对偶区间集概念格上区间集协调集的判定方法

doi:10.11896/jsjkx.190500098

Abstract

Abstract: The dual interval-set concept lattice is generated by introducing the interval set into the dual concept lattice.It extends the extension and intension of the dual concept from the classical sets to the interval sets,which makes it to be a mathematical tool to describe uncertain concepts.As one of the core topics of data mining,attribute reduction is a method to study the essential characteristics of concept lattice.It simplifies the representation of the concept by removing redundant attributes.This paper mainly discussed the judgment approaches of the interval-set consistent sets of the dual interval-set concept lattices.Firstly,based on the isomorphisim for the structure of the dual interval-set concept lattices,interval-set consistent sets were defined,and a series of judgment theorems were then investigated for the dual interval-set concept lattices.Then,the method about obtaining attribute reduction interval-set by using the interval-set consistent set was described.

Key words: Attribute reduction, Dual concept lattice, Dual interval-set concept lattice, Interval set, Interval-set consistent set

CLC Number:

TP182

GUO Qing-chun,MA Jian-min. Judgment Methods of Interval-set Consistent Sets of Dual Interval-set Concept Lattices[J].Computer Science, 2020, 47(3): 98-102.

References

[1]WILLE R.Restructuring lattice theory:an approach based on hierarchies of concepts[C]∥Ordered Sets.Riedel,Dordrecht,1982:445-470.
[2]GANTER B,WILLE R.Formal Concept Analysis:Mathematics Foundations[M].Berlin,Germany,1999.
[3]YAO Y Y.Interval-set algebra for qualitative knowledge representation[C]∥Proceeding of the 5th International Conference on Computing and Information.Society Press,1993:370-374.
[4]YAO Y Y.Wong SKM:Interval approaches for uncertain rea- soning[C]∥International Symposium on Methodologies for Intelligent Systems.1997:381-390.
[5]YAO Y Y.Interval sets and interval-set algebras[C]∥Proceeding of the 8th IEEE International Conference on Cognitive Informatics,Computer Society.2009:309-314.
[6]YAO Y Y.Concept lattices in rough set theory[C]∥Proceeding of 23 International Meeting of North American Fuzzy Information,Processing Society.2004:796-901.
[7]YAO Y Y.Interval set and three-way concept analysis in complete contexts[J].International Journal of Machine Learning & Cybernetics,2017,8(1):3-20.
[8]XU W H,LI J H,WEI L,et al.Formal Concept Analysis:Theory and application[M].Beijing:Beijing Science Press,2016:69-82.
[9]ZHANG W X,WEI L,QI J J.Attribute reduction Theory of Concept Lattice[J].Science in China(Series E),2005,35(6):628-639.
[10]WEI L,QI J J,ZHANG W X.Attribute reduction Theory of Concept Lattice Based on Decision Formal Contexts[J].Science in China(Series E),2008,38(2):195-208.
[11]SHAO M W,LI K W.Attribute reduction in generalized one-sided formal contexts[J].Information Sciences,2017,378:317-327.
[12]LI J H.Rule Acquisition Oriented Reduction Methods for Concept Lattices and Their Implementation Algorithms[D].Xi’an:Xi’an Jiaotong University,2012.
[13]LI J H,MEI S L,LV Y J.Knowledge reduction in real decision formal contexts[J].Information Sciences,2012,189:191-207.
[14]LIU JI M,LIU B X.Research on attribute reduction and its algorithm based on concept lattice isomorphism[J].Computer Applications and Software,2014,31(5):34-36.
[15]LI J J,ZHANG Y L,WU W Z,et al.Attribute Reduction for Formal Context and Consistent Decision Formal Concext and Concept Lattice Generation[J].Chinese Journal of Computers,2014,37(8):1768-1774.
[16]WANG Z,WEI L.Attribute Reduction on Partially-known Formal Concept Lattices for Incomplete Contexts[J].Computer Science,2018,45(1):73-78.
[17]MA J M,CAI M J,ZOU C J.Concept acquisition approach of object-oriented concept lattice[J].International Journal of Machine Learning & Cybernetics,2017,8(1):123-134.
[18]MA J M,LEUNG Y,ZHANG W X.Attribute reductions in object-oriented concept lattices[J].International Journal of Machine Learning & Cybernetics,2014,5(5):789-813.
[19]MA J M,HU L L.Attribute Reductions of Interval-set Concept Lattices for Decision Formal Contexts[J].Pattern Recognition and and Artificial Intelligence,2018,31(7):581-590.
[20]ZHANG E S.Composition and structure on attribute reduction of interval-set concept lattice[J].Journal of ShanDong University(Natural Science),2018,53(8):17-24.
[21]MA J M,ZHANG W X.Axiomatic characterizations of dual concept lattice[J].International Journal of Approximate Reasoning,2013,54(5):690-697.

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Judgment Methods of Interval-set Consistent Sets of Dual Interval-set Concept Lattices

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