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Attribute reduction with fuzzy rough self-information measures. (English) Zbl 1474.68367

Summary: The fuzzy rough set is one of the most effective methods for dealing with the fuzziness and uncertainty of data. However, in most cases this model only considers the information provided by the lower approximation of a decision when it is used to attribute reduction. In a realistic environment, the uncertainty of information is related to lower approximation as well as upper approximation. In this study, we construct four kinds of uncertainty measures by combining fuzzy rough approximations with the concept of self-information. These uncertainty measures can be employed to evaluate the classification ability of attribute subsets. The relationships between these measures are discussed in detail. It is proven that the fourth measure, called relative decision self-information, is better for attribute reduction than the other measures because it considers both the lower and upper approximations of a fuzzy decision. The proposed measures are generalizations of classical measures based on fuzzy rough sets. Finally, we have designed a greedy algorithm for attribute reduction. We validate the effectiveness of the proposed method by comparing the experimental results for efficiency and accuracy with those of three other algorithms using fundamental data.

MSC:

68T37 Reasoning under uncertainty in the context of artificial intelligence
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[1] An, S.; Hu, Q.; Pedrycz, W.; Zhu, P.; Tsang, E. C.C., Data-distribution-aware fuzzy rough set model and its application to robust classification, IEEE Trans. Cybern., 46, 12, 3073-3085 (2016)
[2] Beaubouef, T.; Petry, F. E., Fuzzy rough set techniques for uncertainty processing in a relational database, Int. J. Intell. Syst., 15, 5, 389-424 (2000) · Zbl 0955.68039
[3] Bodjanova, S., Approximation of fuzzy concepts in decision making, Fuzzy Sets Syst., 85, 23-29 (1997) · Zbl 0907.90003
[4] Banerjee, M.; Pal, S. K., Roughness of a fuzzy set, Inf. Sci., 93, 3-4, 235-246 (1996) · Zbl 0879.04004
[5] Chen, D.; Hu, Q.; Yang, Y., Parameterized attribute reduction with Gaussian kernel based fuzzy rough sets, Inf. Sci., 181, 32, 5169-5179 (2011) · Zbl 1239.68059
[6] Chen, D.; Zhang, L.; Zhao, S.; Hu, Q.; Zhu, P., A novel algorithm for finding reducts with fuzzy rough sets, IEEE Trans. Fuzzy Syst., 20, 2, 385-389 (2012)
[7] Chouchoulas, A.; Shen, Q., Rough set-aided keyword reduction for text categorization, Appl Artif Intell, 15, 9, 843-873 (2001)
[8] Cornelis, C.; Jensen, R.; Hurtado, G., Attribute select with fuzzy decision reducts, Inf. Sci., 177, 3-27 (2007)
[9] Dai, J.; Hu, H.; Wu, W.; Qian, Y.; Huang, D., Maximal discernibility pairs based approach to attribute reduction in fuzzy rough sets, IEEE Trans. Fuzzy Syst., 26, 4, 2174-2187 (2018)
[10] Demsar, J., Statistical comparison of classifiers over multiple data sets, J Mach Learn Res, 7, 1-30 (2006) · Zbl 1222.68184
[11] J. Dunn, Multiple comparisons among means, Journal of the American Statistical Association 56 (1961) 52-64. · Zbl 0103.37001
[12] Dubois, D.; Prade, H., Rough fuzzy sets and fuzzy rough sets, Int. J. Gen Syst, 17, 191-209 (1990) · Zbl 0715.04006
[13] Friedman, M., A comparison of alternative tests of significance for the problem of m ranking, Ann. Math. Statist., 11, 86-92 (1940) · JFM 66.1305.08
[14] S. Greco, B. Matarazzo, and R. Slowinski, Fuzzy similarity relation as a basis for rough approximations. In: International Conference on Rough Sets and Current Trends in Computing, Springer, Berlin, Heidelberg, 1998, June, pp. 283-289.
