Horizontal decomposition of data table for finding one reduct

References

• Al-Radaideh, Qasem A., MdNasir Sulaiman, Mohd Hasan Selamat , and Hamidah Ibrahim. 2005. “Approximate Reduct Computation by Rough Sets Based Attribute Weighting.” In International Conference on Granular Computing, July 25--27, edited by Xiaohua Hu, Qing Liu, Andrzej Skowron, Tsau Young Lin, Ronald R. Yager, and Bo Zhang, 383–386. Beijing, China: IEEE.
   Google Scholar
• Bazan, Jan G., Andrzej Skowron, and Piotr Synak. 1994. “Dynamic Reducts as a Tool for Extracting Laws from Decisions Tables.” In Methodologies for Intelligent Systems: 8th International Symposium, ISMIS ’94 Charlotte, North Carolina, USA, 16--19 October 1994 Proceedings, 346-355. Berlin, Heidelberg: Springer, Berlin Heidelberg.
   Google Scholar
• Beynon, Malcolm. 2001. “Reducts within the Variable Precision Rough Sets Model: A Further Investigation.” European Journal of Operational Research 134 (3): 592–605.
   Web of Science ®Google Scholar
• Chen, Degang, Suyun Zhao, Lei Zhang, Yongping Yang, and Xiao Zhang. 2012. “Sample Pair Selection for Attribute Reduction with Rough Set.” IEEE Transactions on Knowledge and Data Engineering 24 (11): 2080–2093.
   Web of Science ®Google Scholar
• Czolombitko, Michal, and Jaroslaw Stepaniuk. 2016. “Attribute Reduction Based on MapReduce Model and Discernibility Measure.” In Computer Information Systems and Industrial Management: 15th IFIP TC8 International Conference, CISIM 2016, Vilnius, Lithuania, September 14–16, 2016 Proceedings, edited by K. Saeed and W. Homenda. Cham: Springer International Publishing.
   Google Scholar
• Degang, Chen, Wang Changzhong, and Hu Qinghua. 2007. “A New Approach to Attribute Reduction of Consistent and Inconsistent Covering Decision Systems with Covering Rough Sets.” Information Sciences 177 (17): 3500–3518.
   Web of Science ®Google Scholar
• Deng, D., and H. Huang. 2006. “A New Discernibility Matrix and Function.” In Rough Sets and Knowledge Technology: First International Conference, RSKT 2006, Chongquing, China, July 24--26, edited by James F. Peters and Yiju Yao, 114–121. Berlin, Heidelberg: Springer.
   Google Scholar
• Dong, Ze, Ming Sun, and Yanyan Yang. 2016. “Fast Algorithms of Attribute Reduction for Covering Decision Systems with Minimal Elements in Discernibility Matrix.” International Journal of Machine Learning and Cybernetics 7 (2): 297–310.
   Web of Science ®Google Scholar
• Grzymala-Busse, J. W. 1991. “An Algorithm for Computing a Single Covering.” In Managing Uncertainty in Expert Systems, edited by J. W. Grzymala-Busse, 66. Netherlands: Kluwer Academic Publishers.
   Google Scholar
• Hońko, Piotr. 2015. “Scalability of Data Decomposition Based Algorithms: Attribute Reduction Problem.” In Pattern Recognition and Machine Intelligence: 6th International Conference, PReMI 2015, Warsaw, Poland, 30 June--3 July 2015, Proceedings, edited by M. Kryszkiewicz, S. Bandyopadhyay, H. Rybinski and S. K. Pal, 387–396. Cham: Springer International Publishing.
   Google Scholar
• Hońko, Piotr. 2016. “Attribute Reduction: A Horizontal Data Decomposition Approach.” Soft Computing 20 (3): 951–966.
   Web of Science ®Google Scholar
• Hu, F., X. Fan, S. X. Yang, and C. Tao. 2006. A Novel Reduction Algorithm Based Decomposition and Merging Strategy. Vol. 344, Lecture Notes in Control and Information Sciences, 790–796. Berlin-Heidelberg: Springer-Verlag.
