基于优势关系的程度粗糙直觉模糊集模型研究
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摘要
针对经典粗糙直觉模糊集理论仅考虑了集合中的最小/最大隶属度与非隶属度,而忽略了介于二者之间的隶属度与非隶属度的问题,从程度粗糙集的角度对其进行了分析研究。首先,将程度粗糙集引入到经典粗糙直觉模糊集模型中,定义了μ′(y)和ν′(y),将其与最小/最大之间的隶属度与非隶属度的值比较。然后,构建新的下、上近似,提出四个模型,即基于优势关系的Ⅰ型、Ⅱ型程度粗糙直觉模糊集模型和基于优势关系的Ⅰ型、Ⅱ型双论域程度粗糙直觉模糊集模型,讨论这些模型的相关性质。这些模型的边界域缩小了,也降低了模糊熵值。最后,通过实例验证了模型的有效性。
For the classical rough intuitionistic fuzzy set theory, only the minimum/maximum of membership and non-membership degree of the set are considered, while the membership and non-membership degree between the minimum and maximum of the set are neglected. Therefore, this problem is analyzed from the perspective of graded rough set in this paper. Firstly, graded rough set is introduced into the classical rough intuitionistic fuzzy set model,μ′(y) and ν′(y) are defined compared with the membership and non-membership degree between the minimum and maximum of the set. Then, the new lower and upper approximations are constructed. And four models are proposed.They are Type-Ⅰ, Type-Ⅱ graded rough intuitionistic fuzzy set models based on dominance relation and Type-Ⅰ, Type-Ⅱ two-universe graded rough intuitionistic fuzzy set models based on dominance relation. The related properties of these models are also discussed. Moreover, the boundaries of these models are narrowed. The value of fuzzy entropy is also reduced. Finally, the validity of these models is verified by examples.
For the classical rough intuitionistic fuzzy set theory, only the minimum/maximum of membership and non-membership degree of the set are considered, while the membership and non-membership degree between the minimum and maximum of the set are neglected. Therefore, this problem is analyzed from the perspective of graded rough set in this paper. Firstly, graded rough set is introduced into the classical rough intuitionistic fuzzy set model,μ′(y) and ν′(y) are defined compared with the membership and non-membership degree between the minimum and maximum of the set. Then, the new lower and upper approximations are constructed. And four models are proposed.They are Type-Ⅰ, Type-Ⅱ graded rough intuitionistic fuzzy set models based on dominance relation and Type-Ⅰ, Type-Ⅱ two-universe graded rough intuitionistic fuzzy set models based on dominance relation. The related properties of these models are also discussed. Moreover, the boundaries of these models are narrowed. The value of fuzzy entropy is also reduced. Finally, the validity of these models is verified by examples.
引文
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[14]汪小燕,沈家兰,申元霞,等.不完备加权程度多粒度粗糙集及粒度约简[J].小型微型计算机系统,2017,38(10):2286-2290.
[15]阎瑞霞,郑建国,翟育明.双论域粗糙集的不确定性度量[J].上海交通大学学报,2011,45(12):1841-1845.
[19]温雪俊.直觉模糊序信息系统的不确定性度量[D].临汾:山西师范大学,2015.
[22]张文修,吴伟志,梁吉业.粗糙集理论与方法[M].北京:科学出版社,2001.
[23]张文修,梁怡,吴伟志.信息系统与知识发现[M].北京:科学出版社,2003.
[2]Yao Y Y,Lin T Y.Generalization of rough sets using modal logics[J].Intelligent Automation&Soft Computing,1996,2(2):103-119.
[3]Zhang Y L,Lei Y B,Li C Q.On a type of rough intuitionistic fuzzy sets and its topological structure[J].Journal of Computational Analysis&Applications,2016,20(3):590-598.
[4]Xue Z A,Si X M,Xue T Y,et al.Multi-granulation covering rough intuitionistic fuzzy sets[J].Journal of Intelligent&Fuzzy Systems,2017,32(1):899-911.
[5]Xue Z A,Wang N,Si X M,et al.Research on multigranularity rough intuitionistic fuzzy cut sets[J].Journal of Henan Normal University(Natural Science Edition),2016,44(5):131-139.
[6]Dai J H,Han H F,Zhang X H,et al.Catoptrical rough set model on two universes using granule-based definition and its variable precision extensions[J].Information Sciences,2017,390:70-81.
