Computer Science ›› 2023, Vol. 50 ›› Issue (11A): 220800051-6.doi: 10.11896/jsjkx.220800051

• Big Data & Data Science • Previous Articles     Next Articles

Algebraic Properties of Rough Set Model Based on Neighborhood System

LIU Yinshan, WANG Hao, QIN Keyun   

  1. School of Mathematics,Southwest Jiaotong University,Chengdu 611756,China
  • Published:2023-11-09
  • About author:LIU Yinshan,born in 1998,postgra-duate.His main research interests include rough set theory,formal concept analysis and fuzzy logic.
    QIN Keyun,born in 1962,Ph.D,professor,Ph.D supervisor.His main research interests include rough set theory,formal concept analysis and fuzzy logic.
  • Supported by:
    National Natural Science Foundation of China(61976130).

Abstract: The rough set model based on neighborhood system is an extension of generalized rough set model based on general binary relation and covering rough set model.In general,different neighborhood systems may generate the same approximation operator.This paper gives the conditions for different neighborhood systems to generate the same approximation operator,and then proposes a method to classify the neighborhood systems based on the approximation operator.In addition,the axiomatic description method of rough approximation operator based on neighborhood system is given.

Key words: Neighborhood system approximation operator, Neighborhood system classification, Axiomatic method

CLC Number: 