   Google Scholar
• Hu, Feng, Guoyin Wang, Hai Huang, and Yu Wu. 2005. “Incremental Attribute Reduction Based on Elementary Sets.” In Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing: 10th International Conference, RSFDGrC 2005, Regina, Canada, 31 August – 3 September 2005, Proceedings, Part I , edited by Dominik \’{S}l\c{e}zak, Guoyin Wang, Marcin Szczuka, Ivo D\"{u}ntsch, and Yiyu Yao, 185-193. Berlin, Heidelberg: Springer, Berlin Heidelberg.
   Google Scholar
• Hu, Keyun, Lili Diao, Yuchang Lu, and Chunyi Shi. 2000. “A Heuristic Optimal Reduct Algorithm.” In Intelligent Data Engineering and Automated Learning---IDEAL 2000. Data Mining, Financial Engineering, and Intelligent Agents: Second International Conference Shatin, N.T., Hong Kong, China, December 13--15, edited by Kwong-Sak Leung, Lai-Wan Chan and Helen Meng, 139–144. Springer.
   Google Scholar
• Hu, Qinghua, Yu Daren, Jinfu Liu, and Wu Congxin. 2008. “Neighborhood Rough Set Based Heterogeneous Feature Subset Selection.” Information Sciences 178 (18): 3577–3594.
   Web of Science ®Google Scholar
• Hu, Qinghua, Yu Daren, Zongxia Xie, and Jinfu Liu. 2006. “Fuzzy Probabilistic Approximation Spaces and Their Information Measures.” IEEE Transactions on Fuzzy Systems 14 (2): 191–201.
   Web of Science ®Google Scholar
• Hu, Xiaohua, and Nick Cercone. 1995. “Learning in Relational Databases: A Rough Set Approach.” Computational Intelligence 11 (2): 323–338.
   Web of Science ®Google Scholar
• Jia, Xiuyi, Wenhe Liao, Zhenmin Tang, and Lin Shang. 2013. “Minimum Cost Attribute Reduction in Decision-theoretic Rough Set Models.” Information Sciences 219: 151–167.
   Web of Science ®Google Scholar
• Jiang, Yu, and Yu Yang. 2016. “Minimal Attribute Reduction with Rough Set Based on Compactness Discernibility Information Tree.” Soft Computing 20 (6): 2233–2243.
   Web of Science ®Google Scholar
• Jing, Fan, Jiang Yunliang, and Liu Yong. 2017. “Quick Attribute Reduction with Generalized Indiscernibility Models.” Information Sciences 397--398: 15–36.
   Web of Science ®Google Scholar
• Jing, Yunge, Tianrui Li, Chuan Luo, Shi-Jinn Horng, Guoyin Wang, and Yu Zeng. 2016. “An Incremental Approach for Attribute Reduction Based on Knowledge Granularity.” Knowledge-Based Systems 104: 24–38.
   Web of Science ®Google Scholar
• Kryszkiewicz, Marzena. 2001. “Comparative Study of Alternative Type of Knowledge Reduction in Inconsistent Systems.” International Journal of Intelligent Systems 16: 105–120.
   Web of Science ®Google Scholar
• Kryszkiewicz, M. 1998. “Rough Set Approach to Incomplete Information Systems.” Information Sciences 112 (1–4): 39–49.
   Web of Science ®Google Scholar
• Li, Fachao, and Jinning Yang. 2016. “A New Approach to Attribute Reduction of Decision Information Systems.” In Proceedings of the 2015 International Conference on Electrical and Information Technologies for Rail Transportation: Transportation Berlin, edited by Yong Qin, Limin Jia, Jianghua Feng, Min An and Lijun Diao. Heidelberg: Springer, Berlin Heidelberg.
   Google Scholar
• Liang, Jiye, Junrong Mi, Wei Wei, and Feng Wang. 2013. “An Accelerator for Attribute Reduction Based on Perspective of Objects and Attributes.” Knowledge-Based Systems. 44: 90–100.
   Web of Science ®Google Scholar
• Liang, Jiye, and Xu Zongben. 2002. “The Algorithm on Knowledge Reduction in Incomplete Information Systems.” International Journal of Uncertainty Fuzziness 10 (1): 95–103.
   Web of Science ®Google Scholar
• Liu, Guilong, Zheng Hua, and Zehua Chen. 2017. “A General Reduction Algorithm for Relation Decision Systems and its Applications.” Knowledge-Based Systems 119: 87–93.
