Skip to main content
Erschienen in: Soft Computing 21/2020

28.04.2020 | Methodologies and Application

Granular matrix method of attribute reduction in formal contexts

verfasst von: Yidong Lin, Jinjin Li, Hongkun Wang

Erschienen in: Soft Computing | Ausgabe 21/2020

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Granular reduction has been of great interests for formal context analysis. From the perspective of granular computing, granular matrices are proposed to represent the extensions and intensions of formal concepts. Within this framework, irreducible elements are studied. Furthermore, similarity degree, information granular and information entropy are developed to specify the significance of attribute. In this case, heuristic approaches for granular reduct are proposed. Finally, several data sets are experimented to demonstrate the feasibility and efficiency of our method. Our methods present a new framework for granular reduction in formal concept analysis.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

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 "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!

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!

Literatur
Zurück zum Zitat Belohlavek R, Baets BD, Konecny J (2014) Granularity of attributes in formal concept analysis. Inf Sci 260(1):149–170MathSciNetMATH Belohlavek R, Baets BD, Konecny J (2014) Granularity of attributes in formal concept analysis. Inf Sci 260(1):149–170MathSciNetMATH
Zurück zum Zitat Carpineto C, Romano G (1996) A lattice conceptual clustering system and its application to browsing retrieval. Mach Learn 24(2):95–122 Carpineto C, Romano G (1996) A lattice conceptual clustering system and its application to browsing retrieval. Mach Learn 24(2):95–122
Zurück zum Zitat Ch AK, Dias SM, Vieira NJ (2015) Knowledge reduction in formal contexts using non-negative matrix factorization. Math Comput Simul 109:46–63MathSciNet Ch AK, Dias SM, Vieira NJ (2015) Knowledge reduction in formal contexts using non-negative matrix factorization. Math Comput Simul 109:46–63MathSciNet
Zurück zum Zitat Chen JK, Mi JS, Lin YJ (2018) A graph approach for knowledge reduction in formal contexts. KnowlBased Syst 148:177–188 Chen JK, Mi JS, Lin YJ (2018) A graph approach for knowledge reduction in formal contexts. KnowlBased Syst 148:177–188
Zurück zum Zitat Dias SM, Vieira NJ (2015) Concept lattices reduction: definition, analysis and classification. Expert Syst Appl 42(20):7084–7097 Dias SM, Vieira NJ (2015) Concept lattices reduction: definition, analysis and classification. Expert Syst Appl 42(20):7084–7097
Zurück zum Zitat Dias SM, Vieira NJ (2017) A methodology for analysis of concept lattice reduction. Inf Sci 396:202–217MathSciNetMATH Dias SM, Vieira NJ (2017) A methodology for analysis of concept lattice reduction. Inf Sci 396:202–217MathSciNetMATH
Zurück zum Zitat Davey BA, Priestley HA (2002) Introduction to lattices and order. Cambridge University Press, CambridgeMATH Davey BA, Priestley HA (2002) Introduction to lattices and order. Cambridge University Press, CambridgeMATH
Zurück zum Zitat Deng W, Zhao HM, Yang XH, Xiong JX, Sun M, Li B (2017) Study on an improved adaptive PSO algorithm for solving multi-objective gate assignment. Appl Soft Comput 59:288–302 Deng W, Zhao HM, Yang XH, Xiong JX, Sun M, Li B (2017) Study on an improved adaptive PSO algorithm for solving multi-objective gate assignment. Appl Soft Comput 59:288–302