[15] Hu, Q.; Zhang, L.; Zhang, D.; Pedrycz, W., Measuring relevance between discrete and continuous features based on neighborhood mutual information, Expert Syst. Appl., 38, 10737-10750 (2011)
[16] Hu, Q.; Yu, D.; Xie, Z.; Liu, J., Fuzzy probabilistic approximation spaces and their information measures, IEEE Trans. Fuzzy Syst., 14, 2, 191-201 (2006)
[17] Jensen, R.; Shen, Q., Fuzzy-rough attribute reduction with application to web categorization, Fuzzy Sets Syst., 141, 3, 469-485 (2004) · Zbl 1069.68609
[18] Jensen, R.; Shen, Q., New approaches to fuzzy-rough attribute selection, IEEE Trans. Fuzzy Syst., 17, 4, 824-838 (2009)
[19] Lang, G.; Li, Q.; Cai, M.; Yang, T.; Xiao, Q., Incremental approaches to knowledge reduction based on characteristic matrices, Int. J. Mach. Learn. Cybern., 8, 203-222 (2017)
[20] Liang, D.; Liu, D.; Pedrycz, W.; Hu, P., Triangular fuzzy decision-theoretic rough sets, Int. J. Approximate Reason., 54, 1087-1106 (2013) · Zbl 1316.68183
[21] Liang, J.; Dang, C.; Chin, K.; Richard, C., A new method for measuring uncertainty and fuzziness in rough set theory, Int. J. Gen Syst, 31, 4, 331-342 (2002) · Zbl 1010.94004
[22] Lin, Y.; Li, Y.; Wang, C.; Chen, J., Attribute reduction for multi-label learning with fuzzy rough set, Knowl.-Based Syst., 152, 51-61 (2018)
[23] Lin, Y.; Chen, H.; Lin, G.; Chen, J.; Ma, Z.; Li, J., Synthesizing decision rules from multiple information sources: a neighborhood granulation viewpoint, Int. J. Mach. Learn. Cybern., 9, 11, 1919-1928 (2018)
[24] Mi, J.; Leung, Y.; Zhao, H.; Feng, T., Generalized fuzzy rough sets determined by a triangular norm, Inf. Sci., 178, 16, 3203-3213 (2008) · Zbl 1151.03344
[25] F. Min, Z. Zhang, W. Zhai, R. Shen, Frequent pattern discovery with tri-partition alphabets, Information Sciences 507 (2020) 715-732.
[26] Maji, P.; Garai, P., An fuzzy-rough attribute selection: criteria of max-dependency, max-relevance, min-redundancy, and max-significance, Appl. Soft Comput., 17, 1-14 (2012)
[27] N. N. Moresi, t. M. M. Yakont, Axiomatic for fuzzy rough sets, Fuzzy sets and systems 100 (1-3) (1998) 327-342. · Zbl 0938.03085
[28] Moser, B., On the T-transitivity of kernels, Fuzzy Sets Syst., 157, 1787-1796 (2006) · Zbl 1100.68095
[29] Moser, B., On representing and generating kernels by fuzzy equivalence relations, J. Mach. Learn. Res., 7, 2603-2620 (2006) · Zbl 1222.68269
[30] Parthaláin, N. M.; Jensen, R., Unsupervised fuzzy-rough set-based dimensionality reduction, Inf. Sci., 229, 106-121 (2013) · Zbl 1293.68233
[31] Qian, Y.; Liang, J.; Wu, W.; Dang, C., Information granularity in fuzzy binary GrC model, IEEE Trans. Fuzzy Syst., 19, 2, 253-264 (2011)
[32] Radzikowska, A. M.; Kerre, E. E., A comparative study of fuzzy rough sets, Fuzzy Sets Syst., 126, 22, 137-155 (2002) · Zbl 1004.03043
[33] Mieszkowicz-Rolka, L. Rolka, Variable precision fuzzy rough sets, Transactions on Rough sets, In: LNCS-3100, Berlin, Germany; Springer (2004) 144-160. · Zbl 1104.68767
[34] Shannon, C. E., A Mathematical theory of communication, Bell Syst. Tech. J., 27, 379-423 (1948) · Zbl 1154.94303
[35] Su, L.; Zhu, W., Dependence space of topology and its application to attribute reduction, Int. J. Mach. Learn. Cybern., 9, 4, 691-698 (2018)
[36] Sun, L.; Zhang, X.; Qian, Y.; Xu, J.; Zhang, S.; Yun, Tian, Joint neighborhood entropy-based gene selection method with fisher score for tumor classification, Appl. Intell., 49, 4, 1245-1259 (2019)
