Due to the complexity and uncertainty of the physical world, as well as the limitation of human ability to comprehend, it is very difficult for the traditional rough set to effectively deal with the real decision making information system consisted of a lot of preference information, grey information and noise data. In view of this, the thought and method of the grey system is used to construct the variable precision rough set model based on dominance grey degree in the paper. The method, to begin with, based on the new results of the grey number and grey degree, the concept of dominance grey degree is proposed to determine the dominance relationship between objects, so that it is used to substitute for the indiscernibility relationship of variable precision rough set, and then the variable precision rough set model based on dominance grey degree is established, and then its natures are discussed, finally an examples is used to validate the effectiveness and applicability of the model. The result shows that the proposed model has a certain tolerant ability by adjusting the threshold parameter, and then it can realize the scientific decision-making by effectively extracting decision rules.
[1] Pawlak Z. Rough sets[J]. International Journal of Information and Computer Sciences, 1982, 49(5):415-422.
[2] Pawlak Z, Skowron A. Rough sets:Some extensions[J]. Information Sciences, 2007, 177(1):28-40.
[3] 刘勇, 王育红, 钱吴永. 基于马尔科夫链的动态冲突分析模型[J]. 中国管理科学, 2015, 23(SI):325-332.
[4] Greco S, Matarazzo B, Slowinski R. Rough approximation of a preference relation by dominance relations[J]. European Journal of Operational Research, 1999,117(1):63-83.
[5] Greco S, Matarazzo B, Slowinski R, et al. An algorithm for induction of decision rules consistent with dominance principle[J]. Lecture Notes in Artificial Intelligence, 2001,2005:304-313.
[6] Yao Y Y, Sai Ying. Mining ordering rules using rough set theory[J]. Bulletin of International Rough Set Society, 2001,5(1-2):99-106.
[7] Greco S, Matarazzo B, Slowinski R. Rough sets methodology for sorting problems in preference of multiple attributes and criteria[J]. European Journal of Operational Research, 2002, 138(2):247-259.
[8] Greco S, Matarazzo B, Slowinski R. Rough approximation by dominance relations[J]. International Journal of Intelligent systems, 2002, 17(2):153-171.
[9] Sun Bingzhen, Gong Zengtai, Chen Degang. Rough set theory for interval-valued fuzzy information systems[J]. Information Sciences, 2008, 178(8):1968-1985.
[10] 骆公志, 杨晓江.变精度优势粗糙集属性约简择优算法[J]. 中国管理科学, 2009,17(2):169-175.
[11] 翟永健, 张宏. 不完备信息系统中的优势关系多粒度粗糙集[J]. 南京理工大学学报, 2012, 36(1):66-72.
[12] Yang Xibei, Yang Jingyu, Wu Chen, et al. Dominance-based rough set approach and knowledge reductions in incomplete ordered information system[J]. Information Sciences, 2008, 178(4):1219-1234.
[13] Yang Xibei, Yu Dongjun, Yang Jingyu, et al. Dominance-based rough set approach to incomplete interval-valued information system[J]. Data & Knowledge engineering, 2009, 68(11):1331-1347.
[14] Qian Yuhua, Liang Jiye, Dang Chuangyin Interval ordered information systems[J]. Computer and Mathematics with Applications, 2008, 56(8):1994-2009.
[15] Qian Yuhua, Liang Jiye, Song Peng, et al. On dominance relations in disjunctive set-valued ordered information systems[J]. International Journal of Information Technology & Decision Making, 2010, 9(1):9-33.
[16] Qian Yuhua, Liang Jiye, Song peng, el ta. Evaluation of the decision performance of the decision rule set from an ordered decision table[J]. Knowledge-Based Systems, 2012,36(12):39-50.
[17] 施玉杰, 杨宏志, 徐久成. α-先验概率优势关系下的粗糙集模型研究[J]. 南京大学学报(自然科学), 2016,(5):899-908.
[18] Song Peng, Liang Jiye, Qian Yuhua. A two-grade approach to ranking interval data[J]. Knowledge-Based Systems, 2012, 27:234-244.
[19] 李佳, 梁吉业, 庞天杰. 一种基于优势粗糙集的多属性决策排序方法[J]. 南京大学学报(自然科学), 2016,(5):844-849
[20] Hu Qinghua, Yu Daren, Guo Maozu. Fuzzy preference based rough sets[J]. Information Sciences, 2010, 180(10):2003-2022.
[21] 江效尧, 黄兵. 优势模糊区间目标粗糙集模型的群决策规则获取及应用[J]. 南京大学学报(自然科学), 2012,48(4):429-434.
[22] 黄兵, 魏大宽. 基于距离的直觉模糊粗糙集模型及应用[J]. 系统工程理论与实践, 2011,3(17):1356-1363.
[23] Huang Bing, Li Huaxiong, Wei Dakuan. Dominance-based rough set model in intuitionistic fuzzy information systems[J]. Knowledge-Based Systems, 2012, 28:115-123.
[24] Huang Bing, Zhuang Yuliang, Li Huaxiong, et al. A dominance intuitionistic fuzzy-rough set approach and its applications[J]. Applied Mathematical Modeling, 2013, 37(12):7128-7141.
[25] Liu Yong, Li Lin. Intuitionistic Fuzzy Rough Set Model Based on Conflict Distance and Application[J]. Applied Soft Computing, 2015,(31):266-273.
[26] Liu Yong, Lin Yi, Zhao Huanhuan. Variable precision intuitionistic fuzzy rough set model and application based on conflict distance[J]. Expert Systems, 2015:32(2):220-227.
[27] Liu Sifeng, Lin Yong. Grey systems theory and applications[M]. Berlin Heidelberg:Springer-Verlag, 2011:169-190.
[28] 谢乃明, 刘思峰. 考虑概率分布的灰数排序方法[J]. 系统工程理论与实践, 2009, 29(4):169-175.
[29] Liu Yong, Forrest J, Xie Naiming. Ranking grey numbers based on dominance grey degrees[J]. Journal of Systems Engineering and Electronics, 2014,25(4):618-626.
[30] 菅利荣, 达庆利, 陈伟达. 基于粗糙集的不一致信息系统规则获取方法[J]. 中国管理科学, 2003,11(4):91-95.
[31] 鲍新中, 张建斌, 刘澄. 基于粗糙集条件信息熵的权重确定方法[J]. 中国管理科学, 2009, 17(3):131-135.
[32] 潘郁, 菅利荣, 达庆利. 多标准决策表中发现概率规则的变精度粗糙集方法[J]. 中国管理科学, 2005,13(1):95-100.
[33] 刘勇, 菅利荣. 杂合灰色聚类与变精度粗糙模糊集的概率决策方法及应用[J]. 管理工程学报, 2013, 27(3):110-117.
