Skip to main content
Top
Published in: International Journal of Machine Learning and Cybernetics 1/2020

30-04-2019 | Original Article

Local attribute reductions of formal contexts

Authors: Keyun Qin, Hong Lin, Yuting Jiang

Published in: International Journal of Machine Learning and Cybernetics | Issue 1/2020

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Attribute reductions is an important topic in formal concept analysis. The existing attribute reduction approaches are dominated by global reductions and there is very limited investigation on local reductions. This paper is devoted to the study of decision rule specific reduction for formal decision context and concept specific reduction for formal context. The notion of decision rule specific reduction is proposed and the related reduction methods are presented. The relationships between existing reduction approaches and decision rule specific reduction approaches are analyzed. Accordingly, we make an analysis of attributes based on three-way classification by using reductions. Furthermore, the notion of concept specific reduction for formal context is proposed and the concept specific reduction methods are examined. The relationship between concept specific reduction and decision rule specific reduction is surveyed.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Show more products
Literature
1.
go back to reference Belohlavek R, Vychodil V (2006) Formal concept analysis with constraints by closure operators. LNAI 4068:131–143MATH Belohlavek R, Vychodil V (2006) Formal concept analysis with constraints by closure operators. LNAI 4068:131–143MATH
2.
go back to reference Beydoun G (2009) Formal concept analysis for an e-learning semantic web. Expert Syst Appl 36(8):10952–10961 Beydoun G (2009) Formal concept analysis for an e-learning semantic web. Expert Syst Appl 36(8):10952–10961
3.
go back to reference Carpineto C, Romano G (2004) Exploiting the potential of concept lattices for information retrieval with CREDO. J UCS 10(8):985–1013MATH Carpineto C, Romano G (2004) Exploiting the potential of concept lattices for information retrieval with CREDO. J UCS 10(8):985–1013MATH
4.
go back to reference Chen DG, Tsang EC (2005) On the local reduction of information system. LNCS 3930:588–594 Chen DG, Tsang EC (2005) On the local reduction of information system. LNCS 3930:588–594
5.
go back to reference Chen DG, Zhao SY (2010) Local reduction of decision system with fuzzy rough sets. Fuzzy Sets Syst 161:1871–1883MathSciNetMATH Chen DG, Zhao SY (2010) Local reduction of decision system with fuzzy rough sets. Fuzzy Sets Syst 161:1871–1883MathSciNetMATH
6.
go back to reference Dias SM, Vieira NJ (2015) Concept lattices reduction: definition, analysis and classification. Expert Syst Appl 42:7084–7097 Dias SM, Vieira NJ (2015) Concept lattices reduction: definition, analysis and classification. Expert Syst Appl 42:7084–7097
7.
go back to reference Elloumi S, Jaam J, Hasnah A, Jaoua A, Nafkha I (2004) A multi-level conceptual data reduction approach based on the lukasiewicz implication. Inf Sci 163:253–262MathSciNetMATH Elloumi S, Jaam J, Hasnah A, Jaoua A, Nafkha I (2004) A multi-level conceptual data reduction approach based on the lukasiewicz implication. Inf Sci 163:253–262MathSciNetMATH
8.
go back to reference Formica A (2010) Concept similarity in fuzzy formal concept analysis for semantic web. Int J Uncertain Fuzz Knowl Based Syst 18(2):153–167MathSciNet Formica A (2010) Concept similarity in fuzzy formal concept analysis for semantic web. Int J Uncertain Fuzz Knowl Based Syst 18(2):153–167MathSciNet
9.
go back to reference Formica A (2012) Semantic web search based on rough sets and fuzzy formal concept analysis. Knowl Based Syst 26:40–47 Formica A (2012) Semantic web search based on rough sets and fuzzy formal concept analysis. Knowl Based Syst 26:40–47
10.
go back to reference Ganter B, Wille R (1999) Formal concept analysis: mathematical foundations. Springer, BerlinMATH Ganter B, Wille R (1999) Formal concept analysis: mathematical foundations. Springer, BerlinMATH
11.
go back to reference Klimes J (2014) Using formal concept analysis for control in cyber-physical systems. Proced Eng 69:1518–1522 Klimes J (2014) Using formal concept analysis for control in cyber-physical systems. Proced Eng 69:1518–1522
12.
go back to reference Konecny J (2017) On attribute reduction in concept lattices: methods based on discernibility matrix are outperformed by basic clarification and reduction. Inf Sci 415:199–212 Konecny J (2017) On attribute reduction in concept lattices: methods based on discernibility matrix are outperformed by basic clarification and reduction. Inf Sci 415:199–212
13.