[37] Sun, L.; Zhang, X.; Qian, Y.; Xu, J.; Zhang, S., Feature selection using neighborhood entropy-based uncertainty measures for gene expression data classification, Inf. Sci., 502, 18-41 (2019) · Zbl 1453.68186
[38] Shen, Q.; Chouchoulas, A., A fuzzy-rough approach for generating classification rules, Pattern Recogn., 35, 11, 341-354 (2002)
[39] Sun, B.; Ma, W.; Qian, Y., Multigranulation fuzzy rough set over two universes and its application to decision making, Knowl.-Based Syst., 123, 61-74 (2017)
[40] Sun, B.; Ma, W.; Chen, X., Fuzzy rough set on probabilistic approximation space over two universes and its application to emergency decision-making, Exp. Syst., 32, 4, 507-521 (2015)
[41] Tsang, E. C.C.; Chen, D.; Yeung, D. S.; Wang, X. Z., Attribute reduction using fuzzy rough sets, IEEE Trans. Fuzzy Syst., 16, 5, 1130-1141 (2008)
[42] Wang, C.; Huang, Y.; Shao, M.; Chen, D., Uncertainty measures for general fuzzy relations, Fuzzy Sets Syst., 360, 82-96 (2019) · Zbl 1423.68516
[43] Wang, C.; Huang, Y.; Shao, M.; Fan, X., Fuzzy rough set-based attribute reduction using distance measures, Knowl.-Based Syst., 164, 205-212 (2019)
[44] Wang, C.; Qi, Y.; Shao, M.; Hu, Q.; Chen, D.; Qian, Y.; Lin, Y., A fitting model for feature selection with fuzzy rough sets, IEEE Trans. Fuzzy Syst., 25, 4, 741-753 (2017)
[45] Wang, C.; Shao, M.; He, Q.; Qian, Y.; Qi, Y., Feature subset selection based on fuzzy neighborhood rough sets, Knowl.-Based Syst., 111, 1, 173-179 (2016)
[46] Wu, W.; Zhang, W., Constructive and axiomatic approaches of fuzzy approximation operators, Inf. Sci., 159, 233-254 (2004) · Zbl 1071.68095
[47] Wu, W.; Shao, M.; Wang, X., Using single axioms to characterize (S, T)-intuitionistic fuzzy rough approximation operators, Int. J. Mach. Learn. Cybern., 10, 1, 27-42 (2019)
[48] Xu, W.; Li, W., Granular computing approach to two-way learning based on formal concept analysis in fuzzy datasets, IEEE Trans. Cybern., 46, 2, 366-379 (2016)
[49] Yang, Y.; Chen, D.; Wang, H., Active sample selection based incremental algorithm for attribute reduction with rough sets, IEEE Trans. Fuzzy Systems, 25, 4, 825-838 (2017)
[50] Yang, Y.; Chen, D.; Wang, H.; Tsang, E. C.C.; Zhang, D., Fuzzy rough set based incremental attribute reduction from dynamic data with sample arriving, Fuzzy Sets Syst., 312, 66-86 (2017) · Zbl 1368.68301
[51] Yeung, D.; Chen, D.; Tsang, C.; Lee, W.; Wang, X., On the generalization of fuzzy rough sets, IEEE Trans. Fuzzy Syst., 13, 3, 343-361 (2005)
[52] Zeng, Z.; Li, T.; Liu, D.; Zhang, J.; Chen, H., A fuzzy rough set approach for incremental feature selection on hybrid information systems, Fuzzy Sets Syst., 258, 1, 39-60 (2015) · Zbl 1335.68274
[53] Zhao, S.; Chen, H.; Li, C.; Du, X.; Sun, H., A novel approach to building a robust fuzzy rough classifier, IEEE Trans. Fuzzy Syst., 23, 4, 769-786 (2015)
[54] Zhao, S.; Tsang, C.; Chen, D., The model of fuzzy variable precision rough sets, IEEE Trans. Fuzzy Syst., 17, 2, 451-467 (2009)
[55] Zhang, X.; Bo, C.; Smarandache, F.; Dai, J., New inclusion relation of neutrosophic sets with application and related lattice structure, Int. J. Mach. Learn. Cybernet., 9, 10, 1753-1763 (2018)
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