Optimal Granularity Selections in Consistent Incomplete Multi-granular Labeled Decision Systems
WU Weizhi, CHEN Ying, XU Youhong, GU Shenming
Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province, Zhejiang Ocean University, Zhoushan 316022 School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan 316022
Abstract Aiming at knowledge acquisition in incomplete information systems with multi-granular labels, the concept of incomplete multi-granular labeled information systems is firstly introduced.Similarity relations of an incomplete multi-granular labeled information system are then defined.Representations of information granules with different levels of granulation as well as their relationships are also explored.Lower and upper approximations based on similarity relations with different levels of granulation are further defined and their properties are presented.Finally, by belief and plausibility functions in Dempster-Shafer theory of evidence, optimal granularity selections in consistent incomplete multi-granular labeled decision systems are discussed.
[1] ZADEH L A. Fuzzy Sets and Information Granularity // GUPTA N, RAGADE R, YAGER R R, eds. Advances in Fuzzy Set Theory and Applications. Amsterdam, the Netherland: North-Holland, 1979: 3-18. [2] ZADEH L A. Towards a Theory of Fuzzy Information Granulation and Its Centrality in Human Reasoning and Fuzzy Logic. Fuzzy Sets and Systems, 1997, 90(2): 111-127. [3] HOBBS J R. Granularity // Proc of the 9th International Joint Conference on Artificial Intelligence. Los Angeles, USA, 1985, I: 432-435. [4] LIN T Y. Granular Computing: From Rough Sets and Neighborhood Systems to Information Granulation and Computing in Words // Proc of the European Congress on Intelligent Techniques and Soft Computing. Aachen, Germany, 1997: 1602-1606. [5] LIN T Y. Granular Computing: Structures, Representations, and Applications // WANG G Y, LIU Q, YAO Y Y, et al., eds. Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. Berlin, Germany: Springer, 2003: 16-24. [6] YAO Y Y. Granular Computing: Basic Issues and Possible Solutions // Proc of the 5th Joint Conference on Information Sciences. Atlantic City, USA, 2000, I: 186-189. [7] 张 铃,张 拔.基于商空间的问题求解:粒度计算的理论基础.北京:清华大学出版社, 2014. (ZHANG L, ZHANG B. Quotient Space Based Problem Solving: A Theoretical Foundation of Granular Computing. Beijing, China: Tsinghua University Press, 2014.) [8] PAWLAK Z. Rough Sets: Theoretical Aspects of Reasoning about Data. Norwell, USA: Kluwer Academic Publishers, 1991. [9] KRYSZKIEWICZ M. Rough Set Approach to Incomplete Information Systems. Information Sciences, 1998, 112(1/2/3/4): 39-49. [10] LI D Y, ZHANG B, LEUNG Y. On Knowledge Reduction in Inconsistent Decision Information Systems. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2004, 12(5): 651-672. [11] SHAO M W, ZHANG W X. Dominance Relation and Rules in an Incomplete Ordered Information System. International Journal of Intelligent Systems, 2005, 20(1): 13-27. [12] SUN B Z, MA W M, GONG Z T. Dominance-Based Rough Set Theory over Interval-Valued Information Systems. Expert Systems, 2014, 31(2): 185-197. [13] LEUNG Y, WU W Z, ZHANG W X. Knowledge Acquisition in Incomplete Information Systems: A Rough Set Approach. European Journal of Operational Research, 2006, 168(1): 164-180. [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, DNAG C Y. Incomplete Multi-granulation Rough Set. IEEE Trans on Systems, Man and Cybernetics(Systems and Humans), 2010, 40(2): 420-431. [16] YANG X B, SONG X N, CHEN Z H, et al. On Multigranulation Rough Sets in Incomplete Information System. International Journal of Machine Learning and Cybernetics, 2012, 3(3): 223-232. [17] WU W Z, LEUNG Y. Theory and Applications of Granular Labelled Partitions in Multi-scale Decision Tables. Information Sciences, 2011, 181(18): 3878-3897. [18] WU W Z, LEUNG Y. Optimal Scale Selection for Multi-scale Decision Tables. International Journal of Approximate Reasoning, 2013, 54(8): 1107-1129. [19] 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. [20] GU S M, WU W Z. Knowledge Acquisition in Inconsistent Multi-scale Decision Systems // YAO J T, RAMANNA S, WANG G Y, et al., eds. Lecture Notes in Computer Science. Berlin, Germany: Springer, 2011, 6954: 669-678. [21] WU W Z. Attribute Reduction Based on Evidence Theory in Incomplete Decision Systems. Information Sciences, 2008, 178(5): 1355-1371.
2016, Vol. 29 
