计算机科学 ›› 2022, Vol. 49 ›› Issue (11A): 211100224-5.doi: 10.11896/jsjkx.211100224
冉虹, 候婷, 贺龙雨, 秦克云
RAN Hong, HOU Ting, HE Long-yu, QIN Ke-yun
摘要： 针对模糊邻域系统,提出了基于一般模糊逻辑算子的模糊粗糙上、下近似算子并探讨了算子的基本性质。然后将邻域系统串行、自反、对称、一元、欧几里得的概念推广到模糊邻域系统。最后研究了当模糊邻域系统是串行、自反、对称、一元、欧几里得时模糊粗糙近似算子的相关代数结构。
中图分类号:
| [1]PAWLAK Z.Rough sets[J].International Journal of Computer &Information Sciences,1982,11(5):341-356. [2]QIAN Y H,LIANG X Y,WANG Q,et al.Local rough set:A solution to rough data analysis in big data[J].International Journal of Approximate Reasoning,2018,97:38-63. [3]KANEIWA K,KUDO Y.A sequential pattern mining algorithm using rough set theory[J].International Journal of Approximate Reasoning,2011,52(6):881-893. [4]WAN J H,CHEN H M,LI T R,et al.Dynamic interaction feature selection based on fuzzy rough set[J].Information Sciences,2021,581:891-911. [5]WANG G Q,LI T R,ZHANG P F,et al.Double-local roughsets for efficient data mining[J].Information Sciences,2021,571:475-498. [6]YAO Y Y.Constructive and algebraic methods of method theory of rough sets[J].Information Sciences,1998,109(1):21-47. [7]YAO Y Y.Relational interpretations of neighborhood operators and approximation operators[J].Information Sciences,1998,111(1):239-259. [8]ZHU W.Topological approaches to covering rough sets[J].Information Sciences,2007,177:1499-1508. [9]BONIKOWSKI Z,BRYNIARSKI E,WY-BRANIEC-SKAR-DOWSKA U.Extensions and in-tentions in the rough set theory[J].Information Sciences,1998,107:149-167. [10]YAO Y Y,YAO B X.Covering based rough set approximations[J].Information Sciences,2012,200:91-107. [11]ZHU P,XIE H Y,WEN Q Y.A unified view of consistent functions[J].Soft Computing,2017,21(9):2189-2199. [12]ZADEH L A.Fuzzy sets[J].Information and Control,1965,8(3):338-353. [13]DOBOIS D,PRADE H.Rough fuzzy sets and fuzzyrough sets[J].International Journal of General System,1990,17:191-209. [14]LIN T Y.Granular computing on binary I:data mining andneighborhood systems[M]//Rough Sets and Knowledge Disco-very.Berlin:Springer,1998:107-121. [15]ZHAO F F,LI L Q.Axiomatization on generalized neighbor-hood system-based rough sets[J].Soft Computing,2018,22(18):6099-6110. [16]FANG J M,CHEN P W.One-to-one corres-pondence between fuzzifying topologies and fuzzy preorders[J].Fuzzy Sets and Systems,2007,158(16):1814-1822. [17]FANG J M,YUE Y L.K.Fan’s theorem in fuzzifying topology[J].Information Sciences,2004,162(3/4):139-146. [18]HERRLICH H,ZHANG D X.Categorical properties of probabilistic convergence spaces[J].Applied Categorical Structures,1998,6(3):495-513. [19]YING M S.A new approach for fuzzy topology(I)[J].Fuzzy Sets System,1991,39(3):495-513. [20]LI L Q,JIN Q,YAO B X,et al.A rough set model based on fuzzifying neighborhood systems [J].Soft Computing,2020,24(8):6085-6099. [21]ZHANG Y L,LI C Q,LIN M L,et al.Relationships betweengeneralized rough sets based on covering and reflexive neighborhood systems[J].Information Sciences,2015,319:56-67. [22]LIAU C J,LIN E B,SYAU Y R.On consistent functions for neighborhood systems[J].International Journal of Approximate Reasoning,2020,121:39-58. [23]SUN X R,LIU H W.On the constructions of t-norms on boun-ded lattices[J].Information Sciences,2021,575:173-184. [24]GERA Z,DOMBI J.Type-2 implications on non-interactive fuzzytruth values[J].Fuzzy Sets and Systems,2008,159:3014-3032. [25]DANA P.Prime,minimal prime and maximal ideals spaces in residuated lattices[J].Fuzzy Sets and Systems,2021,405:47-64. [26]MA Z M,HU B Q.Topological and lattice structures of L-fuzzy rough sets determined by lower and upper sets[J].Information Sciences,2013,218:194-204. |
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