  • TP182
[1]PAWLAK Z.Rough sets[J].International Journal of Computer &Information Sciences,1982,11(5):341-356.
[2]WANG G Y,FU S,YANG J,et al.A Review of Research on Multi-Granularity Cognition Based Intelligent Computing[J].Chinese Journal of Computers,2022 45(6):1161-1175.
[3]YAO Y Y,LIN T Y.Generalization of rough sets using modal logics[J].Intelligent Automation & Soft Computing,1996,2(2):103-119.
[4]ZAKOWSKI W.Approximations in the space(u,π)[J].Demonstratio Mathematica,1983,16(3):761-770.
[5]DUBOIS D,PRADE H.Rough fuzzy sets and fuzzy rough sets[J].International Journal of General System,1990,17(2/3):191-209.
[6]LiN T Y,HUANG K J,LIU Q,et al.Rough sets,neighborhood systems and approximation[C]//Proceedings of the Fifth International Symposium on Methodologies of Intelligent Systems.1990:130-141.
[7]LIN T Y.Topological and fuzzy rough sets[M]//Intelligent Decision Support.Springer,Dordrecht,1992:287-304.
[8]LIN T Y.Neighborhood systems-A qualitative theory for fuzzy and rough sets[J].Advances in Machine Intelligence and Soft Computing,1997,4:132-155.
[9]SIERPINSKI W.General topology[M].Courier Dover Publications,2020.
[10]DAY M M.Convergence,closure and neighborhoods[J].Duke Mathematical Journal,1944,11(1):181-199.
[11]ATIK E,EL FATTAH A,NAWAR A,et al.Rough approxima-tion models via graphs based on neighborhood systems[J].Granular Computing,2021,6(4):1025-1035.
[12]SYAU Y R,LIN E B.Neighborhood systems and covering approximation spaces[J].Knowledge-Based Systems,2014,66:61-67.
[13]ZHANG Y L,LI C Q,LIN M L,et al.Relationships between generalized rough sets based on covering and reflexive neighborhood system[J].Information Sciences,2015,319:56-67.
[14]WANG G Y,YAO Y Y,YU H.A survey on rough set theory and applications[J].Chinese Journal of Computers,2009,32(7):1229-1246.
[15]LIN T Y,LIU Q.Rough approximate operators:axiomaticrough set theory[M]//Rough Sets,Fuzzy Sets and Knowledge Discovery. Springer,London,1994:256-260.
[16]ZHU F,HE H C.The axiomatization of the rough set[J].Chinese Journal of Computers(Chinese Edition),2000,23(3):330-333.
[17]SUN H,LIU D Y,LI W.The minimization of axiom groups of rough set[J].Chinese Journal of Computers(Chinese Edition),2002,25(2):202-209.
[18]YAO Y Y.Constructive and algebraic methods of the theory of rough sets[J].Information Sciences,1998,109(1/2/3/4):21-47.
[19]Thiele H.On axiomatic characterisations of crisp approximation operators[J].Information Sciences,2000,129(1/2/3/4):221-226.
[20]ZHANG Y L,LI J,WU W Z.On axiomatic characterizations of three pairs of covering based approximation operators[J].Information Sciences,2010,180(2):274-287.
[21]ZHANG Y L,LUO M K.On minimization of axiom sets characterizing covering-based approximation operators[J].Information Sciences,2011,181(14):3032-3042.
[22]ZHAO F,LI L.Axiomatization on generalized neighborhoodsystem-based rough sets[J].Soft Computing,2018,22(18):6099-6110.
[23]MORSI N N,YAKOUT M M.Axiomatics for fuzzy rough sets[J].Fuzzy Sets and Systems,1998,100(1/2/3):327-342.
[24]THIELE H.On axiomatic characterizations of fuzzy approximation operators[C]//International Conference on Rough Sets and Current Trends in Computing.Berlin:Springer,2000:277-285.
[25]THIELE H.On axiomatic characterization of fuzzy approximation operators.II.The rough fuzzy set based case[C]//Proceedings 31st IEEE International Symposium on Multiple-Valued Logic.IEEE,2001:330-335.
[26]WU W Z,LEUNG Y,MI J S.On characterizations of(I,T)-fuzzy rough approximation operators[J].Fuzzy Sets and Systems,2005,154(1):76-102.
[27]ZHOU L,WU W Z.On generalized intuitionistic fuzzy rough approximation operators[J].Information Sciences,2008,178(11):2448-2465.
[28]YAO Y Y.Relational interpretations of neighborhood operators and rough set approximation operators[J].Information Sciences,1998,111(1/2/3/4):239-259.
[29]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.
[1] LI Teng, LI Deyu, ZHAI Yanhui, ZHANG Shaoxia. Optimal Granularity Selection and Attribute Reduction in Meso-granularity Space [J]. Computer Science, 2023, 50(10): 71-79.
[2] KONG Jiabin, LYU Jianwen, LIU Jiangnan, DU Wenxuan. Recognition Method of Component Names in Patent Documents Based on the Algorithm of Word Frequency Difference and Library of Left-segmentation Words [J]. Computer Science, 2023, 50(7): 229-236.
[3] CONG Yingnan, WANG Zhaoyu, ZHU Jinqing. Reconstructing the Right to Algorithm Explanation --Full Algorithm Development Flow Governance and Hierarchical Classification Interpretation Framework [J]. Computer Science, 2023, 50(7): 347-354.
[4] YANG Ye, WU Weizhi, ZHANG Jiaru. Optimal Scale Selection and Rule Acquisition in Inconsistent Generalized Decision Multi-scale Ordered Information Systems [J]. Computer Science, 2023, 50(6): 131-141.
[5] LI Yanyan, QIN Keyun. Topological Properties of Generalized Rough Approximation Operators Based on Objects [J]. Computer Science, 2023, 50(2): 173-177.
[6] RAN Hong, HOU Ting, HE Long-yu, QIN Ke-yun. Fuzzy Rough Sets Model Based on Fuzzy Neighborhood Systems [J]. Computer Science, 2022, 49(11A): 211100224-5.
[7] WANG Jie, LI Xiao-nan, LI Guan-yu. Adaptive Attention-based Knowledge Graph Completion [J]. Computer Science, 2022, 49(7): 204-211.
[8] FANG Lian-hua, LIN Yu-mei, WU Wei-zhi. Optimal Scale Selection in Random Multi-scale Ordered Decision Systems [J]. Computer Science, 2022, 49(6): 172-179.
[9] XU Si-yu, QIN Ke-yun. Topological Properties of Fuzzy Rough Sets Based on Residuated Lattices [J]. Computer Science, 2022, 49(6A): 140-143.
[10] CAI Xiao-juan, TAN Wen-an. Improved Collaborative Filtering Algorithm Combining Similarity and Trust [J]. Computer Science, 2022, 49(6A): 238-241.
[11] CONG Ying-nan, WANG Zhao-yu, ZHU Jin-qing. Insights into Dataset and Algorithm Related Problems in Artificial Intelligence for Law [J]. Computer Science, 2022, 49(4): 74-79.
[12] WANG Zi-yin, LI Lei-jun, MI Ju-sheng, LI Mei-zheng, XIE Bin. Attribute Reduction of Variable Precision Fuzzy Rough Set Based on Misclassification Cost [J]. Computer Science, 2022, 49(4): 161-167.
[13] LI Yan-yan, QIN Ke-yun. On Topological Properties of Generalized Rough Approximation Operators [J]. Computer Science, 2022, 49(3): 263-268.
[14] ZHAO Yang, NI Zhi-wei, ZHU Xu-hui, LIU Hao, RAN Jia-min. Multi-worker and Multi-task Path Planning Based on Improved Lion Evolutionary Algorithm forSpatial Crowdsourcing Platform [J]. Computer Science, 2021, 48(11A): 30-38.
[15] XU Jin. Construction and Application of Knowledge Graph for Industrial Assembly [J]. Computer Science, 2021, 48(6A): 285-288.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!