Zurück zum Zitat Deng W, Xu JJ, Zhao HM (2019) An improved ant colony optimization algorithm based on hybrid strategies for scheduling problem. IEEE Access 7:20281–20292 Deng W, Xu JJ, Zhao HM (2019) An improved ant colony optimization algorithm based on hybrid strategies for scheduling problem. IEEE Access 7:20281–20292
Zurück zum Zitat Fenza G, Senatore S (2010) Friendly web services selection exploiting fuzzy formal concept analysis. Soft Comput 14(8):811–819 Fenza G, Senatore S (2010) Friendly web services selection exploiting fuzzy formal concept analysis. Soft Comput 14(8):811–819
Zurück zum Zitat Ganter BB, Wille R (1999) Formal concept analysis. Springer, BerlinMATH Ganter BB, Wille R (1999) Formal concept analysis. Springer, BerlinMATH
Zurück zum Zitat Huang CC, Li JH, Dias SM (2016) Attribute significance, consistency measure and attribute reduction in formal concept analysis. Neural Netw World 26(6):607–623 Huang CC, Li JH, Dias SM (2016) Attribute significance, consistency measure and attribute reduction in formal concept analysis. Neural Netw World 26(6):607–623
Zurück zum Zitat Huang CC, Li JH, Mei CL, Wu WZ (2017) Three-way concept learning based on cognitive operators: an information fusion viewpoint. Int J Approx Reason 83:218–242MathSciNetMATH Huang CC, Li JH, Mei CL, Wu WZ (2017) Three-way concept learning based on cognitive operators: an information fusion viewpoint. Int J Approx Reason 83:218–242MathSciNetMATH
Zurück zum Zitat Hao SF, Shi CY, Niu ZD, Cao LB (2018) Concept coupling learning for improving concept lattice-based document retrieval. Eng Appl Artif Intell 69:65–75 Hao SF, Shi CY, Niu ZD, Cao LB (2018) Concept coupling learning for improving concept lattice-based document retrieval. Eng Appl Artif Intell 69:65–75
Zurück zum Zitat Kumar CA, Srinivas S (2010) Concept lattice reduction using fuzzy K-means clustering. Expert Syst Appl 37(3):2696–2704 Kumar CA, Srinivas S (2010) Concept lattice reduction using fuzzy K-means clustering. Expert Syst Appl 37(3):2696–2704
Zurück zum Zitat Kang XP, Li DY, WangS S, Qu KS (2012) Formal concept analysis based on fuzzy granularity base for different granulations. Fuzzy Sets Syst 203:33–48MathSciNetMATH Kang XP, Li DY, WangS S, Qu KS (2012) Formal concept analysis based on fuzzy granularity base for different granulations. Fuzzy Sets Syst 203:33–48MathSciNetMATH
Zurück zum Zitat Kardos F, Pócs J, Pócsová J (2016) On concept reduction based on some graph properties. Knowl-Based Syst 93:67–74 Kardos F, Pócs J, Pócsová J (2016) On concept reduction based on some graph properties. Knowl-Based Syst 93:67–74
Zurück zum Zitat Liu M, Shao MW, Zhang WX, Wu C (2007) Reduction method for concept lattices based on rough set theory and its application. Comput Math Appl 53(9):1390–1410MathSciNetMATH Liu M, Shao MW, Zhang WX, Wu C (2007) Reduction method for concept lattices based on rough set theory and its application. Comput Math Appl 53(9):1390–1410MathSciNetMATH
Zurück zum Zitat Li JH, Mei CL, Lv YJ (2011) A heuristic knowledge-reduction method for decision formal contexts. Comput Math Appl 61(4):1096–1106MathSciNetMATH Li JH, Mei CL, Lv YJ (2011) A heuristic knowledge-reduction method for decision formal contexts. Comput Math Appl 61(4):1096–1106MathSciNetMATH
Zurück zum Zitat Li JH, Mei CL, Lv YJ (2011) Knowledge reduction in decision formal contexts. Knowl-Based Syst 24(5):709–715MATH Li JH, Mei CL, Lv YJ (2011) Knowledge reduction in decision formal contexts. Knowl-Based Syst 24(5):709–715MATH
