Computer Science

Computer Science ›› 2025, Vol. 52 ›› Issue (11): 49-61.doi: 10.11896/jsjkx.250700019

• Database & Big Data & Data Science • Previous Articles     Next Articles

Optimal Scale Combinations and Attribute Reduction for Partially Incomplete Generalized Multi- scale Data

ZHOU Shilin, WU Weizhi, LI Tongjun   

  1. School of Information Engineering,Zhejiang Ocean University,Zhoushan,Zhejiang 316022,China
  • Received:2025-07-04 Revised:2025-08-24 Online:2025-11-15 Published:2025-11-06
  • About author:ZHOU Shilin,born in 2002,postgra-duate.His main research interests include rough sets and granular computing.
    WU Weizhi,born in 1964,Ph.D,professor,is a member of CCF(No.09246S).His main research interests include rough sets,granular computing,data mining and artificial intelligence.
  • Supported by:
    National Natural Science Foundation of China(12371466).

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Abstract: For the issue of knowledge acquisition in partially incomplete generalized multi-scale data sets,firstly,this paper pro-poses a method to transform a partially incomplete generalized multi-scale decision system into a generalized multi-scale set-valued decision one.Then,a tolerance relation on the object sets under each scale combination with each attribute subset in the obtained generalized multi-scale set-valued decision system is then constructed.Corresponding tolerance classes are also built.Upper and lower approximations,belief and plausibility degrees of sets with respect to each tolerance relation as well as information quantities of the attribute subset are subsequently presented.Six types of optimal scale combinations in a consistent generalized multi-scale set-valued decision system are further defined and their relationships are examined.It is rigorously demonstrated that five types of optimal scale combinations are equivalent while there is no static relationship between the concept of information quantity optimal scale combination with any of the other five types.Finally,an attribute reduction approach based on a belief optimal scale combination in a consistent generalized multi-scale set-valued decision system is developed,and an illustrative example is employed to explain the calculation of a belief optimal scale reduct.

Key words: Attribute reduction, Granular computing, Optimal scale combinations, Partially incomplete generalized multi-scale decision systems, Rough sets

CLC Number: 

