可变直觉模糊多粒度粗糙集模型及其近似分布约简算法
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摘要
为了在多粒度粗糙集模型中对目标概念达到更好的近似逼近效果,首先将直觉模糊粗糙集与多粒度粗糙集结合,提出直觉模糊多粒度粗糙集模型。由于该模型的目标近似存在过于宽松的缺陷,因此通过引入参数的方式对所提模型进行改进,提出一种可变直觉模糊多粒度粗糙集模型,并证明了该模型的有效性,同时基于该模型提出了相应的近似分布约简算法。在仿真实验结果中,所提出的下近似分布约简结果比已提出的模糊多粒度决策理论粗糙集约简和多粒度双量化决策理论粗糙集多了2~4个属性,所提出的上近似分布约简算法比这些算法少了1~5个属性,同时约简结果的近似精度拥有了更为合理且优越的表现。因此,理论和实验结果均验证了所提的可变直觉模糊多粒度粗糙集模型在近似逼近和数据降维方面均具有更高的优越性。
In order to obtain a better approximate approximation effect in multi-granulation rough set model for target conception, an intuitionistic fuzzy rough set and a multi-granulation rough set were combined together and a model of intuitionistic fuzzy multi-granulation rough set was proposed. Due to the loose defect of the target approximation of the model,a variable intuitionistic fuzzy multi-granulation rough set model was proposed by introducing parameters to improve the proposed model, and the validity of this model was proved. In addition, on the basis of this model, a corresponding approximate distribution reduction algorithm was also proposed. The simulation results show that, compared with the existing fuzzy multi-granulation decision-theoretic rough set and multi-granulation double-quantitative decision-theoretic rough set, the proposed lower approximation distribution reduction algorithm has 2 to 4 attributes more than that of them, and the proposed upper approximate distribution reduction algorithm has 1 to 5 attributes less than that of them; meanwhile, the approximation accuracy of reduction results is more reasonable and superior. Theoretical analysis and experimental results verify that the proposed variable intuitionistic fuzzy multi-granulation rough set model has higher superiority in terms of approximating approximation and reducing dimensions.
In order to obtain a better approximate approximation effect in multi-granulation rough set model for target conception, an intuitionistic fuzzy rough set and a multi-granulation rough set were combined together and a model of intuitionistic fuzzy multi-granulation rough set was proposed. Due to the loose defect of the target approximation of the model,a variable intuitionistic fuzzy multi-granulation rough set model was proposed by introducing parameters to improve the proposed model, and the validity of this model was proved. In addition, on the basis of this model, a corresponding approximate distribution reduction algorithm was also proposed. The simulation results show that, compared with the existing fuzzy multi-granulation decision-theoretic rough set and multi-granulation double-quantitative decision-theoretic rough set, the proposed lower approximation distribution reduction algorithm has 2 to 4 attributes more than that of them, and the proposed upper approximate distribution reduction algorithm has 1 to 5 attributes less than that of them; meanwhile, the approximation accuracy of reduction results is more reasonable and superior. Theoretical analysis and experimental results verify that the proposed variable intuitionistic fuzzy multi-granulation rough set model has higher superiority in terms of approximating approximation and reducing dimensions.
引文
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[20]XU W,GUO Y.Generalized multigranulation double-quantitative decision-theoretic rough set[J].Knowledge-Based Systems,2016,105:190-205.
[21]邢清华,刘付显.直觉模糊集隶属度与非隶属度函数的确定方法[J].控制与决策,2009,24(3):393-397.(XING Q H,LIU FX.Method of determining membership and nonmembership function in intuitionistic fuzzy sets[J].Control and Decision,2009,24(3):393-397.)
[2]ZHANG X,MEI C,CHEN D,et al.Feature selection in mixed data:a method using a novel fuzzy rough set-based information entropy[J].Pattern Recognition,2016,56:1-15.
[3]ZENG A,LI T,HU J,et al.Dynamical updating fuzzy rough approximations for hybrid data under the variation of attribute values[J].Information Sciences,2016,378(1):363-388.