[7]Liu H,Zhu F,Lin Z Q.Matrix representation of rough sets based on two universes[J].Computer Engineering and Applications,2015,51(24):154-158.
[8]Lu J,Li D Y,Zhai Y H,et al.Granular structure of type-2fuzzy rough sets over two universes[J].Symmetry,2017,9(11):284.
[9]Luo S Q,Xu W H.Rough atanassov.s intuitionistic fuzzy sets model over two universes and its applications[J].The Scientific World Journal,2014,2014:1-13.
[10]Sun B Z,Ma W M,Qian Y H.Multigranulation fuzzy rough set over two universes and its application to decision making[J].Knowledge-Based Systems,2017,123:61-74.
[11]Zhang X Y,Xie S C,Mo Z W.Graded rough sets[J].Journal of Sichuan Normal University(Natural Science Edition),2010,33(1):12-16.
[12]Huang B,Guo C X,Li H X,et al.An intuitionistic fuzzy graded covering rough set[J].Knowledge-Based Systems,2016,107:155-178.
[13]Shen J L,Wang X Y,Shen Y X.Variable grade multigranulation rough set[J].Journal of Chinese Computer System,2016,37(5):1012-1016.
[14]Wang X Y,Shen J L,Shen Y X,et al.Incomplete weighted graded multi-granulation rough set and granular reduction[J].Journal of Chinese Computer Systems,2017,38(10):2286-2290.
[15]Yan R X,Zheng J G,Zhai Y M.Uncertainty measures of rough set over dual-universes[J].Journal of Shanghai Jiao Tong University,2011,45(12):1841-1845.
[16]Huang B,Li H X,Wei D K.Dominance-based rough set model in intuitionistic fuzzy information systems[J].KnowledgeBased Systems,2012,28:115-123.
[17]Rizvi S,Naqvi H J,Nadeem D.Rough intuitionistic fuzzy sets[C]//Proceedings of the 6th Joint Conference on Information Sciences,Research Triangle Park,Mar 8-13,2002.Durham:Association for Intelligent Machinery,2002,6:101-104.
[18]Radzikowska A M.Rough approximation operations based on IF sets[C]//LNCS 4029:Proceedings of the 8th International Conference on Artificial Intelligence and Soft Computing,Zakopane,Jun 25-29,2006.Berlin,Heidelberg:Springer,2006:528-537.
[19]Wen X J.Uncertainty measurement for intuitionistic fuzzy ordered information system[D].Linfen:Shanxi Normal University,2015.
[20]Liu G L.Rough set theory based on two universal sets and its applications[J].Knowledge-Based Systems,2010,23(2):110-115.
[21]Pei D W,Xu Z B.Rough set models on two universes[J].International Journal of General Systems,2004,33(5):569-581.
[22]Zhang W X,Wu W Z,Liang J Y.Rough set theory and method[M].Beijing:Science Press,2001.
[23]Zhang W X,Liang Y,Wu W Z.Information systems and knowledge discovery[M].Beijing:Science Press,2003.
[24]Wang H Q,Jiang Y H,Jiang X M,et al.Automatic vessel segmentation on fundus images using vessel filtering and fuzzy entropy[J].Soft Computing,2017,22(5):1501-1509.
[5]薛占熬,王楠,司小朦,等.多粒度粗糙直觉模糊集截集的研究[J].河南师范大学学报(自然科学版),2016,44(5):131-139.
[7]刘慧,祝峰,林姿琼.双论域粗糙集的矩阵表示[J].计算机工程与应用,2015,51(24):154-158.
[11]张贤勇,谢寿才,莫智文.程度粗糙集[J].四川师范大学学报(自然科学版),2010,33(1):12-16.
[13]沈家兰,汪小燕,申元霞.可变程度多粒度粗糙集[J].小型微型计算机系统,2016,37(5):1012-1016.
[14]汪小燕,沈家兰,申元霞,等.不完备加权程度多粒度粗糙集及粒度约简[J].小型微型计算机系统,2017,38(10):2286-2290.
[15]阎瑞霞,郑建国,翟育明.双论域粗糙集的不确定性度量[J].上海交通大学学报,2011,45(12):1841-1845.
[19]温雪俊.直觉模糊序信息系统的不确定性度量[D].临汾:山西师范大学,2015.
[22]张文修,吴伟志,梁吉业.粗糙集理论与方法[M].北京:科学出版社,2001.
[23]张文修,梁怡,吴伟志.信息系统与知识发现[M].北京:科学出版社,2003.