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A rough set approach for the discovery of classification rules in interval-valued information systems. (English) Zbl 1184.68409
Summary: A novel rough set approach is proposed in this paper to discover classification rules through a process of knowledge induction which selects decision rules with a minimal set of features for classification of real-valued data. A rough set knowledge discovery framework is formulated for the analysis of interval-valued information systems converted from real-valued raw decision tables. The minimal feature selection method for information systems with interval-valued features obtains all classification rules hidden in a system through a knowledge induction process. Numerical examples are employed to substantiate the conceptual arguments.
MSC:
68T05Learning and adaptive systems
68T10Pattern recognition, speech recognition
68T37Reasoning under uncertainty
68U35Information systems (hypertext navigation, interfaces, decision support, etc.)
References:
[1]Beynon, M. J.: Stability of continuous value discretisation: an application within rough set theory, International journal of approximate reasoning 35, No. 1, 29-53 (2004) · Zbl 1075.68088 · doi:10.1016/S0888-613X(03)00057-4
[2]Bodjanova, S.: Approximation of fuzzy concepts in decision making, Fuzzy sets and systems 85, 23-29 (1997) · Zbl 0907.90003 · doi:10.1016/0165-0114(95)00404-1
[3]Chan, C. C.; Grzymala-Busse, J. W.: On the two local inductive algorithms: PRISM and LEM2, Foundations of computing and decision sciences 19, 185-204 (1994)
[4]Chmielewski, M. R.; Grzymala-Busse, J. W.: Global discretization of continuous attributes as preprocessing for machine learning, International journal of approximate reasoning 15, No. 4, 319-331 (1996) · Zbl 0949.68560 · doi:10.1016/S0888-613X(96)00074-6
[5]Dembczynski, K.; Greco, S.; Slowinski, R.: Methodology of rough-set-based classification and sorting with hierarchical structure of attributes and criteria, Control and cybernetics 31, No. 4, 891-920 (2002) · Zbl 1179.93031
[6]Dubois, D.; Prade, H.: Rough fuzzy sets and fuzzy rough sets, International journal of general systems 17, 191-208 (1990) · Zbl 0715.04006 · doi:10.1080/03081079008935107
[7]Duntsch, I.; Gediga, G.: Uncertainty measures of rough set prediction, Artificial intelligence 106, 109-137 (1998) · Zbl 0909.68040 · doi:10.1016/S0004-3702(98)00091-5
[8]Greco, S.; Matarazzo, B.; Slowinski, R.: Handling missing values in rough set analysis of multi-attribute and multi-criteria decision problems, Lnai 1711, 146-157 (1999) · Zbl 1037.91510
[9]Greco, S.; Inuiguchi, M.; Slowinski, R.: Fuzzy rough sets and multiple-premise gradual decision rules, International journal of approximate reasoning 41, No. 2, 179-211 (2006) · Zbl 1093.68114 · doi:10.1016/j.ijar.2005.06.014
[10]Greco, S.; Matarazzo, B.; Slowinski, R.: Rough sets theory for multicriteria decision analysis, European journal of operational research 129, 1-47 (2001) · Zbl 1008.91016 · doi:10.1016/S0377-2217(00)00167-3
[11]Grzymala-Busse, J. W.: On the unknown attribute values in learning from examples, Lnai 542, 368-377 (1991)
[12]Grzymala-Busse, J. W.; Stefanowski, J.: Three discretization methods for rule induction, International journal of intelligent systems 16, No. 1, 29-38 (2001) · Zbl 0969.68145 · doi:10.1002/1098-111X(200101)16:1<29::AID-INT4>3.0.CO;2-0
[13]Grzymala-Busse, J. W.: LERS – a system for learning from examples based on rough sets, Intelligent decision support – handbook of applications and advances of the rough sets theory, 3-18 (1992)
[14]Han, J.; Cai, Y.; Cercone, N.: Data-driven discovery of quantitative rules in relational databases, IEEE transactions on knowledge and data engineering 5, No. 1, 29-40 (1993)
[15]Hong, T. P.; Wang, T. T.; Wang, S. L.: Knowledge acquisition from quantitative data using the rough-set theory, Intelligent data analysis 4, 289-304 (2000)
[16]Kim, D.: Data classification based on tolerant rough set, Pattern recognition 34, 1613-1624 (2001)
[17]De Korvin, A.; Mckeegan, C.; Kleyle, R.: Knowledge acquisition using rough sets when membership values are fuzzy sets, Journal of intelligent and fuzzy systems 6, 237-244 (1998)
[18]Kryszkiewicz, M.: Rough set approach to incomplete information systems, Information sciences 112, 39-49 (1998) · Zbl 0951.68548 · doi:10.1016/S0020-0255(98)10019-1
[19]Kryszkiewicz, M.: Rules in incomplete information systems, Information sciences 113, 271-292 (1999) · Zbl 0948.68214 · doi:10.1016/S0020-0255(98)10065-8
[20]Kryszkiewicz, M.: Comparative study of alternative types of knowledge reduction in inconsistent systems, International journal of intelligent systems 16, 105-120 (2001) · Zbl 0969.68146 · doi:10.1002/1098-111X(200101)16:1<105::AID-INT8>3.0.CO;2-S
[21]Leung, Y.; Li, D.: Maximal consistent block technique for rule acquisition in incomplete information systems, Information sciences 153, 85-106 (2003) · Zbl 1069.68605 · doi:10.1016/S0020-0255(03)00061-6
