Summarization of information systems based on rough set theory
Pages 1001 - 1015
Abstract
In the rough set theory proposed by Pawlak, the concept of reduct is very important. The reduct is the minimum attribute set that preserves the partition of the universe. A great deal of research in the past has attempted to reduce the representation of the original table. The advantage of using a reduced representation table is that it can summarize the original table so that it retains the original knowledge without distortion. However, using reduct to summarize tables may encounter the problem of the table still being too large, so users will be overwhelmed by too much information. To solve this problem, this article considers how to further reduce the size of the table without causing too much distortion to the original knowledge. Therefore, we set an upper limit for information distortion, which represents the maximum degree of information distortion we allow. Under this upper limit of distortion, we seek to find the summary table with the highest compression. This paper proposes two algorithms. The first is to find all summary tables that satisfy the maximum distortion constraint, while the second is to further select the summary table with the greatest degree of compression from these tables.
References
[1]
Azam N. and Yao J., Game-theoretic rough sets for recommender systems, Knowledge-Based Systems 72 (2014), 96–107.
[2]
Chen D. and Zhao S., Local reduction of decision system with fuzzy rough sets, Fuzzy Sets and Systems 161 (2010), 1971–1883.
[3]
Chen D., Zhang X., Wang X. and Liu Y., Uncertainty learning of rough set-based prediction under a holistic framework, Information Sciences 463-464 (2018), 129–151.
[4]
Chen Y., Zhu Q. and Xu H., Finding rough set reducts with fish swarm algorithm, Knowledge-Based Systems 81 (2015), 22–29.
[5]
Chen Y., Miao D. and Wang R., A rough set approach to feature selection based on ant colony optimization, Pattern Recognition Letters 31 (2010), 226–233.
[6]
Eskandari S. and Javidi M.M., Online streaming feature selection using rough sets, International Journal of Approximate Reasoning 69 (2016), 35–57.
[7]
Fan T.F., Liau C.J. and Liu D.R., Dominance-based fuzzy rough set analysis of uncertain and possibilistic data tables, International Journal of Approximate Reasoning 52 (2011), 1283–1297.
[8]
Hamouda S.K.M., Wahed M.E., Abo Alez R.H. and Riad K., Robust breast cancer prediction system based on rough set theory at National Cancer Institute of Egypt, Computer Methods and Programs in Biomedicine 153 (2018), 259–268.
[9]
Hu F., Wang G., Huang H. and Wu Y. Incremental attribute reduction based on elementary sets, in: Proceedings of International Conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular-Soft Computing, Berlin, Heidelberg, 2005, pp. 185–193.
[10]
Huang W., Wang H.H., Liu Z. and Wang L., Image de-noising and enhancement based on rough set and principal component analysis, in Proceedings of International Conference on Inventive Computing and Informatics (ICICI), 2017, pp. 536–539.
[11]
Nguyen H.S. and Ślęzak D., “Approximate reducts and association rules,” in International Workshop on Rough Sets, Fuzzy Sets, Data Mining, and Granular-Soft Computing, 1999, pp. 137–145.
[12]
Jothi G. and Inbarani H., Hybrid tolerance rough set–firefly based supervised feature selection for mri brain tumor image classification, Applied Soft Computing 46 (2016), 639–651.
[13]
Kryszkiewicz M., Rough set approach to incomplete information systems, Information Sciences 112 (1998), 39–49.
[14]
Lin Y., Li Y., Wang C. and Chen J., Attribute reduction for multi-label learning with fuzzy rough set, Knowledge-Based Systems 152 (2018), 51–61.
[15]
Lu Z., Qin Z., Zhang Y. and Fang J., A fast feature selection approach based on rough set boundary regions, Pattern Recognition Letters 36 (2014), 81–88.
[16]
Ma X.M. and Liang C., Application of rough set theory in coal gangue image process, in Proceedings of Fifth International Conference on Information Assurance and Security, 2009, pp. 87–90.
[17]
Meng Z. and Shi Z., Extended rough set-based attribute reduction in inconsistent incomplete decision systems, Information Sciences 204 (2012), 44–69.
[18]
Mi J.-S., Wu W.-Z. and Zhang W.-X., Approaches to knowledge reduction based on variable precision rough set model, Information Sciences 159 (2004), 255–272.
[19]
Miao D., Zhao Y., Yao Y., Li H. and Xu F., Relative reducts in consistent and inconsistent decision tables of the Pawlak rough set model, Information Sciences 179 (2009), 4140–4150.
[20]
Pawlak Z. and Skowron A., Rudiments of rough sets, Information Sciences 177 (2007), 3–27.
[21]
Pawlak Z., Rough sets and intelligent data analysis, Information Sciences 147 (2002), 1–12.
[22]
Pawlak Z., AI and intelligent industrial applications: the rough set perspective, Cybernetics and Systems 31 (2000), 227–252.
[23]
Pawlak Z., Rough set approach to knowledge-based decision support, European Journal of Operational Research 99 (1997), 48–57.
[24]
Pawlak Z., Rough Sets: Theoretical Aspects of Reasoning about Data, vol. 9, Springer Science & Business Media, 1991.
[25]
Pawlak Z., Rough sets, International Journal of Computer & Information Sciences 11 (1982), 341–356.
[26]
Pawlak Z. and Sowinski R., Rough set approach to multi-attribute decision analysis, European Journal of Operational Research 72 (1994), 443–459.
[27]
Qian Y., Liang X., Wang Q., Liang J., Liu B., Skowron A., Yao Y., Ma J. and Dang C., Local rough set: a solution to rough data analysis in big data, International Journal of Approximate Reasoning 97 (2018), 38–63.
