Scale Combinations in Inconsistent Generalized Multi-scale Decision Systems
WU Weizhi1,2, ZHUANG Yubin1,2, TAN Anhui1,2, XU Youhong1,2
1.School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan 316022 2.Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province, Zhejiang Ocean University, Zhoushan 316022
Abstract To investigate knowledge acquisition in the sense of decision rules in inconsistent generalized multi-scale decision systems, the concept of scale combinations in generalized multi-scale information systems is firstly introduced.Information granules with different scale combinations as well as their relationships from generalized multi-scale information systems are then represented.Lower and upper approximations of sets with different scale combinations are further defined and their properties are explored.Finally, optimal scale combinations in inconsistent generalized multi-scale decision systems are discussed.Belief and plausibility functions in the Dempster-Shafer theory of evidence are employed to characterize optimal scale combinations in inconsistent generalized multi-scale decision systems.
Fund:Supported by National Natural Science Foundation of China(No.61573321,41631179,61602415), Natural Science Foundation of Zhejiang Province(No.LY18F030017)
About author:: (WU Weizhi(Corresponding author), Ph.D., professor. His research interests include rough sets, granular computing, data mining and artificial intelligence.)(ZHUANG Yubin, master student. His research interests include rough sets and data mining.)(TAN Anhui, Ph.D., lecturer. His research interests include rough sets, granular computing, data mining and artificial intelligence.)(XU Youhong, master, associate professor. Her research interests include rough sets, granular computing and artificial intelligence.)
[1] BARGIELA A, PEDRYCZ W. Granular Computing: An Introduction. Boston, USA: Kluwer Academic Publishers, 2002. [2] BARGIELA A, PEDRYCZ W. Toward a Theory of Granular Computing for Human-Centered Information Processing. IEEE Transactions on Fuzzy Systems, 2008, 16(2): 320-330. [3] LIN T Y. Granular Computing: Structures, Representations, and Applications // Proc of the 9th International Conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. Berlin, Germany: Springer, 2003: 16-24. [4] YAO Y Y. Granular Computing: Basic Issues and Possible Solutions // Proc of the 5th Joint Conference on Computing and Information. Durham, UK: Duke University Press, 2000: 186-189. [5] 苗夺谦,王国胤,刘 清,等.粒计算的过去、现在与展望.北京:科学出版社, 2007. (MIAO D Q, WANG G Y, LIU Q, et al. Granular Computing: Past, Present and Future. Beijing, China: Science Press, 2007.) [6] 苗夺谦,李德毅,姚一豫,等.不确定性与粒计算.北京:科学出版社, 2011. (MIAO D Q, LI D Y, YAO Y Y, et al. Uncertainty and Granular Computing. Beijing, China: Science Press, 2011.) [7] PAWLAK Z. Rough Sets: Theoretical Aspects of Reasoning about Data. Boston, USA: Kluwer Academic Publishers, 1991. [8] INUIGUCHI M, HIRANO S, TSUMOTO S. Rough Set Theory and Granular Computing. Berlin, Germany: Springer, 2002. [9] LIN T Y, YAO Y Y, ZADEH L A. Data Mining, Rough Sets and Granular Computing. New York, USA: Physica-Verlag, 2002. [10] 徐伟华,米据生,吴伟志.基于包含度的粒计算方法与应用.北京:科学出版社, 2015. (XU W H, MI J S, WU W Z. Granular Computing Methods and Applications Based on Inclusion Degree. Beijing, China: Science Press, 2015.) [11] PEDRYCZ W, SKOWRON A, KREINOVICH V. Handbook of Granular Computing. New York, USA: Wiley, 2008. [12] 张文修,梁 怡,吴伟志.信息系统与知识发现.北京:科学出版社, 2003. (ZHANG W X, LIANG Y, WU W Z. Information Systems and Knowledge Discovery. Beijing, China: Science Press, 2003.) [13] 段 洁,胡清华,张灵均,等.基于邻域粗糙集的多标记分类特征选择算法.