   Web of Science ®Google Scholar
• Liu, Guilong, Zheng Hua, and Jiyang Zou. 2018. “Local Attribute Reductions for Decision Tables (to appear).” Information Sciences 422 (Supplement C): 204–217.
   Google Scholar
• Lv, Ping, Jin Qian, and Xiaodong Yue. 2016. “Incremental Attribute Reduction Algorithm for Big Data Using MapReduce.” Journal of Computational Methods in Sciences and Engineering 16 (3): 641–652.
   Web of Science ®Google Scholar
• Mi, Ju-Sheng, Wu Wei-Zhi, and Wen-Xiu Zhang. 2004. “Approaches to Knowledge Reduction Based on Variable Precision Rough Set Model.” Information Sciences 159 (2): 255–272.
   Google Scholar
• Miao, Duoqian, Yan Zhao, Yiyu Yao, H. X. Li, and Feifei Xu. 2009. “Relative Reducts in Consistent and Inconsistent Decision Tables of the Pawlak Rough Set Model.” Information Sciences 179 (24): 4140–4150.
   Web of Science ®Google Scholar
• Nguyen, Hung S. 2006. “Approximate Boolean Reasoning: Foundations and Applications in Data Mining.” Transactions on Rough Sets V 4100: 334–506.
   Google Scholar
• Nguyen, S. H., A. Skowron, and P. Synak. 1998. “Discovery of Data Patterns with Applications to Decomposition and Classification Problems.” Chap. 4. In Rough Sets in Knowledge Discovery 2: Applications, Case Studies and Software Systems. Vol. 19, Studies in Fuzziness and Soft Computing, edited by Lech Polkowski and Andrzej Skowron, 55–97. Heidelberg, Germany: Physica-Verlag.
   Google Scholar
• Pawlak, Z. 1991. Rough Sets. Theoretical Aspects of Reasoning about Data. Dordrecht: Kluwer Academic.
   Google Scholar
• Pawlak, Zdzislaw, and Andrzej Skowron. 2007. “Rudiments of Rough Sets.” Information Sciences 177 (1): 3–27.
   Web of Science ®Google Scholar
• Qian, Yuhua, Jiye Liang, Witold Pedrycz, and Chuangyin Dang. 2010. “Positive Approximation: An Accelerator for Attribute Reduction in Rough Set Theory.” Artificial Intelligence 174 (9–10): 597–618.
   Web of Science ®Google Scholar
• Skowron, A., and C. Rauszer. 1992. “The Discernibility Matrices and Functions in Information Systems.” In Intelligent Decision Support, edited by Roman S{\l}owi{\’{n}}ski, 331–362. Amsterdam: Springer.
   Google Scholar
• \’{S}l\v{e}zak, Dominik. 1998. “Searching for Frequential Reducts in Decision Tables with Uncertain Objects.” In Rough Sets and Current Trends in Computing: First International Conference, RSCTC’98 Warsaw, Poland, 22--26 June 1998 Proceedings, 52-59. Berlin, Heidelberg: Springer, Berlin Heidelberg.
   Google Scholar
• \’{S}l\v{e}zak, Dominik. 2002. “Approximate Entropy Reducts.” Fundamenta informaticae 53 (3, 4): 365–390.
   Web of Science ®Google Scholar
• \’{S}l\v{e}zak, Dominik. 2015. “On Generalized Decision Functions: Reducts, Networks and Ensembles.” In Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing: 15th International Conference, RSFDGrC 2015, Tianjin, China, November 20–23, 2015, Proceedings, edited by Y. Yao, Q. Hu, H. Yu and J. Grzymala-Busse, 13–23. Cham: Springer International Publishing.
   Google Scholar
• Stawicki, Sebastian, Dominik \’{S}l\v{e}zak, Andrzej Janusz, and Sebastian Widz. 2017. “Decision Bireducts and Decision Reducts -- A Comparison.” International Journal of Approximate Reasoning 84 (Supplement C): 75–109.
   Google Scholar
• Stepaniuk, J. 2008. Rough-Granular Computing in Knowledge Discovery and Data Mining. Vol. 152, Studies in Computational Intelligence. Berlin Heidelberg: Springer-Verlag.