[28]
Qian Y., Liang J., Li D., Wang F. and Ma N., Approximation reduction in inconsistent incomplete decision tables, Knowledge-Based Systems 23 (2010), 427–433.
[29]
Qiang Z., Wei-jun P., Xin-ping Z. and Xuan W., Enhancement method for infrared dim-small target images based on rough set, in Proceedings of 4th International Conference on Information Science and Control Engineering (ICISCE), 2017, pp. 301–306.
[30]
Raza M.S. and Qamar U., A heuristic based dependency calculation technique for rough set theory, Pattern Recognition 81 (2018), 309–325.
[31]
Salvatore G., Matarazzo B. and Slowinski R., Rough sets theory for multicriteria decision analysis, European Journal of Operational Research 129 (2001), 1–47.
[32]
Skowron A. and Rauszer C., The Discernibility Matrices and Functions in Information Systems, in Intelligent Decision Support: Handbook of Applications and Advances of the Rough Sets Theory, R. Słinowiński, Ed., ed Dordrecht: Springer Netherlands, 1992, pp. 331–362.
[33]
Song J., Tsang E.C.C., Chen D. and Yang X., Minimal decision cost reduct in fuzzy decision-theoretic rough set model, Knowledge-Based Systems 126 (2017), 104–112.
[34]
Sun B., Ma W., Li B. and Li X., Three-way decisions approach to multiple attribute group decision making with linguistic information-based decision-theoretic rough fuzzy set, International Journal of Approximate Reasoning 93 (2018), 424–442.
[35]
Suo M., An R., Zhou D. and Li S., Grid-clustered rough set model for self-learning and fast reduction, Pattern Recognition Letters 106 (2018), 61–68.
[36]
Susmaga R. and Slowinski R., Generation of rough sets reducts and constructs based on inter-class and intra-class information, Fuzzy Sets and Systems 274 (2015), 124–142.
[37]
Tan A., Wu W.Z., Li J.J. and Lin G., Evidence-theory-based numerical characterization of multigranulation rough sets in incomplete information systems, Fuzzy Sets and Systems 294 (2016), 18–35.
[38]
Wang X., Yang J., Teng X., Xia W. and Jensen R., Feature selection based on rough sets and granule swarm optimization, Pattern Recognition Letters 28 (2007), 459–471.
[39]
Wei W., Wu X., Liang J., Cui J. and Sun Y., Discernibility matrix based incremental attribute reduction for dynamic data, Knowledge-Based Systems 140 (2018), 142–157.
[40]
Wroblewski J. Finding minimal reducts using genetic algorithms, in: Proccedings of the Second Annual Join Conference on Infromation Science, 1995, pp. 186-189.
[41]
Wu W.-Z., Attribute reduction based on evidence theory in incomplete decision systems, Information Sciences 178 (2008), 1355–1371.
[42]
Yang X., Yang J., Wu C. and Yu D., Dominance-based rough set approach and knowledge reductions in incomplete ordered information system, Information Sciences 178 (2008), 1219–1234.
[43]
Yang Y.Y., Chen D., Wang H., Tsang E.C.C. and Zhang D.L., Fuzzy rough set based incremental attribute reduction from dynamic data with sample arriving, Fuzzy Sets and Systems 312 (2017), 66–86.
[44]
Zhan J., Liu Q. and Herawan T., A novel soft rough set: Soft rough hemirings and corresponding multicriteria group decision making, Applied Soft Computing 54 (2017), 393–402.
[45]
Zhan J., Jiang H. and Yao Y., Covering-based variable precision fuzzy rough sets with PROMETHEE-EDAS methods, Information Sciences 538 (2020), 314–336.
[46]
Zhang X., Mei C., Chen D. and Li J., Feature selection in mixed data: A method using a novel fuzzy rough set-based information entropy, Pattern Recognition 56 (2016), 1–15.
[47]
Zhang K., Zhan J. and Wang X., TOPSIS-WAA method based on a covering-based fuzzy rough set: an application to rating problem, Information Sciences 539 (2020), 397–421.
[48]
Zhang K., Zhan J. and Wu W.Z., On multi-criteria decision-making method based on a fuzzy rough set model with fuzzy α-neighborhoods, IEEE Transactions on Fuzzy Systemsα (2020), 1–15.
[49]
Zhang J., Wang J., Li D., He H. and Sun J. A new heuristic reduct algorithm base on rough sets theory, in: Proceedings of International Conference on Web-Age Information Management, Berlin, Heidelberg, 2003, pp. 247–253.
[50]
Zhang X., Mei C., Chen D. and Yang Y., A fuzzy rough set-based feature selection method using representative instances, Knowledge-Based Systems 151 (2018), 216–229.
[51]
Zeng A., Li T.R., Liu D., Zhang J.B. and Chen H. M., A fuzzy rough set approach for incremental feature selection on hybrid information systems, Fuzzy Sets and Systems 258 (2015), 39–60.
[52]
Zhong N., Dong J. and Ohsuga S., Using Rough Sets with Heuristics for Feature Selection, Journal of Intelligent Information Systems 16 (2001), 199–214.
[53]
Zhu Y., Jing N. and Chen W., A novel image retrieval model based on semantic information and probability rough set analysis method, in Proceedings of 2nd Asia-Pacific Conference on Intelligent Robot Systems (ACIRS), 2017, pp. 23–27.
[54]
Ziarko W., Variable precision rough set model, Journal of Computer and System Sciences 46 (1993), 39–59.
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Published: 01 January 2021
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