go back to reference Kuznetsov SO (2001) Machine learning on the basis of formal concept analysis. Autom Rem Control 62(10):1543–1564MATH Kuznetsov SO (2001) Machine learning on the basis of formal concept analysis. Autom Rem Control 62(10):1543–1564MATH
14.
go back to reference Kuznetsov SO (2004) Complexity of learning in concept lattices from positive and negative examples. Discret Appl Math 142:111–125MathSciNetMATH Kuznetsov SO (2004) Complexity of learning in concept lattices from positive and negative examples. Discret Appl Math 142:111–125MathSciNetMATH
15.
go back to reference Li JH, Mei CL, Lv YJ (2011) Knowledge reduction in decision formal contexts. Knowl Based Syst 24:709–715MATH Li JH, Mei CL, Lv YJ (2011) Knowledge reduction in decision formal contexts. Knowl Based Syst 24:709–715MATH
16.
go back to reference Li JH, Mei CL, Lv YJ (2012) Knowledge reduction in real decision formal contexts. Inf Sci 189:191–207MathSciNetMATH Li JH, Mei CL, Lv YJ (2012) Knowledge reduction in real decision formal contexts. Inf Sci 189:191–207MathSciNetMATH
17.
go back to reference Li JH, Mei CL, Lv YJ (2012) Knowledge reduction in formal decision contexts based on an order-preserving mapping. Int J Gener Syst 41:143–161MathSciNetMATH Li JH, Mei CL, Lv YJ (2012) Knowledge reduction in formal decision contexts based on an order-preserving mapping. Int J Gener Syst 41:143–161MathSciNetMATH
18.
go back to reference Li JH, Mei CL, Wang J, Zhang X (2014) Rule-preserved object compression in formal decision contexts using concept lattices. Knowl Based Syst 71:435–445 Li JH, Mei CL, Wang J, Zhang X (2014) Rule-preserved object compression in formal decision contexts using concept lattices. Knowl Based Syst 71:435–445
19.
go back to reference Li JH, Huang C, Mei CL, Yin YQ (2017) An intensive study on rule acquisition in formal decision contexts based on minimal closed label concept lattices. Intell Autom Soft Comput 23:519–533 Li JH, Huang C, Mei CL, Yin YQ (2017) An intensive study on rule acquisition in formal decision contexts based on minimal closed label concept lattices. Intell Autom Soft Comput 23:519–533
20.
go back to reference Li JH, Kumar CA, Mei CL, Wang XZ (2017) Comparison of reduction in formal decision contexts. Int J Approx Reason 80:100–122MathSciNetMATH Li JH, Kumar CA, Mei CL, Wang XZ (2017) Comparison of reduction in formal decision contexts. Int J Approx Reason 80:100–122MathSciNetMATH
21.
go back to reference Li JY, Wang X, Wu WZ, Xu YH (2017) Attribute reduction in inconsistent formal decision contexts based on congruence relations. Int J Mach Learn Cybern 8:81–94 Li JY, Wang X, Wu WZ, Xu YH (2017) Attribute reduction in inconsistent formal decision contexts based on congruence relations. Int J Mach Learn Cybern 8:81–94
22.
go back to reference Liu GL, Hua Z, Zhou JY (2018) Local attribute reductions for decision tables. Inf Sci 422:204–217MathSciNet Liu GL, Hua Z, Zhou JY (2018) Local attribute reductions for decision tables. Inf Sci 422:204–217MathSciNet
23.
go back to reference Outrata J, Vychodil V (2012) Fast algorithm for computing fixpoints of Galois connections induced by object-attribute relational data. Inf Sci 185:114–127MathSciNetMATH Outrata J, Vychodil V (2012) Fast algorithm for computing fixpoints of Galois connections induced by object-attribute relational data. Inf Sci 185:114–127MathSciNetMATH
24.
go back to reference Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 11:341–356MATH Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 11:341–356MATH
25.
go back to reference Pei D, Mi JS (2011) Attribute reduction in decision formal context based on homomorphism. Int J Mach Learn Cybern 2:289–293 Pei D, Mi JS (2011) Attribute reduction in decision formal context based on homomorphism. Int J Mach Learn Cybern 2:289–293
26.
go back to reference Pineda-Bautista BB, Carrasco-Ochoa JA, Martinez-Trinidad JF (2011) General framework for class-specific feature selection. Expert Syst Appl 38:10018–10024 Pineda-Bautista BB, Carrasco-Ochoa JA, Martinez-Trinidad JF (2011) General framework for class-specific feature selection. Expert Syst Appl 38:10018–10024
27.
go back to reference Poelmans J, Elzinga P, Viaene S, Dedene G (2010) Formal concept analysis in knowledge discovery: a survey. In: International conference on conceptual structures, pp 139–153 Poelmans J, Elzinga P, Viaene S, Dedene G (2010) Formal concept analysis in knowledge discovery: a survey. In: International conference on conceptual structures, pp 139–153
28.
go back to reference Ren RS, Wei L (2016) The attribute reductions of three-way concept lattices. Knowl Based Syst 99:92–102 Ren RS, Wei L (2016) The attribute reductions of three-way concept lattices. Knowl Based Syst 99:92–102
29.
