system for learning from examples based on rough sets. In Intelligent Decision Support. Handbook of Applications and Advances of the Rough Sets Theory, ed. by SlowinskiR., Kluwer Academic Publishers, Dordrecht, Boston, London, 1992, pp. 3–18.
22.
WangJ. and WangJ., Reduction algorithms based on discernibility matrix: The order attributes method, Journal of Computer Science and Technology16(6) (2001), 489–504.
23.
HuF. and WangG.Y., Quick reduction algorithm based on attribute order, Chinese Journal of Computer30(8) (1435), 1429–1435. (in Chinese).
24.
YaoY.Y., ZhaoY., WangJ. and HanS.Q., A model of machine learning based on user preference of attributes. Transactions on Rough Sets VIII, Springer-Verlag, 2008, pp. 332–351.
25.
GuanL.H., WangG.Y. and YuH., Incremental algorithm of Pawlak reduction based on attribute order, Journal of Southwest Jiaotong University46(3) (2011), 461–468. (in Chinese).
26.
GuanL.H., WangG.Y. and HuF., A decision rules mining algorithm based on attribute order, Control and Decision27(2) (2012), 313–316. (in Chinese).
27.
HanS.Q. and ZhaoM., Reduct theory. Tsinghua University Press, Beijing, 2010. (in Chinese).
28.
ZhangL. and ZhangB., Theory and applications of problem solving, (2nd ed.). Tsinghua University Press, Beijing, 2007. (in Chinese).
