Comparative Study on Optimal Granularities in Inconsistent Multi-granular Labeled Decision Systems
WU Weizhi, CHEN Chaojun, LI Tongjun, XU Youhong
School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan 316022 Key Laboratory of Oceanographic Big Data Mining & Application of Zhejiang Province, Zhoushan 316022
Abstract：To study knowledge representation and knowledge acquisition in inconsistent decision systems with multi-granular labels, the concept of multi-granular labeled information systems is firstly introduced. Indiscernibility relations on the universe of discourse in a multi-granular labeled information system are defined. Representations of equivalence classes with different levels of granulation as well as their relationships are also explored. Lower and upper approximations of sets with different levels of granulation are further defined and their properties are presented. Finally, concepts of eight types of consistence and optimal granularity with various meanings in inconsistent multi-granular labeled decision systems are proposed and their relationships are examined.
[1] LIN T Y. Granular Computing: From Rough Sets and Neighborhood Systems to Information Granulation and Computing in Words [C/OL]. [2016-04-20]. http://xanadu.cs.sjsu.edu/~drtylin/publications/paperList/101_34rsnsigcw3.pdf. [2] 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. [3] Yao Y Y. Granular Computing: Basic Issues and Possible Solutions[C/OL]. [2016-05-25]. http://www2.cs.uregina.ca/~yyao/PAPERS/basic.pdf. [4] 张 铃,张 钹.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.) [5] INUIGUCHI M, HIRANO S, TSUMOTO S. Rough Set Theory and Granular Computing. Berlin, Germany: Springer, 2002. [6] LIN T Y, YAO Y Y, ZADEH L A. Data Mining, Rough Sets and Granular Computing. New York, USA: Physica-Verlag, 2002. [7] PEDRYCZ W. Granular Computing: Analysis and Design of Intelligent Systems. Boca Raton, USA: CRC Press, 2013. [8] YAO J T. Recent Developments in Granular Computing: A Bibliometrics Study // Proc of the IEEE International Conference on Gra-nular Computing. New York, USA: IEEE, 2008: 74-79. [9] YAO J T, VASILAKOS A V, PEDRYCZ W. Granular Computing: Perspectives and Challenges. IEEE Trans on Cybernetics, 2013, 43(6): 1977-1989. [10] YAO Y Y. Information Granulation and Rough Set Approximation. International Journal of Intelligent Systems, 2001, 16(1): 87-104. [11] 苗夺谦,王国胤,刘 清,等.粒计算: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 the Future Perspectives. Beijing, China: Science Press, 2007.) [12] PAWLAK Z. Rough Sets: Theoretical Aspects of Reasoning about Data. Boston, USA: Kluwer Academic Publishers, 1991. [13] QIAN Y H, LIANG J Y, YAO Y Y, et al. MGRS: A Multi-granulation Rough Set. Information Sciences, 2010, 180(6): 949-970. [14] QIAN Y H, LIANG J Y, DANG C Y. Incomplete Multigranulation Rough Set. IEEE Trans on Systems, Man, and Cybernetics(Systems and Humans), 2010, 40(2): 420-431. [15] 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. [16] WU W Z, LEUNG Y. Theory and Applications of Granular Labeled Partitions in Multi-scale Decision Tables. Information Sciences, 2011, 181(18): 3878-3897. [17] WU W Z, LEUNG Y. Optimal Scale Selection for Multi-scale Decision Tables. International Journal of Approximate Reasoning, 2013, 54(8): 1107-1129. [18] 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. [19] 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. [20] 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.) [21] 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.) [22] 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), 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.) [23] 顾沈明,吴伟志,徐优红.不完备多标记信息系统中粒度研究.南京大学学报(自然科学), 2013, 49(5): 567-573. (GU S M, WU W Z, XU Y H. On Granulation in Incomplete Multi-labeled Information Systems. Journal of Nanjing University(Natural Sciences), 2013, 49(5): 567-573.) [24] 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(C): 398-410. [25] WU W Z, QIAN Y H, LI T J, et al. On Rule Acquisition in Incomplete Multi-scale Decision Tables. Information Sciences, 2016. 378: 282-302. [26] 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.
2016, Vol. 29 
