Model of Multi-granulation Neighborhood Rough Intuitionistic Fuzzy Sets
XUE Zhan′ao, SI Xiaomeng, YUAN Yilin, XIN Xianwei
College of Computer and Information Engineering, Henan Normal University, Xinxiang 453007 Henan Engineering Laboratory of Intelligence Business and Internet of Things, Henan Normal University, Xinxiang 453007
Abstract:The combination of the multi-granulation neighborhood rough set and the intuitionistic fuzzy set is further researched in this paper. Firstly, the concepts of the intuitionistic fuzzy covering-based rough membership and non-membership are defined for dealing with the heterogeneous data including categorical attributes and numerical attributes. Secondly, a multi-granulation neighborhood rough intuitionistic fuzzy set model is established based on different attribute set sequences and different neighborhood radii. Then, the properties of multi-granulation neighborhood rough intuitionistic fuzzy set are discussed. Next, the approximate sets of the optimistic and pessimistic multi-granulation neighborhood rough intuitionistic fuzzy sets are constructed and their properties are discussed. Finally, these models are illustrated with examples. Example analysis shows the models can handle the heterogeneous data including categorical attributes and numerical attributes more accurately.
[1] PAWLAK Z. Rough Sets. International Journal of Computer and Information Sciences, 1982, 11(5): 341-356. [2] LIN T Y, HUANG K J, LIU Q, et al. Rough Sets, Neighborhood Systems and Approximation // Proc of the 5th International Sympo-sium on Methodologies of Intelligent Systems. London, UK: Springer, 1990: 130-141. [3] 杨习贝,杨静宇.邻域系统粗糙集模型.南京理工大学学报(自然科学版), 2012, 36(2): 291-295. (YANG X B, YANG J Y. Rough Set Model Based on Neighborhood System. Journal of Nanjing University of Science and Technology(Natural Science), 2012, 36(2): 291-295.) [4] QIAN Y H, LIANG J Y, YAO Y Y, et al. MGRS: A Multi-granulation Rough Set. Information Sciences, 2010, 180(6): 949-970. [5] QIAN Y H, LIANG J Y, DANG C Y. Incomplete Multi-granulations Rough Set. IEEE Transactions on Systems, Man and Cybernetics(Systems and Humans), 2010, 40(2): 420-431. [6] QIAN Y H, LIANG J Y, WEI W. Pessimistic Rough Decision. Journal of Zhejiang Ocean University(Natural Science), 2010, 29(5): 440-449. [7] 张 明,程 科,杨习贝,等.基于加权粒度的多粒度粗糙集.控制与决策, 2015, 30(2): 222-228. (ZHANG M, CHENG K, YANG X B, et al. Multigranulation Rough Set Based on Weighted Granulations. Control and Decision, 2015, 30(2): 222-228.) [8] 马 睿,刘文奇.基于集值信息系统的多粒度粗糙集.系统工程与电子技术, 2014, 36(5): 920-925. (MA R, LIU W Q. Multi-granulation Rough Set Model Based on Set-Valued Information System. Systems Engineering and Electro-nics, 2014, 36(5): 920-925.) [9] XU W H, WANG Q R, ZHANG X.T. Multi-granulation Rough Sets Based on Tolerance Relations. Soft Computing, 2013, 17(7): 1241-1252. [10] 徐 怡,杨宏健,纪 霞.基于双重粒化准则的邻域多粒度粗糙集模型.控制与决策, 2015, 30(8): 1469-1478. (XU Y, YANG H J, JI X. Neighborhood Multi-granulation Rough Set Model Based on Double Granulate Criterion. Control and Decision, 2015, 30(8): 1469-1478.) [11] ATANASSOV K T. Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems, 1986, 20(1): 87-96. [12] ATANASSOV K T. New Operations Defined over the Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems, 1994, 61(2): 137-142. [13] ATANASSOV K T. More on Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems, 1989, 33(1): 37-45. [14] WU X D, ZHU X Q, WU G Q, et al. Data Mining with Big Data. IEEE Transactions on Knowledge and Data Engineering, 2014, 26(1): 97-107. [15] PETERS G, CRESPO F, LINGRAS P, et al. Soft Clustering-Fuzzy and Rough Approaches and Their Extensions and Derivatives. International Journal of Approximate Reasoning, 2013, 54(2): 307-322. [16] DAI J H, TIAN H W. Fuzzy Rough Set Model for Set-Valued Data. Fuzzy Sets and Systems, 2013, 229: 54-68. [17] BONIKOWSKI Z, BRYNIARSKI E, WYBRANIEC-SKARDOWSKA U. Extensions and Intentions in the Rough Set Theory. Information Sciences, 1998, 107(1/2/3/4): 149-167. [18] PAWLAK Z. Rough Sets: Theoretical Aspects of Reasoning about Data. Boston, USA: Kluwer Academic Publishers, 1991.
[19] 薛占熬,司小朦,朱泰隆,等.覆盖粗糙直觉模糊集模型的研究.计算机科学, 2016, 43(1): 44-48, 68. (XUE Z A, SI X M, ZHU T L, et al. On the Model of Covering-Based Rough Intuitionistic Fuzzy Sets. Computer Science, 2016, 43(1): 44-48, 68.) [20] 郭郁婷,李进金,李克典,等.多粒度覆盖粗糙直觉模糊集模型.南京大学学报(自然科学版), 2015, 51(2): 438-446. (GUO Y T, LI J J, LI K D, et al. Multi-granulation Covering Rough-Intuitionistic Fuzzy Set Model. Journal of Nanjing University (Natural Science), 2015, 51(2): 438-446.)