  • TP182
[1]PEDRYC Z W.Granular computing for data analytics:a manifesto of human-centric computing[J].IEEE/CAA Journal of Automatica Sinica,2018,5(6):1025-1034.
[2]LIN T Y.Granular computing:structures,representations,and applications[C]//Proceedings of the 9th International Confe-rence on Rough Sets,Fuzzy Sets,Data Mining,and Granular Computing.Berlin:Springer,2003:16-24.
[3]ZADEH L A.Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic[J].Fuzzy Sets and Systems,1997,90(2):111-127.
[4]HOBBS J R.Granularity[C]//Proceedings of the 9th International Joint Conference on Artificial Intelligence.San Francisco:Morgan Kaufmann,1985:432-435.
[5]YAO Y Y.Granular computing:basic issues and possible solutions[C]//Proceedings of the 5th Joint Conference on Information Sciences.New Jersey:Association for IntelligentMachine-ry,2000:186-189.
[6]YAO J T.Information granulation and granular relationships[C]//2005 IEEE International Conference on Granular Computing.IEEE,2005:326-329.
[7]MENCAR C,FANELLI A M.Interpretability constraints forfuzzy information granulation[J].Information Sciences,2008,178(24):4585-4618.
[8]PEDRYCZ W.Granular computing for machine learning:pursuing new development horizons[J].IEEE Transactions on Cybernetics,2025,55(1):460-471.
[9]DENG X Y,LI J H,QIAN Y H,et al.An emerging incremental fuzzy concept-cognitive learning model based on granular computing and conceptual knowledge clustering[J].IEEE Transactions on Emerging Topics in Computational Intelligence,2024,8(3):2417-2432.
[10]XUE R X,YI S C,WANG P X.GBDEN:a fast clustering algorithm for large-scale data based on granular ball[J].Computer Science,2024,51(12):166-173.
[11]JING X Y,ZHAO J J,YAN Z,et al.Granular classifier:building traffic granules for encrypted traffic classification based on granular computing[J].Digital Communications and Networks,2024,10(5):1428-1438.
[12]ZHANG L J,LIN G P,LIN Y D,et al.Feature subset selection for multi-scale neighborhood decision information system[J].Pattern Recognition and Artificial Intelligence,2023,36(1):49-59.
[13]CHEN B Y,YUAN Z,PENG D Z,et al.Integrating granularcomputing with density estimation for anomaly detection in high-dimensional heterogeneous data[J].Information Sciences,2025,690:121566.
[14]PAWLAK Z.Rough sets[J].International Journal of Computer and Information Sciences,1982,11(5):341-356.
[15]LI W,WANG X L,YANG B.Three-way decisions with dual hesitant fuzzy covering-based rough set and their applications in medical diagnosis[J].Applied Soft Computing,2024,160:111695.
[16]HAN N N,QIAO J S,LI T B,et al.Multigranulation fuzzy probabilistic rough sets induced by overlap functions and their applications[J].Fuzzy Sets and Systems,2024,481:108893.
[17]YE J,SUN B Z,CHU X L,et al.Valued outranking relation-based heterogeneous multi-decision multigranulation probabilistic rough set and its use in medical decision-making[J].Expert Systems with Applications,2023,228:120296.
[18]JIANG H B,HU B Q.On four novel kinds of fuzzy β-covering-based rough sets and their applications to three-way approximations[J].Fuzzy Sets and Systems,2025,507:109312.
[19]WANG X,HUANG B.Rough set model based on fuzzy purity granular ball [J].Pattern Recognition and Artificial Intelligence,2025,38(3):221-232.
[20]JI X,DUAN W Y,PENG J H,et al.Fuzzy rough set attribute reduction based on decision ball model[J].International Journal of Approximate Reasoning,2025,179:109364.
[21]XU J C,ZHANG S,BAI Q,et al.Attribute reduction algorithm based on fuzzy neighborhood relative decision entropy[J].Computer Science,2025,52(2):165-172.
[22]MA L W,LI M F.Covering rough set models,fuzzy rough set models and soft rough set models induced by covering similarity[J].Information Sciences,2025,689:121520.
[23]WU W Z,LEUNG Y.Theory and applications of granular labelled partitions in multi-scale decision tables[J].Information Sciences,2011,181(18):3878-3897.
[24]LI F,HU B Q.A new approach of optimal scale selection tomulti-scale decision tables[J].Information Sciences,2017,381:193-208.
[25]DEMPSTER A P.Upper and lower probabilities induced by a multivalued mapping[J].The Annals of Mathematical Statistics,1967,38(2):325-339.
[26]SHAFER G.A Mathematical Theory of Evidence[M].Princeton:Princeton University Press,1976.
[27]ZHANG M,XU L D,ZHANG W X,et al.A rough set approach to knowledge reduction based on inclusion degree and evidence reasoning theory[J].Expert Systems,2003,20(5):298-304.
[28]WU W Z.Attribute reduction based on evidence theory in in-complete decision systems[J].Information Sciences,2008,178(5):1355-1371.
[29]WU W Z,LEUNG Y.Optimal scale selection for multi-scale decision tables[J].International Journal of Approximate Reasoning,2013,54(8):1107-1129.
[30]MA J M,ZHANG W X.Information quantity-based attributereduction in set-valued information systems[J].Fuzzy Systems and Mathematics,2013,27(2):177-182.
[31]GUAN Y Y,WANG H K.Set-valued information systems[J].Information Sciences,2006,176(17):2507-2525.
[32]QIAN Y H,DANG C Y,LIANG J Y,et al.Set-valued ordered information systems[J].Information Sciences,2009,179(16):2809-2832.
[33]HUANG Y D,ZHANG Y J,XU J F.Incremental approaches for optimal scale selection in dynamic multi-scale set-valued decision tables[J].International Journal of Machine Learning and Cybernetics,2023,14(6):2251-2270.
[34]HU J,CHEN Y,ZHANG Q H,et al.Optimal scale selection for generalized multi-scale set-valued decision systems[J].Journal of Computer Research and Development,2022,59(9):2027-2038.
[35]KRYSZKIEWICZ M.Rough set approach to incomplete information systems[J].Information Sciences,1998,112(1/2/3/4):39-49.
[36]KRYSZKIEWICZ M.Rules in incomplete information systems[J].Information Sciences,1999,113(3/4):271-292.
[37]WU W Z,QIAN Y H,LI T J,et al.On rule acquisition in incom-plete multi-scale decision tables[J].Information Sciences,2017,378:282-302.
[38]SONG Y,LUO D M,XIE N X,et al.Uncertainty measurement for incomplete set-valued data with application to attribute reduction[J].International Journal of Machine Learning and Cybernetics,2022,13(10):3031-3069.
[39]WANG X X,YIN F,YIN M,et al.Incomplete generalized multi-scale ordered information systems and optimal scale combination selection[C]//2023 3rd International Symposium on Computer Technology and Information Science(ISCTIS).IEEE,2023:796-802.
[40]WANG T Y,YANG B.Optimal scale selection of dynamic incomplete generalized multi-scale fuzzy ordered decision systems based on rough fuzzy sets[J].Fuzzy Sets and Systems,2025,515:109420.
[41]LIANG J Y,QU K S,XU Z B.Reduction of attribute in information systems [J].Systems Engineering-Theory & Practice,2001(12):76-80.
[42]ZHU K,WU W Z,LIU M X.Optimal scale combinations and attribute reduction for consistent generalized multi-scale ordered fuzzy decision systems[J].Pattern Recognition and Artificial Intelligence,2024,37(6):538-556.
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