Rough set theory is a useful method which can effectively deal with imprecise, uncertain information in the information system. Granular computing is a new field of artificial intelligence, multiple granulation is a core concept of granular computing. Multi-granulation rough set is a new research direction of rough set theory, which combined with rough set theory and the idea of granular computing. In the view of granular computing, an equivalence relation is a granulation which composed of several attributes, and a partition of the universe based on a equivalence relation can be regarded as a granularity space. Hence in the multi-granulation rough set, based on different equivalence relations, the universe can be divided into several granularity spaces and the approximation of target concept can be carried out from the multiple granularity spaces. Granularity reduction is one of the important tasks of the multi-granulation rough set research. It is the deletion of unnecessary granularity under the premise of no affection to the target concept or decision rules. Information quantity is introduced into the lower-approximate distribution reduction of pessimistic multi-granulation rough set and the information quantity of a granularity has been defined in the lower-approximate distribution reduction of pessimistic multi-granulation rough set. Then, based on the information quantity, the importance of a granularity has also been defined. A heuristic granularity reduction algorithm of pessimistic multi-granulation rough set is presented. The experimental results show the validity of the algorithm, which provide a theoretical basis for the granularity reduction of multi-granulation rough sets
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References
[1] Pawlak Z. Rough set. International Journal of Computer and Information Science,1982, 11: 341~356.
[2] Lin T Y. Granular Computer on binary relations Ⅱ: Rough set representations and belief functions. Rough Sets and Knowledge Discovery,1998:122~140.
[3] Qian Y H, Liang J Y. Rough set method based on multigranulations. In: Proceeding of the 5th IEEE International Conference on Cognitive Informatics. IEEE Computer Society, Beijing, China, 2006, 297~304.
[4] Qian Y H, Liang J Y, Yao Y Y, et al. MGRS: A multigranulation rough set. Information Sciences, 2010, 180:949~970.
[5] Qian Y H, Liang J Y, Wei W. Pessimistic rough decision. In: The 2nd International Workshop on Rough Sets Theory. IEEE Computer Society, Zhoushan, China, 2010, 440~449.
[6] 张 明, 唐振民, 徐维艳等.可变多粒度粗糙集模型. 模式识别与人工智能, 2012, 25(4): 709~720.
[7] Qian Y H, Liang J Y, Dang C Y. Incomplete multi-granulation rough set. IEEE Transactions on Systems, Man and Cybernetics, Part A, 2010, 40(2): 420~431.
[8] 王丽娟, 杨习贝, 杨静宇等.一种新的不完备多粒度粗糙集. 南京大学学报(自然科学), 2012, 48(7): 436~444.
[9] 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.
[10] 翟永健, 张 宏. 变精度多粒度粗糙集的约简研究. 金陵科技学院学报, 2013, 29(4):1~8.
[11] 李顺勇, 钱宇华. 基于多粒度粗糙决策下的属性约简算法. 中北大学学报, 2013, 34(5):589~592.
[12] 桑妍丽, 钱宇华.一种悲观多粒度粗糙集中的粒度约简算法. 模式识别与人工智能, 2012, 25(3): 361~366.
[13] 梁吉业, 曲开社, 徐宗本.信息系统的属性约简. 系统工程理论与实践, 2001, (12): 76~80.
[14] 张文修, 梁 怡. 不确定性推理原理. 西安: 西安交通大学出版社, 1996, 299.
[15] 黄 兵, 周献中, 张蓉蓉.基于信息量的不完备信息系统属性约简. 系统工程理论与实践, 2005,(4): 55~60.
[16] 马建敏, 张文修, 朱朝晖.基于信息量的序信息系统的属性约简. 系统工程理论与实践, 2010, 30(9): 1679~1683.
[17] 马建敏, 张文修. 基于信息量的集值信息系统的属性约简. 模糊系统与数学, 2013, 27(2): 177~182.
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Footnotes
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