Zurück zum Zitat Li JH, Mei CL, Lv YJ (2012) Knowledge reduction in formal decision contexts based on an order-preserving mapping. Int J Gen Syst 41(2):143–161MathSciNetMATH Li JH, Mei CL, Lv YJ (2012) Knowledge reduction in formal decision contexts based on an order-preserving mapping. Int J Gen Syst 41(2):143–161MathSciNetMATH
Zurück zum Zitat 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
Zurück zum Zitat Li JH, Xie B, Mi JS, Li MZ (2017) On the use of cut set for attribute reduction in L-fuzzy concept lattice. In: International conference on machine learning and cybernetics. IEEE, pp 323–330 Li JH, Xie B, Mi JS, Li MZ (2017) On the use of cut set for attribute reduction in L-fuzzy concept lattice. In: International conference on machine learning and cybernetics. IEEE, pp 323–330
Zurück zum Zitat Li JY, Wang X, Wu WZ, Xu YH (2016) Attribute reduction in inconsistent formal decision contexts based on congruence relations. Int J Mach Learn Cybern 8(1):1–14 Li JY, Wang X, Wu WZ, Xu YH (2016) Attribute reduction in inconsistent formal decision contexts based on congruence relations. Int J Mach Learn Cybern 8(1):1–14
Zurück zum Zitat Li KW, Shao MW, Wu WZ (2017) A data reduction method in formal fuzzy contexts. Int J Mach Learn Cybern 8(4):1145–1155 Li KW, Shao MW, Wu WZ (2017) A data reduction method in formal fuzzy contexts. Int J Mach Learn Cybern 8(4):1145–1155
Zurück zum Zitat Lang GM, Miao DQ, Cai MJ, Zhang ZF (2017) Incremental approaches for updating reducts in dynamic covering information systems. Knowl-Based Syst 134:85–104 Lang GM, Miao DQ, Cai MJ, Zhang ZF (2017) Incremental approaches for updating reducts in dynamic covering information systems. Knowl-Based Syst 134:85–104
Zurück zum Zitat Li LF, Zhang DX (2019) 0–1 linear integer programming method for granule knowledge reduction and attribute reduction in concept lattices. Soft Comput 23(2):383–391MATH Li LF, Zhang DX (2019) 0–1 linear integer programming method for granule knowledge reduction and attribute reduction in concept lattices. Soft Comput 23(2):383–391MATH
Zurück zum Zitat Martin TP, Rahim NHA, Majidian A (2013) A general approach to the measurement of change in fuzzy concept lattices. Soft Comput 17(12):2223–2234MATH Martin TP, Rahim NHA, Majidian A (2013) A general approach to the measurement of change in fuzzy concept lattices. Soft Comput 17(12):2223–2234MATH
Zurück zum Zitat Ma JM, Leung Y, Zhang WX (2014) Attribute reductions in object-oriented concept lattices. Int J Mach Learn Cybern 5(5):789–813 Ma JM, Leung Y, Zhang WX (2014) Attribute reductions in object-oriented concept lattices. Int J Mach Learn Cybern 5(5):789–813
Zurück zum Zitat Ma JM, Cai MJ, Zou CJ (2017) Concept acquisition approach of object-oriented concept lattices. Int J Mach Learn Cybern 8(1):123–134 Ma JM, Cai MJ, Zou CJ (2017) Concept acquisition approach of object-oriented concept lattices. Int J Mach Learn Cybern 8(1):123–134
Zurück zum Zitat Qi JJ (2009) Attribute reduction in formal contexts based on a new discernibility matrix. J Appl Math Comput 30(1–2):305–314MathSciNetMATH Qi JJ (2009) Attribute reduction in formal contexts based on a new discernibility matrix. J Appl Math Comput 30(1–2):305–314MathSciNetMATH
Zurück zum Zitat Rajapakse RK, Denham M (2006) Text retrieval with more realistic concept matching and reinforcement learning. Inf Proces Manag 42(5):1260–1275 Rajapakse RK, Denham M (2006) Text retrieval with more realistic concept matching and reinforcement learning. Inf Proces Manag 42(5):1260–1275
