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The superiority of three-way decisions in probabilistic rough set models. (English) Zbl 1211.68442
Summary: Three-way decisions provide a means for trading off different types of classification error in order to obtain a minimum cost ternary classifier. This paper compares probabilistic three-way decisions, probabilistic two-way decisions, and qualitative three-way decisions of the standard rough set model. It is shown that, under certain conditions when considering the costs of different types of miss-classifications, probabilistic three-way decisions are superior to the other two.
68T37Reasoning under uncertainty
62H30Classification and discrimination; cluster analysis (statistics)
[1]El-Monsef, M. M. E. Abd; Kilany, N. M.: Decision analysis via granulation basedon general binary relation, International journal of mathematics and mathematical sciences (2007) · Zbl 1138.62003 · doi:10.1155/2007/12714
[2]Duda, R. O.; Hart, P. E.: Pattern classification and scene analysis, (1973) · Zbl 0277.68056
[3]T. Fawcett, ROC Graphs: Notes and Practical Considerations for Researchers, lt;http://home.comcast.net/sim;tom.fawcett/publichtml/papers/ROC101.pdf, accessed February 1, 2010.gt;
[4]Forster, M. R.: Key concepts in model selection: performance and generalizability, Journal of mathematical psychology 44, 205-231 (2000) · Zbl 1048.62500 · doi:10.1006/jmps.1999.1284
[5]Goudey, R.: Do statistical inferences allowing three alternative decision give better feedback for environmentally precautionary decision-making, Journal of environmental management 85, 338-344 (2007)
[6]Greco, S.; Matarazzo, B.; Słowiński, R.: Parameterized rough set model using rough membership and Bayesian confirmation measures, International journal of approximate reasoning 49, 285-300 (2007) · Zbl 1191.68678 · doi:10.1016/j.ijar.2007.05.018
[7]J.P. Herbert, J.T. Yao, Game-theoretic risk analysis in decision-theoretic rough sets, in: Proceedings of RSKT’08, LNAI, Vol. 5009, 2008, pp. 132 – 139.
[8]Herbert, J. P.; Yao, J. T.: Criteria for choosing a rough set model, Computers and mathematics with applications 57, 908-918 (2009) · Zbl 1186.91066 · doi:10.1016/j.camwa.2008.10.043
[9]Katzberg, J. D.; Ziarko, W.: Variable precision rough sets with asymmetric bounds, Fuzzy sets and knowledge discovery, 167-177 (1994) · Zbl 0819.68041
[10]W. Kraaij, S. Raaijmakers, P. Elzinga, Maximizing classifier yield for a given accuracy, in: Proceedings 20th Belgian-Netherlands Conference on Artificial Intelligence (BNAIC 2008), 2008.
[11]Li, Y.; Zhang, C.; Swan, J. R.: An information filtering model on the web and its application in jobagent, Knowledge-based systems 13, 285-296 (2000)
[12]Pawlak, Z.: Rough sets, International journal of computer and information sciences 11, 341-356 (1982)
[13]Pawlak, Z.: Rough sets, Theoretical aspects of reasoning about data (1991) · Zbl 0758.68054
[14]Pawlak, Z.; Skowron, A.: Rough membership functions, Advances in the Dempster – Shafer theory of evidence, 251-271 (1994)
[15]Pawlak, Z.; Skowron, A.: Rudiments of rough sets, Information sciences 177, 3-27 (2007) · Zbl 1142.68549 · doi:10.1016/j.ins.2006.06.003
[16]Pawlak, Z.; Wong, S. K. M.; Ziarko, W.: Rough sets: probabilistic versus deterministic approach, International journal of man-machine studies 29, 81-95 (1988) · Zbl 0663.68094 · doi:10.1016/S0020-7373(88)80032-4
[17]Pauker, S. G.; Kassirer, J. P.: The threshold approach to clinical decision making, The new england journal of medicine 302, 1109-1117 (1980)
[18]Schechter, C. B.: Sequential analysis in a Bayesian model of diastolic blood pressure measurement, Medical decision making 8, 191-196 (1988)
[19]Shi, Z. H.; Gong, Z. T.: The further investigation of covering-based rough sets: uncertainty characterization, similarity measure and generalized models, Information sciences 180, 3745-3763 (2010) · Zbl 1205.68430 · doi:10.1016/j.ins.2010.06.020
[20]D. Ślecedil;zak, Rough sets and Bayes factor, LNCS Transactions on Rough Sets III, LNCS, Vol. 3400, 2005, pp. 202 – 229.
