Computer Science ›› 2016, Vol. 43 ›› Issue (2): 68-71.doi: 10.11896/j.issn.1002-137X.2016.02.015

Previous Articles     Next Articles

Rough Set Algebra of Multi-granulation

KONG Qing-zhao and WEI Zeng-xin   

  • Online:2018-12-01 Published:2018-12-01

Abstract: It is well known that a rough set algebra is a set algebra with added dual pair of rough approximation operators.On the one hand,we discussed the classical rough set algebra of multi-granulation by axiomatic approach.It is shown that the classical rough set algebra does not possess good properties.On the other hand,we defined the concept of monotone equivalence relations.Moreover,multi-granulation approximation operators based on monotone equivalence relations were defined.We discussed the properties of the rough set algebra based on monotone equivalence relations and got many excellent results.

Key words: Multi-granulation,Rough set algebra,Monotone equivalence relation,Approximation operators

[1] Boixader D,Jacas J,Recasens J.Upper and lower approxima-tions of fuzzy sets [J].International Journal of General Systems,2000,29(4):555-568
[2] Dubois D,Prade H.Rough fuzzy sets and fuzzy rough sets[J].International Journal of General Systems,1990,17(2/3):191-209
[3] Inuiguchi M.Generalizations of rough sets:from crisp to fuzzy cases[C]∥Tsumoto S,Slowinski R,Komorowski J,et al.,eds.Rough Sets and Current Trends in Computing.2004:26-37
[4] Mi J S,Leung Y,Wu W Z.An uncertainty measure in partition-based fuzzy rough sets[J].International Journal of General Systems,2005,34(1):77-90
[5] Mi J S,Zhang W X.An axiomatic characterization of a fuzzy generalization of rough sets[J].Information Sciences,2004,160(1-4):235-249
[6] Pei D W,Xu Z B.Rough set models on two universes[J].International Journal of General Systems,2004,33(5):569-581
[7] Slowinski R,Vanderpooten D.A generalized definition of rough approximations based on similarity[J].IEEE Transactions on Knowledge and Data Engineering,2000,12(2):331-336
[8] Comer S.An algebraic approach to the approximation of information[J].Foundamenta Informaticae,1991,14(14):492-502
[9] Lin T Y,Liu Q.Rough approximate operators:axiomatic rough set theory[C]∥Ziarko W,ed.Rough sets,Fuzzy sets and Konw-ledge Discovery.Springer,Berlin,1994:256-260
[10] Pomykala J A.Approximation operations in approximation space[J].Bulletin of the Polish Academy of Sciences:Mathematics,1987,35(1):653-662
[11] Yao Y Y.Two views of the theory of rough sets in finite universes[J].International Journal of Approximate Reasoning,1996,15(4):291-317
[12] Yao Y Y.Constructive and algebraic methods of the theory of rough sets[J].Information Sciences,1998,109(1-4):21-47
[13] Vakarelov D.A model logic for similarity relations in Pawlak knowledge representation systems[J].Foundamenta Informaticae,1991,15:61-79
[14] Wiweger R.On topology rough sets[J].Bulletin of Polish Academy of Sciences:Mathematics,1989,37:89-93
[15] Wu W Z,Leung Y,Zhang W X.Connections between rough set theory and Dempster-Shafer theory of evidence[J].International Journal of General Systems,2002,31(4):405-430
[16] Yao Y Y,Lingras P J.Interpretations of belief functions in the theory of roughs[J].Information Sciences,1998,104(1/2):81-106
[17] Wu W Z,Mi J S,Zhang W X.Generalized fuzzy rough sets[J].Information Sciences,2003,151(3):263-282
[18] Wu W Z,Zhang W X,Xu Z B.Characterizating Rough Fuzzy Sets in Constructive and Axiomatic Approaches[J].Chinese Journal of Computers,2004,7(2):197-203(in Chinese) 吴伟志,张文修,徐宗本,等.粗糙模糊集的构造与公理化方法[J].计算机学报,2004,27(1):197-203
[19] Xu Y H.Fuzzy rough set algebras [J].Fuzzy Systems andMathematics,2007,1(2):121-128(in Chinese) 徐优红.模糊粗糙集代数[J].模糊系统与数学,2007,21(2):121-128
[20] Qian Y H,Liang J Y,Yao Y Y,et al.MGRS:A multi-granulation rough set[J].Information Sciences,2010,180(6):949-970
[21] Qian Y H,Liang J Y,Wei W.Pessimistic rough decision[C]∥2nd International Workshop on Rough Sets Theory.Zhoushan,2010:19-21
[22] Qian Y H,Liang J Y,Yao Y Y,et al.Incomplete multigranulationrough set[J].IEEE Transactions on Systems,Man and Cybernetics,Part A,2010,40(2):420-431
[23] She Y H,He X L.On the structure of the multigranulationrough set model[J].Knowledge-based Systems,2012,36(6):81-92
[24] Xu W H,Wang Q R,Zhang X T.Multi-granulation fuzzy rough sets in a fuzzy tolerance approximation space[J].International Journal of Fuzzy Systems,2011,13(4):246-259
[25] Zhang W X,Wu W Z,Liang J Y,et al.The theory and method of rough sets [M].Beijing:Science Press,2001(in Chinese) 张文修,吴伟志,梁吉业,等.粗糙集理论与方法[M].北京:科学出版社,2001

No related articles found!
Full text



No Suggested Reading articles found!