计算机研究与发展, 2015, 52(1): 56-65. (DUAN J, HU Q H, ZHANG L J, et al. Feature Selection for Multi-label Classification Based on Neighborhood Rough Sets. Journal of Computer Research and Development, 2015, 52(1): 56-65.) [14] QIAN Y H, LIANG J Y, YAO Y Y, et al. MGRS: A Multi-granulation Rough Set. Information Sciences, 2010, 180(6): 949-970. [15] QIAN Y H, LIANG J Y, DANG C Y. Incomplete Multi-granulation Rough Set. IEEE Transactions on Systems, Man, and Cybernetics(Systems and Humans), 2010, 40(2): 420-431. [16] YANG X B, SONG X N, CHEN Z H. On Multigranulation Rough Sets in Incomplete Information System. International Journal of Machine Learning and Cybernetics, 2012, 3(3): 223-232. [17] LIN G P, LIANG J Y, QIAN Y H. Multigranulation Rough Sets: From Partition to Covering. Information Sciences, 2013, 241: 101-118. [18] SUN B Z, MA W M, QIAN Y H. Multigranulation Fuzzy Rough Set over Two Universes and Its Application to Decision Making. Knowledge-Based Systems, 2017, 123: 61-74. [19] ZHU P F, HU Q H, ZUO W M, et al. Multi-granularity Distance Metric Learning via Neighborhood Granule Margin Maximization. Information Sciences, 2014, 282: 321-331 [20] ZHU P F, HU Q H. Adaptive Neighborhood Granularity Selection and Combination Based on Margin Distribution Optimization. Information Sciences, 2013, 249: 1-12. [21] WU W Z, LEUNG Y. Theory and Applications of Granular Labelled Partitions in Multi-scale Decision Tables. Information Sciences, 2011, 181(18): 3878-3897. [22] 吴伟志,高仓健,李同军.序粒度标记结构及其粗糙近似.计算机研究与发展, 2014, 51(12): 2623-2632. (WU W Z, GAO C J, LI T J. Ordered Granular Labeled Structures and Rough Approximations. Journal of Computer Research and Development, 2014, 51(12): 2623-2632.) [23] 戴志聪,吴伟志.不完备多粒度序信息系统的粗糙近似.南京大学学报(自然科学版), 2015, 51(2): 361-367. (DAI Z C, WU W Z. Rough Approximations in Incomplete Multi-granular Ordered Information Systems. Journal of Nanjing University(Natural Sciences), 2015, 51(2): 361-367.) [24] WU W Z, LEUNG Y. Optimal Scale Selection for Multi-scale Decision Tables. International Journal of Approximate Reasoning, 2013, 54(8): 1107-1129. [25] 吴伟志,陈 颖,徐优红,等.协调的不完备多粒度标记决策系统的最优粒度选择.模式识别与人工智能, 2016, 29(2): 108-115. (WU W Z, CHEN Y, XU Y H, et al. Optimal Granularity Selections in Consistent Incomplete Multi-granular Labeled Decision Systems. Pattern Recognition and Artificial Intelligence, 2016, 29(2): 108-115.) [26] 吴伟志,陈超君,李同军,等.不协调多粒度标记决策系统最优粒度的对比.模式识别与人工智能, 2016, 29(12): 1095-1103. (WU W Z, CHEN C J, LI T J, et al. Comparative Study on Optimal Granularities in Inconsistent Multi-granular Labeled Decision Systems. Pattern Recognition and Artificial Intelligence, 2016, 29(12): 1095-1103.) [27] WU W Z, QIAN Y H, LI T J, et al. On Rule Acquisition in Incomplete Multi-scale Decision Tables. Information Sciences, 2017, 378: 282-302. [28] GU S M, WU W Z. On Knowledge Acquisition in Multi-scale Decision Systems. International Journal of Machine Learning and Cybernetics, 2013, 4(5): 477-486. [29] GU S M, WU W Z. Knowledge Acquisition in Inconsistent Multi-scale Decision Systems // Proc of the 6th International Conference on Rough Sets and Knowledge Technology. Berlin, Germany: Springer, 2011: 669-678. [30] 顾沈明,顾金燕,吴伟志,等.不完备多粒度决策系统的局部最优粒度选择.计算机研究与发展, 2017, 54(7): 1500-1509. (GU S M, GU J Y, WU W Z, et al. Local Optimal Granularity Selections in Incomplete Multi-granular Decision Systems. Journal of Computer Research and Development, 2017, 54(7): 1500-1509.) [31] SHE Y H, LI J H, YANG H L. A Local Approach to Rule Induction in Multi-scale Decision Tables. Knowledge-Based Systems, 2015, 89: 398-410 [32] XIE J P, YANG M H, LI J H, et al. Rule Acquisition and Optimal Scale Selection in Multi-scale Formal Decision Contexts and Their Applications to Smart City. Future Generation Computer Systems, 2017, 73(1): 1-30. [33] HAO C, LI J H, FAN M, et al. Optimal Scale Selection in Dynamic Multi-scale Decision Tables Based on Sequential Three-Way Decisions. Information Sciences, 2017, 415/416: 213-232. [34] LI F, HU B Q. A New Approach of Optimal Scale Selection to Multi-scale Decision Tables. Information Sciences, 2017, 381: 193-208. [35] LI F, HU B Q, WANG J. Stepwise Optimal Scale Selection for Multi-scale Decision Tables via Attribute Significance. Knowledge-Based Systems, 2017, 129: 4-16. [36] XU Y H, WU W Z, TAN A H. Optimal Scale Selections in Consistent Generalized Multi-scale Decision Tables // Proc of the International Joint Conference on Rough Sets. Berlin, Germany: Springer, 2017: 185-198. [37] SHAFER G. A Mathematical Theory of Evidence. New York, USA: Princeton University Press, 1976. [38] WU W Z, ZHANG M, LI H Z, et al. Knowledge Reduction in Random Information Systems via Dempster-Shafer Theory of Evidence. Information Sciences, 2005, 174(3/4): 143-164.
2018, Vol. 31 
