基于剩余格的模糊粗糙集的拓扑性质

doi:10.11896/jsjkx.210200123

摘要/Abstract

摘要： 研究了基于剩余格的L-模糊粗糙集模型的拓扑结构,给出了由模糊蕴涵确定的下近似算子诱导的L-模糊拓扑并讨论了它的基本性质。其中的知识为一般L-模糊关系,无需假设其自反性及强串行性。借助L-模糊关系的传递闭包构造了相应的L-模糊拓扑的内部算子及闭包算子。研究了不同的L-模糊关系确定的下近似算子诱导的L-模糊拓扑空间之间的关系,并借助相应的拓扑提出了一种L-模糊关系分类方法。

关键词: 近似算子, 模糊粗糙集, 模糊关系, 模糊拓扑, 剩余格

Abstract: This paper is devoted to the study of the topological structure of L-fuzzy rough sets based on residuated lattices.The L-fuzzy topologies induced by the lower approximation operators determined by fuzzy implication operators are presented and its basic properties being discussed.The knowledge of the L-fuzzy approximation space is a general L-fuzzy relation,and there is no need to assume its reflexivity and strong seriality.Based on the transitive closures of the L-fuzzy relations,the interior operators and closure operators of the corresponding L-fuzzy topologies are constructed.The relationships among L-fuzzy topologies induced by lower approximation operators corresponding to different L-fuzzy relations are investigated,and a classification method for L-fuzzy relations is presented by using related topologies.

Key words: Approximation operator, Fuzzy relation, Fuzzy rough sets, Fuzzy topology, Residuated lattices

中图分类号:

TP182

许思雨, 秦克云. 基于剩余格的模糊粗糙集的拓扑性质[J]. 计算机科学, 2022, 49(6A): 140-143. https://doi.org/10.11896/jsjkx.210200123

XU Si-yu, QIN Ke-yun. Topological Properties of Fuzzy Rough Sets Based on Residuated Lattices[J]. Computer Science, 2022, 49(6A): 140-143. https://doi.org/10.11896/jsjkx.210200123

参考文献

[1] PAWLAK Z.Rough Sets[J].Journal of Computer and Information Science,1982,11(5):341-356.
[2] PAWLAK Z.Rough Sets Theoretical Aspects of ReasoningAbout Data [M].Kluwer Academic Publishers,Dordrecht & Boston,1991.
[3] ZHANG W X.Rough Set Theory and Method [M].Beijing:Science Press,2001.
[4] WANG C Y,QI Y,SHAO M,et al.A fitting model for feature selection with fuzzy rough sets[J].IEEE Transaction on Fuzzy Systems,2017,25(4):741-753.
[5] ZHAN J,MASOOD MALIK H,AKRAM M.Novel decision-making algorithms based on intuitionistic fuzzy rough environment[J].International Journal of Machine Learning & Cybernetics,2018,8(6):1459-1485.
[6] DUBOIS D,PRADE H.Rough fuzzy sets and fuzzy rough sets[J].International Journal of General Systems,1990,17(2/3):191-209.
[7] MORSI N N,YAKOUT M M.Axiomatics for fuzzy rough sets[J].Fuzzy Sets and Systems,1998,100(1):327-342.
[8] RADZIKOWSKA A M,KERRE E E.A comparative study offuzzy rough sets[J].Fuzzy Sets and Systems,2002,126(2):137-155.
[9] YANG B,HU B Q.A fuzzy covering-based rough set model and its generalization over fuzzy lattice[J].Information Sciences,2016,367-368:463-486.
[10] YANG B,HU B Q.On some types of fuzzy covering-basedrough sets[J].Fuzzy Sets and Systems,2017,312:36-65.
[11] ZHAN J M,ZHANG X H,YAO Y Y.Covering based multigranulation fuzzy rough sets and corresponding applications[J].Artificial Intelligence Review,2020,53(2):1093-1126.
[12] ZHANG X H,WANG J Q.Fuzzy β-covering approximationspaces[J].International Journal of Approximate Reasoning,2020,126:27-47.
[13] WANG C,WANG Y,SHAO M,et al.Fuzzy rough attribute reduction for categorical data[J].IEEE Transactions on Fuzzy Systems,2020,28(5):818-830.
[14] LIU G L,ZHENG H,ZOU J Y.Relations arising from coverings and their topological structures[J].International Journal Approximate Reasoning,2017,80:348-358.
[15] ZIARKO W.Variable precision rough set model[J].Journal of Computer and System Sciences,1993,46:39-59.
[16] MIESZKOWICZ-ROLKA A,ROLKA L.Variable precisionfuzzy rough sets[J].Lecture Notes in Computer Sciences,2004,3100:144-160.
[17] ZHAO S,TSANG E C C,CHEN D.The model of fuzzy variable precision rough sets[J].IEEE Transactions on Fuzzy Systems,2009,17(2):451-467.
[18] RADZIKOWSKA A M,KERRE E E.Fuzzy rough sets based on residuated lattices[J].Lecture Notes in Computer Sciences,2004,3135:278-296.
[19] WANG C Y,ZHANG X G,WU Y H.New results on singleaxioms for L-fuzzy rough approximation operators[J].Fuzzy Sets and Systems,2020,380:131-149.
[20] SHE Y H,WANG G J.An axiomatic approach of fuzzy rough sets based on residuated lattices[J].Computers and Mathe-matics with Applications,2009,58(1):189-201.
[21] YU H,ZHAN W.On the topological properties of generalized rough sets[J].Information Sciences,2014,263:141-152.
[22] WU H S,LIU G L.The relationships between topologies and generalized rough sets[J].International Journal of Approximate Reasoning,2020,119:313-324.
[23] YANG L Y,XU L S.Topological properties of generalized approximation spaces[J].Information Sciences,2011,181:3570-3580.
[24] QIN K Y,YANG J L,PEI Z.Generalized rough sets based on transitive and reflexive relations[J].Information Sciences,2008,178:4138-4141.
[25] WANG C Y.Topological characterizations of generalized fuzzy rough sets[J].Fuzzy Sets and Systems,2017,312:109-125.
[26] QIN K Y,ZHENG P.On the topological properties of fuzzyrough sets[J].Fuzzy Sets and Systems,2004,151(3):601-613.
[27] WANG C Y.Topological structures of L-fuzzy rough sets and similarity sets of L-fuzzy relations[J].International Journal of Approximate Reasoning,2017,83:160-175.
[28] MA Z M,HU B Q.Topological and lattices structures of L-fuzzyrough sets determined by lower and upper sets[J].Information Sciences,2013,218:194-204.
[29] HAO J,LI Q G.The relationship between L-fuzzy rough set and L-topology[J].Fuzzy Sets Systems,2011,178(1):74-83.
[30] BĔLOHLÁVEK R.Some properties of residuated lattices[J].Czechoslovak Mathematical Journal,2003,53(1):161-171.
[31] PEI D W.The characterization of residuated lattices and regular residuated lattices[J].Acta-Mathematica Sinica,2002,45:271-278.
[32] GOGUEN J A.L-fuzzy sets[J].Journal of Mathematical Ana-lysis and Applications,1967,18:145-174.
[33] WANG Z D,WANG Y,TANG K M.Some properties of L-fuzzy approximation spaces based on bounded integral residuated lattices[J].Information Sciences,2014,278:110-126.

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