   Google Scholar
• Suraj, Z. 1996. “Discovery of Concurrent Data Models from Experimental Tables: A Rough Set Approach.” Fundamenta informaticae 28 (3–4): 353–376.
   Google Scholar
• Swiniarski, R. 2001. “Rough Sets Methods in Feature Reduction and Classification.” International Journal of Applied Mathematics and Computer Science 11 (3): 565–582.
   Google Scholar
• Swiniarski, Roman W., and A. Skowron. 2003. “Rough Set Methods in Feature Selection and Recognition.” Pattern Recognition Letters 24 (6): 833–849.
   Web of Science ®Google Scholar
• Teng, Shu Hua, Min Lu, A-Feng Yang, Jun Zhang, Yongjian Nian, and Mi He “Efficient Attribute Reduction from the Viewpoint of Discernibility.” Information Sciences 326 :297–314.
   Web of Science ®Google Scholar
• Thi, Vu Duc, and Nguyen Long Giang. 2013. “A Method for Extracting Knowledge from Decision Tables in Terms of Functional Dependencies.” Cybernetics and Information Technologies 13 (1): 73–82.
   Google Scholar
• Wang, Pai Chou. 2011. “Efficient Hash-based Approximate Reduct Generation.” In International Conference on Granular Computing, November 8--10, edited by Tzung-Pei Hong, Yasuo Kudo, Mineichi Kudo, Tsau Young Lin, Been-Chian Chien, Shyue-Liang Wang, Masahiro Inuiguchi and Guilong Liu, 703–707. Kaohsiung, Taiwan: IEEE.
   Google Scholar
• Wang, Changzhong, Qiang He, Degang Chen, and Hu Qinghua. 2014. “A Novel Method for Attribute Reduction of Covering Decision Systems.” Information Sciences 254: 181–196.
   Web of Science ®Google Scholar
• Wei, Wei, Jiye Liang, Yuhua Qian, Feng Wang, and Chuangyin Dang. 2010. “Comparative Study of Decision Performance of Decision Tables Induced by Attribute Reductions.” International Journal of General Systems 39 (8): 813–838.
   Web of Science ®Google Scholar
• Wei, Wei, Jiye Liang, Junhong Wang, and Yuhua Qian. 2013. “Decision-relative Discernibility Matrices in the Sense of Entropies.” International Journal of General Systems 42 (7): 721–738.
   Web of Science ®Google Scholar
• Wroblewski, Jakub. 2001. “Ensembles of Classifiers Based on Approximate Reducts.” Fundamenta informaticae 47 (3–4): 351–360.
   Web of Science ®Google Scholar
• Xie, Jun, Xuefen Shen, Haifeng Liu, and Xinying Xu. 2013. “Research on an Incremental Attribute Reduction Based on Relative Positive Region.” Journal of Computational Information Systems 9 (16): 6621–6628.
   Google Scholar
• Yao, Yiyu, and Yan Zhao. 2008. “Attribute Reduction in Decision-theoretic Rough Set Models.” Information Sciences 178 (17): 3356–3373.
   Web of Science ®Google Scholar
• Ye, D. Y., and Z. J. Chen. 2002. “A New Discernibility Matrix and the Computation of a Core.” Acta Electronica Sinica 30 (7): 1086–1088.
   Google Scholar
• Ye, M., and C. Wu. 2010. “Decision Table Decomposition Using Core Attributes Partition for Attribute Reduction.” In 5th International Conference on Computer Science and Education (ICCSE). Vol. 23, August 24--27, 23–26. Hefei, China: IEEE.
   Google Scholar
• Zhang, Xiao, Changlin Mei, Degang Chen, and Jinhai Li. 2013. “Multi-confidence Rule Acquisition Oriented Attribute Reduction of Covering Decision Systems via Combinatorial Optimization.” Knowledge-Based Systems 50: 187–197.
   Web of Science ®Google Scholar
• Zhang, Wen-Xiu, Ju-Sheng Mi, and Wu Wei-Zhi. 2003. “Approaches to Knowledge Reductions in Inconsistent Systems.” International Journal of Intelligent Systems 18 (9): 989–1000.
   Web of Science ®Google Scholar