[21]Śle&cedil, D.; Zak: Degrees of conditional (in)dependence: a framework for approximate Bayesian networks and examples related to the rough set-based feature selection, Information sciences 179, 197-209 (2009)
[22]Śle&cedil, D.; Zak; Wróblewski, J.; Eastwood, V.; Synak, P.: Brighthouse: an analytic data warehouse for ad-hoc queries, Proceedings of the VLDB endowment 1, 1337-1345 (2008)
[23]Śle&cedil, D.; Zak; Ziarko, W.: The investigation of the Bayesian rough set model, International journal of approximate reasoning 40, 81-91 (2005)
[24]S. Tsumoto, Accuracy and coverage in rough set rule induction, in: Proceedings of RSCTC’02, LNAI, Vol. 2475, , 2002, pp. 373 – 380. · Zbl 1013.68567 · doi:http://link.springer.de/link/service/series/0558/bibs/2475/24750373.htm
[25]Tsumoto, S.: Contingency matrix theory: statistical dependence in a contingency table, Information sciences 179, 1615-1627 (2009) · Zbl 1176.68168 · doi:10.1016/j.ins.2008.11.023
[26], Categories and concepts, theoretical views and inductive data analysis (1993)
[27]Wald, A.: Sequential tests of statistical hypotheses, The annals of mathematical statistics 16, 117-186 (1945) · Zbl 0060.30207 · doi:10.1214/aoms/1177731118
[28]S.K.M. Wong, W. Ziarko, A Probabilistic Model of Approximate Classification and Decision Rules with Uncertainty in Inductive Learning, Technical Report CS-85-23, Department of Computer Science, University of Regina, 1985.
[29]Wong, S. K. M.; Ziarko, W.: Comparison of the probabilistic approximate classification and the fuzzy set model, Fuzzy sets and systems 21, 357-362 (1987) · Zbl 0618.60002 · doi:10.1016/0165-0114(87)90135-7
[30]Woodward, P. W.; Naylor, J. C.: An application of Bayesian methods in SPC, The statistician 42, 461-469 (1993)
[31]Yao, Y. Y.: Probabilistic approaches to rough sets, Expert systems 20, 287-297 (2003)
[32]Y.Y. Yao, A note on definability and approximations, LNCS Transactions on Rough Sets VII, LNCS, Vol. 4400, 2007, pp. 274 – 282.
[33]Y.Y. Yao, Decision-theoretic rough set models, in: Proceedings of RSKT’07, LNAI, Vol. 4481, 2007, pp. 1 – 12.
[34]Yao, Y. Y.: Probabilistic rough set approximations, International journal of approximation reasoning 49, 255-271 (2008)
[35]Yao, Y. Y.: Interpreting concept learning in cognitive informatics and granular computing, IEEE transactions on system, man and cybernetics, B 39, 855-866 (2009)
[36]Yao, Y. Y.: Three-way decisions with probabilistic rough sets, Information sciences 180, 341-353 (2010)
[37]Yao, Y. Y.; Wong, S. K. M.: A decision theoretic framework for approximating concepts, International journal of man-machine studies 37, 793-809 (1992)
[38]Yao, Y. Y.; Wong, S. K. M.; Lingras, P. J.: A decision-theoretic rough set model, Methodologies for intelligent systems 5, 17-24 (1990)
[39]Yao, Y. Y.; Zhao, Y.: Attribute reduction in decision-teoretic rough set models, Information sciences 178, 3356-3373 (2008) · Zbl 1156.68589 · doi:10.1016/j.ins.2008.05.010
[40]Y.Y. Yao, B. Zhou, Micro and macro evaluation of classification rules, in: Proceedings of the Seventh IEEE International Conference on Cognitive Informatics (ICCI’08), 2008, pp. 441 – 448.
[41]W.Q. Zhao, Y.L. Zhu, An email classification scheme based on decision-theoretic rough set theory and analysis of email security, in: Proceeding of 2005 IEEE Region 10 TENCON, doi:10.1109/TENCON.2005.301121.
[42]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
[43]Ziarko, W.: Probabilistic approach to rough sets, International journal of approximate reasoning 49, 272-284 (2008) · Zbl 1191.68705 · doi:10.1016/j.ijar.2007.06.014