×

Induction of ordinal classification rules from decision tables with unknown monotonicity. (English) Zbl 1341.91046

Summary: We are considering induction of ordinal classification rules, which assign objects to preference-ordered decision classes, within the dominance-based rough set approach. In order to extract such rules, it is necessary to define dominance inconsistencies with respect to a set of condition attributes containing at least one ordinal condition attribute. Furthermore, it is also assumed that we know if there exist increasing or decreasing monotonicity relationships between the values of ordinal condition and decision attributes. Very often, however, this information is unknown a priori. One solution to this issue is to transform the ordinal condition attributes with unknown directions of preference to pairs of attributes with supposed inverse monotonic relationships. Both local and global monotonicity relationships can be represented by decision rules induced from transformed decision tables. However, in some cases, transforming a decision table in this way is overcomplex. In this paper, we propose the inconsistency rates based on dominance and fuzzy preference relations that have the capacity of discovering monotonic relationships directly from data rather than induced decision rules. Moreover, we propose a refined transformation method by introducing an additional monotonicity checking using these inconsistency rates to determine whether an ordinal condition attribute should be cloned or not. Experiments are also provided to evaluate the usefulness of the refined transformation method.

MSC:

91B06 Decision theory
03E72 Theory of fuzzy sets, etc.
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
Full Text: DOI

References:

[1] Alpaydin, E., Introduction to machine learning, 37-39 (2010), The MIT Press, Chapter 2 · Zbl 1191.68485
[2] Błaszczyński, J.; Greco, S.; Słowiński, R., Multi-criteria classification—A new scheme for application of dominance-based decision rules, European Journal of Operational Research, 181, 1030-1044 (2007) · Zbl 1121.90073
[3] Błaszczyński, J.; Greco, S.; Słowiński, R., Inductive discovery of laws using monotonic rules, Engineering Applications of Artificial Intelligence, 25, 2, 284-294 (2012)
[4] Błaszczyński, J.; Greco, S.; Słowiński, R.; Szela̧g, M., On variable consistency dominance-based rough set approaches, Third Int. Conf. Rough Sets and Current Trends in Computing RSCTC 2006, 191-202 (2006) · Zbl 1162.68520
[5] Błaszczyński, J.; Greco, S.; Słowiński, R.; Szela̧g, M., Monotonic variable consistency rough set approaches, International Journal of Approximate Reasoning, 50, 979-999 (2009) · Zbl 1191.68673
[6] Błaszczyński, J.; Słowiński, R.; Szela̧g, M., Sequential covering rule induction algorithm for variable consistency rough set approaches, Information Sciences, 181, 5, 987-1002 (2011)
[7] Błaszczyński, J.; Słowiński, R.; Szela̧g, M., Induction of ordinal classification rules from incomplete data, (Yao, J. T.; Yang, Y.; Słowiński, R.; Greco, S.; Li, H.; Mitra, S.; Polkowski, L., Rough sets and current trends in computing, Lecture Notes in Computer Science, Vol. 7413 (2012), Springer Berlin Heidelberg), 56-65
[8] Dash, M.; Liu, H., Consistency-based search in feature selection, Artificial Intelligence, 151, 155-176 (2003) · Zbl 1082.68791
[9] Dembczyński, K.; Greco, S.; Słowiński, R., Rough set approach to multiple criteria classification with imprecise evaluations and assignments, European Journal of Operational Research, 198, 2, 626-636 (2009) · Zbl 1163.90540
[10] Greco, S.; Inuiguchi, M.; Słowiński, R., Dominance-based rough set approach using possibility and necessity measures, (Alpigini, J.; Peters, J.; Skowron, A.; Zhong, N., Rough sets and current trends in computing, LNAI, Vol. 2475 (2002), Springer-Verlag: Springer-Verlag Berlin), 85-92 · Zbl 1013.91502
[11] Greco, S.; Matarazzo, B.; Słowiński, R., Rough approximation of a preference relation by dominance relations, European Journal of Operational Research, 117, 63-83 (1999) · Zbl 0998.90044
[12] Greco, S.; Matarazzo, B.; Słowiński, R., Dealing with missing data in rough set analysis of multi-attribute and multi-criteria decision problems, (Zanakis, S. H.; Doukidis, G.; Zopounidis, C., Decision making: Recent developments and worldwide applications (2000), Kluwer: Kluwer Dordrecht), 295-316
[13] Greco, S.; Matarazzo, B.; Słowiński, R., Fuzzy dominance-based rough set approach, (Masulli, F.; Parenti, R.; Pasi, G., Advances in fuzzy systems and intelligent technologies (2000), Shaker Publishing: Shaker Publishing Maastricht), 56-66
[14] Greco, S.; Matarazzo, B.; Słowiński, R., A fuzzy extension of the rough set approach to multicriteria and multiattribute sorting, (Fodor, J.; Baets, B. D.; Perny, P., Preferences and decisions under incomplete information (2000), Physica-Verlag: Physica-Verlag Heidelberg), 131-154 · Zbl 0990.90137
[15] Greco, S.; Matarazzo, B.; Słowiński, R., Rough sets theory for multicriteria decision analysis, European Journal of Operational Research, 129, 1-47 (2001) · Zbl 1008.91016
[16] Greco, S.; Matarazzo, B.; Słowiński, R., Rough approximation by dominance relations, International Journal of Intelligent Systems, 17, 153-171 (2002) · Zbl 0997.68135
[17] Greco, S.; Matarazzo, B.; Słowiński, R.; Stefanowski, J., Handling missing values in rough set analysis of multi-attribute and multi-criteria decision problems, Seventh International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing RSFDGrC’99, 146-157 (1999) · Zbl 1037.91510
[18] Greco, S.; Matarazzo, B.; Słowiński, R.; Stefanowski, J., An algorithm for induction of decision rules consistent with dominance principle, (Ziarko, W.; Yao, Y., Rough sets and current trends in computing (2001), Springler-Verlag: Springler-Verlag Berlin), 304-313 · Zbl 1014.68545
[19] Greco, S.; Matarazzo, B.; Słowiński, R.; Stefanowski, J., Variable consistency model of dominance-based rough sets approach, Rough Sets and Current Trends in Computing Lecture Notes in Computer Science, 2005/2001, 170-181 (2001) · Zbl 1014.68544
[20] Hu, Q.; Yu, D.; Guo, M., Fuzzy preference based rough sets, Information Sciences, 180, 2003-2022 (2010) · Zbl 1200.68232
[21] Hu, Q. H.; Yu, D. R.; Wu, C. X., Fuzzy preference rough sets, IEEE Conference on granular computing GrC2008 (2008)
[22] 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) · Zbl 1191.68681
[23] Mitchell, T. M., Machine learning, 66-68 (1997), McGraw-Hill, Chapter 3 · Zbl 0913.68167
[24] Pawlak, Z., Rough sets, International Journal of Computer and Information Sciences, 11, 341-356 (1982) · Zbl 0501.68053
[25] Pawlak, Z., Some issues on rough sets, Transactions on Rough Sets I, LNCS, 3100, 1-58 (2004) · Zbl 1104.68108
[26] Słowiński, R.; Greco, S.; Matarazzo, B., Rough set based decision support, (Burke, E.; Kendall, G., Search methodologies: Introductory tutorials in optimization and decision support techniques (2005), Springer-Verlag: Springer-Verlag New York), 475-527, Chapter 16
[27] Słowiński, R.; Greco, S.; Matarazzo, B., Rough sets in decision making, (Meyers, R., Encyclopedia of complexity and systems science (2009), Springer: Springer New York), 7753-7786
[28] Tsai, Y.; Cheng, C.; Chang, J., Entropy-based fuzzy rough classification approach for extracting classification rules, Expert Systems with Applications, 31, 2, 436-443 (2006)
[29] Wilcoxon, F., Individual comparisons by ranking methods, Biometrics Bulletin, 1, 80-83 (1945)
[30] Yang, X. B.; Yang, J. Y.; Wu, C.; Yu, D. J., Dominance based rough set approach and knowledge reductions in incomplete ordered information system, Information Sciences, 178, 4, 1219-1234 (2008) · Zbl 1134.68057
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.