[22]Leung, Y.; Wu, W. Z.; Zhang, W. X.: Knowledge acquisition in incomplete information systems: a rough set approach, European journal of operational research 168, No. 1, 164-180 (2006) · Zbl 1136.68528 · doi:10.1016/j.ejor.2004.03.032
[23]Lingras, P. J.; Yao, Y. Y.: Data mining using extensions of the rough set model, Journal of the American society for information science 49, 415-422 (1998)
[24]Mi, J. S.; Leung, Y.; Wu, W. Z.: An uncertainty measure in partition-based fuzzy rough sets, International journal of general systems 34, 77-90 (2005) · Zbl 1125.03309 · doi:10.1080/03081070512331318329
[25]Mi, J. S.; Wu, W. Z.; Zhang, W. X.: Approaches to knowledge reductions based on variable precision rough sets model, Information sciences 159, 255-272 (2004) · Zbl 1076.68089 · doi:10.1016/j.ins.2003.07.004
[26]Mi, J. S.; Zhang, W. X.: An axiomatic characterization of a fuzzy generalization of rough sets, Information sciences 160, No. 1 – 4, 235-249 (2004) · Zbl 1041.03038 · doi:10.1016/j.ins.2003.08.017
[27]Mrozek, A.: Rough sets and dependency analysis among attributes in computer implementations of expert’s inference models, International journal of man – machine studies 30, No. 4, 457-473 (1989) · Zbl 0668.68094 · doi:10.1016/S0020-7373(89)80028-8
[28]Pawlak, Z.: Rough sets, International journal of information and computer sciences 11, 341-356 (1982)
[29]Pawlak, Z.: Rough sets: theoretical aspects of reasoning about data, (1991) · Zbl 0758.68054
[30]Pawlak, Z.: Rough classification, International journal of human – computer studies 51, 369-383 (1999)
[31]Polkowski, L.; Skowron, A.: Rough sets in knowledge discovery 1: methodology and applications, 2: applications, (1998)
[32]Polkowski, L.; Tsumoto, S.; Lin, T. Y.: Rough set methods and applications, (2000)
[33]Shafer, G.: A mathematical theory of evidence, (1976)
[34]Skowron, A.: Boolean reasoning for decision rules generation, Lnai 689, 295-305 (1993)
[35]Skowron, A.; Rauszer, C.: The discernibility matrices and functions in information systems, Intelligent decision support-handbook of applications and advances of the rough sets theory, 331-362 (1992)
[36]Slezak, D.; Ziarko, W.: The investigation of the Bayesian rough set model, International journal of approximate reasoning 40, No. 1 – 2, 81-91 (2005) · Zbl 1099.68089 · doi:10.1016/j.ijar.2004.11.004
[37]Slowinski, R.; Vanderpooten, D.: Similarity relation as a basis for rough approximations, Advances in machine intelligence and soft-computing 6, 17-33 (1997)
[38]Slowinski, R.; Vanderpooten, D.: A generalized definition of rough approximations based on similarity, IEEE transactions on knowledge and data engineering 12, 331-336 (2000)
[39]Stefanowski, J.: On rough set based approaches to induction of decision rules, Rough sets in knowledge discovery 1, 500-529 (1998) · Zbl 0927.68094
[40]Stefanowski, J.; Vanderpooten, D.: A general two stage approach to rule induction for examples, Rough sets, fuzzy sets and knowledge discovery, 317-325 (1994) · Zbl 0941.68697
[41]Wu, W. Z.; Leung, Y.; Zhang, W. X.: Connections between rough set theory and Dempster – Shafer theory of evidence, International journal of general systems 31, No. 4, 405-430 (2002) · Zbl 1007.03049 · doi:10.1080/0308107021000013626
[42]Wu, W. Z.; Mi, J. S.; Zhang, W. X.: Generalized fuzzy rough sets, Information sciences 151, 263-282 (2003) · Zbl 1019.03037 · doi:10.1016/S0020-0255(02)00379-1
[43]Wu, W. Z.; Zhang, W. X.: Neighborhood operator systems and approximations, Information sciences 144, 201-217 (2002) · Zbl 1019.68109 · doi:10.1016/S0020-0255(02)00180-9
[44]Wu, W. Z.; Zhang, W. X.: Constructive and axiomatic approaches of fuzzy approximation operators, Information sciences 159, No. 3 – 4, 233-254 (2004) · Zbl 1071.68095 · doi:10.1016/j.ins.2003.08.005
[45]Wu, W. Z.; Zhang, W. X.; Li, H. Z.: Knowledge acquisition in incomplete fuzzy information systems via rough set approach, Expert systems 20, No. 5, 280-286 (2003)
[46]Yasdi, R.: Combining rough sets learning and neural learning: method to deal with uncertain and imprecise information, Neuralcomputing 7, No. 1, 61-84 (1996) · Zbl 0833.68101 · doi:10.1016/0925-2312(93)E0046-G
[47]Yao, Y. Y.: Generalized rough set model, Rough sets in knowledge discovery 1, 286-318 (1998)
[48]Yao, Y. Y.: Two views of the theory of rough sets in finite universes, International journal of approximate reasoning 15, No. 4, 291-317 (1996)
[49]Yao, Y. Y.: Information granulation and rough set approximation, International journal of intelligent systems 16, No. 1, 87-104 (2001)
[50]Zhang, W. X.; Mi, J. S.; Wu, W. Z.: Approaches to knowledge reductions in inconsistent systems, International journal of intelligent systems 18, 989-1000 (2003) · Zbl 1069.68606 · doi:10.1002/int.10128
[51]Ziarko, W.: Variable precision rough set model, Journal of computer and system sciences 46, 39-59 (1993) · Zbl 0764.68162 · doi:10.1016/0022-0000(93)90048-2