[4]张钧波,李天瑞,潘毅,等.云平台下基于粗糙集的并行增量知识更新算法[J].软件学报,2015,26(5):1064-1078.(ZHANG JB,LI T R,PAN Y,et al.Parallel and incremental algorithm for knowledge update based on rough sets in cloud platform[J].Journal of Software,2015,26(5):1064-1078.)
[5]ZIARKO W.Variable precision rough set model[J].Journal of Computer and System Sciences,1993,46(1):39-59.
[6]DUBOID D,PRADE H.Rough fuzzy sets and fuzzy rough sets[J].International Journal of General Systems,1990,17(2/3):191-209.
[7]张植明,白云超,田景峰.基于覆盖的直觉模糊粗糙集[J].控制与决策,2010,25(9):1369-1373.(ZHANG Z M,BAI Y C,TIAN J F.Intuitionistic fuzzy rough sets based on intuitionistic fuzzy coverings[J].Control and Decision,2010,25(9):1369-1373.)
[8]LIN T Y.Rough sets,neighborhood systems and approximation[J].World Journal of Surgery,1986,10(2):189-94.
[9]QIAN Y,LIANG J,YAO Y,et al.MGRS:a multi-granulation rough set[J].Information Sciences:an International Journal,2010,180(6):949-970.
[10]QIAN Y,LIANG J,DANG C.Incomplete multigranulation rough set[J].IEEE Transactions on Systems,Man and CyberneticsPart A:Systems and Humans,2010,40(2):420-431.
[11]谭安辉,李进金,吴伟志.多粒度粗糙集和覆盖粗糙集间的近似与约简关系[J].模式识别与人工智能,2016,29(8):691-697.(TAN A H,LI J J,WU W Z.Approximation and reduction relationships between multi-granulation rough sets and covering rough sets[J].Pattern Recognition and Artificial Intelligence,2016,29(8):691-697)
[12]张明,唐振民,徐维艳,等.可变多粒度粗糙集模型[J].模式识别与人工智能,2012,25(4):709-720.(ZHANG M,TANG ZM,XU W Y,et al.Variable multigranulation rough set model[J].Pattern Recognition and Artificial Intelligence,2012,25(4):709-720.)
[13]ATANASSOV K T.Intuitionistic fuzzy sets[J].Fuzzy Sets&Systems,1986,20(1):87-96.
[14]ZHANG X,CHEN D,TSANG E C C.Generalized dominance rough set models for the dominance intuitionistic fuzzy information systems[J].Information Sciences,2017,378:1-25.
[15]LIU Y,LIN Y.Intuitionistic fuzzy rough set model based on conflict distance and applications[J].Expert Systems,2015,31:266-273.
[16]HUANG B,GUO C-X,LI H-X,et al.Hierarchical structures and uncertainty measures for intuitionistic fuzzy approximation space[J].Information Sciences,2016,336:92-114.
[17]姚晟,徐风,赵鹏,等.基于邻域量化容差关系粗糙集模型的特征选择算法[J].模式识别与人工智能,2017,30(5):416-428.(YAO S,XU F,ZHAO P,et al.Feature selection algorithm based on neighborhood valued tolerance relation rough set model[J].Pattern Recognition and Artificial Intelligence,2017,30(5):416-428.)
[18]马福民,陈静雯,张腾飞.基于双重粒化准则的邻域多粒度粗集快速约简算法[J].控制与决策,2017,32(6):1121-1127.(MAF M,CHEN J W,ZHANG T F.Quick attribute reduction algorithm for neighborhood multi-granulation rough set based on double granulate criterion[J].Control and Decision,2017,32(6):1121-1127.)
[19]LIN G,LIANG J,QIAN Y,et al.A fuzzy multigranulation decision-theoretic approach to multi-source fuzzy information systems[J].Knowledge-Based Systems,2016,91:102-113.
[20]XU W,GUO Y.Generalized multigranulation double-quantitative decision-theoretic rough set[J].Knowledge-Based Systems,2016,105:190-205.
[21]邢清华,刘付显.直觉模糊集隶属度与非隶属度函数的确定方法[J].控制与决策,2009,24(3):393-397.(XING Q H,LIU FX.Method of determining membership and nonmembership function in intuitionistic fuzzy sets[J].Control and Decision,2009,24(3):393-397.)