go back to reference Sampath S, Sprenkle S, Gibson E, Pollock L, Greenwald AS (2007) Applying concept analysis to user-session-based testing of web applications. IEEE Trans Softw Eng 33(10):643–658 Sampath S, Sprenkle S, Gibson E, Pollock L, Greenwald AS (2007) Applying concept analysis to user-session-based testing of web applications. IEEE Trans Softw Eng 33(10):643–658
30.
go back to reference Shao MW, Li KW (2017) Attribute reduction in generalized one-sided formal contexts. Inf Sci 378:317–327MathSciNet Shao MW, Li KW (2017) Attribute reduction in generalized one-sided formal contexts. Inf Sci 378:317–327MathSciNet
31.
go back to reference Shao MW, Leung Y, Wu WZ (2014) Rule acquisition and complexity reduction in formal decision contexts. Int J Approx Reason 55:259–274MathSciNetMATH Shao MW, Leung Y, Wu WZ (2014) Rule acquisition and complexity reduction in formal decision contexts. Int J Approx Reason 55:259–274MathSciNetMATH
32.
go back to reference Shao MW, Yang HZ, Wu WZ (2015) Knowledge reduction in formal fuzzy contexts. Knowl Based Syst 73:265–275 Shao MW, Yang HZ, Wu WZ (2015) Knowledge reduction in formal fuzzy contexts. Knowl Based Syst 73:265–275
33.
go back to reference Skowron A, Rauszer C (1992) The discernibility matrices and functions in information systems. In: Slowinski R (ed) Intelligent decision support, handbook of applications and advances of the rough sets theory. Kluwer Academic, Dordrecht, pp 331–362 Skowron A, Rauszer C (1992) The discernibility matrices and functions in information systems. In: Slowinski R (ed) Intelligent decision support, handbook of applications and advances of the rough sets theory. Kluwer Academic, Dordrecht, pp 331–362
34.
go back to reference Wei L, Qi JJ (2010) Relation between concept lattice reduction and rough set reduction. Knowl Based Syst 23:934–938 Wei L, Qi JJ (2010) Relation between concept lattice reduction and rough set reduction. Knowl Based Syst 23:934–938
35.
go back to reference Wei L, Qi J, Zhang W (2008) Attribute reduction theory of concept lattice based on decision formal contexts. Sci China Ser F Inf Sci 51(7):910–923MathSciNetMATH Wei L, Qi J, Zhang W (2008) Attribute reduction theory of concept lattice based on decision formal contexts. Sci China Ser F Inf Sci 51(7):910–923MathSciNetMATH
36.
go back to reference Wille R (1982) Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival I (ed) Ordered sets. Springer, Dordrecht, pp 445–470 Wille R (1982) Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival I (ed) Ordered sets. Springer, Dordrecht, pp 445–470
37.
go back to reference Wu WZ, Leung Y, Mi JS (2009) Granular computing and knowledge reduction in formal contexts. IEEE Trans Knowl Data Eng 21(10):1461–1474 Wu WZ, Leung Y, Mi JS (2009) Granular computing and knowledge reduction in formal contexts. IEEE Trans Knowl Data Eng 21(10):1461–1474
38.
go back to reference Yao Y (2004) A comparative study of formal concept analysis and rough set theory in data analysis. In: International conference on rough sets and current trends in computing, Springer, pp 59–68 Yao Y (2004) A comparative study of formal concept analysis and rough set theory in data analysis. In: International conference on rough sets and current trends in computing, Springer, pp 59–68
39.
go back to reference Yao Y, Zhang XY (2017) Class-specific attribute reducts in rough set theory. Inf Sci 418:601–618 Yao Y, Zhang XY (2017) Class-specific attribute reducts in rough set theory. Inf Sci 418:601–618
40.
go back to reference Zhang ML, Wu L (2015) LIFT: multi-label learning with label-specific features. IEEE Trans Pat Ana and Mach Intell 37:107–120 Zhang ML, Wu L (2015) LIFT: multi-label learning with label-specific features. IEEE Trans Pat Ana and Mach Intell 37:107–120
41.
go back to reference Zhang WX, Qiu GF (2005) Uncertain decision making based on rough sets. Publishin of Tsinghua University, Beijing Zhang WX, Qiu GF (2005) Uncertain decision making based on rough sets. Publishin of Tsinghua University, Beijing
42.
go back to reference Zhang W, Wei L, Qi J (2005) Attribute reduction theory and approach to concept lattice. Sci China Ser F Inf Sci 48(6):713–726MathSciNetMATH Zhang W, Wei L, Qi J (2005) Attribute reduction theory and approach to concept lattice. Sci China Ser F Inf Sci 48(6):713–726MathSciNetMATH
Metadata
Title
Local attribute reductions of formal contexts
Authors
Keyun Qin
Hong Lin
Yuting Jiang
Publication date
30-04-2019
Publisher
Springer Berlin Heidelberg
Published in
International Journal of Machine Learning and Cybernetics / Issue 1/2020
Print ISSN: 1868-8071
Electronic ISSN: 1868-808X
DOI
https://doi.org/10.1007/s13042-019-00956-z

Other articles of this Issue 1/2020

International Journal of Machine Learning and Cybernetics 1/2020 Go to the issue