Zurück zum Zitat Shao MW, Leung Y, Wu WZ (2014) Rule acquisition and complexity reduction in formal decision contexts. Int J Approx Reason 55(1):259–274MathSciNetMATH Shao MW, Leung Y, Wu WZ (2014) Rule acquisition and complexity reduction in formal decision contexts. Int J Approx Reason 55(1):259–274MathSciNetMATH
Zurück zum Zitat Shao MW, Leung Y (2014) Relations between granular reduct and dominance reduct in formal contexts. Knowl-Based Syst 65:1–11 Shao MW, Leung Y (2014) Relations between granular reduct and dominance reduct in formal contexts. Knowl-Based Syst 65:1–11
Zurück zum Zitat Shao MW, Leung Y, Wang XZ, Wu WZ (2016) Granular reducts of formal fuzzy contexts. Knowl-Based Syst 114:156–166 Shao MW, Leung Y, Wang XZ, Wu WZ (2016) Granular reducts of formal fuzzy contexts. Knowl-Based Syst 114:156–166
Zurück zum Zitat Tan AH, Li JJ, Lin GP (2015) Connections between covering-based rough sets and concept lattices. Int J Approx Reason 56:43–58MathSciNetMATH Tan AH, Li JJ, Lin GP (2015) Connections between covering-based rough sets and concept lattices. Int J Approx Reason 56:43–58MathSciNetMATH
Zurück zum Zitat Valtchev P, Missaoui R, Godin R (2004) Formal concept analysis for knowledge discovery and data mining: the new challenges. In: International conference on formal concept analysis, Springer, Berlin, Heidelberg, pp 352–371 Valtchev P, Missaoui R, Godin R (2004) Formal concept analysis for knowledge discovery and data mining: the new challenges. In: International conference on formal concept analysis, Springer, Berlin, Heidelberg, pp 352–371
Zurück zum Zitat Wille R (1982) Restructuring lattice theory: an approach based on hierarachies of concepts. In: Rival I (ed) Oredered sets. Reidel, Dordrecht, pp 445–470 Wille R (1982) Restructuring lattice theory: an approach based on hierarachies of concepts. In: Rival I (ed) Oredered sets. Reidel, Dordrecht, pp 445–470
Zurück zum Zitat Will R (2005) Formal concept analysis as mathematical theory of concepts and concept hierarchies, Formal concept analysis, Ganter B et al, des., Springer-Verlag, pp 1–33 Will R (2005) Formal concept analysis as mathematical theory of concepts and concept hierarchies, Formal concept analysis, Ganter B et al, des., Springer-Verlag, pp 1–33
Zurück zum Zitat Wille R (2002) Why can concept lattices support knowledge discovery in databases? J Exp Theor Artif Intell 14(2–3):81–92MATH Wille R (2002) Why can concept lattices support knowledge discovery in databases? J Exp Theor Artif Intell 14(2–3):81–92MATH
Zurück zum Zitat Wei L, Qi JJ, Zhang WX (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 JJ, Zhang WX (2008) Attribute reduction theory of concept lattice based on decision formal contexts. Sci China Ser F Inf Sci 51(7):910–923MathSciNetMATH
Zurück zum Zitat 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
Zurück zum Zitat Wei L, Qi JJ (2010) Relation between concept lattice reduction and rough set reduction. Knowl-Based Syst 23(8):934–938 Wei L, Qi JJ (2010) Relation between concept lattice reduction and rough set reduction. Knowl-Based Syst 23(8):934–938
Zurück zum Zitat Yang B, Hu BQ (2018) Matrix representations and interdependency on L-fuzzy covering-based approximation operators. Int J Approx Reason 96:57–77MathSciNetMATH Yang B, Hu BQ (2018) Matrix representations and interdependency on L-fuzzy covering-based approximation operators. Int J Approx Reason 96:57–77MathSciNetMATH
Zurück zum Zitat Zhao HM, Liu HD, Xu JJ, Deng W (2019) Performance prediction using high-order differential mathematical morphology gradient spectrum entropy and extreme learning machine. IEEE Trans Instrum Meas 1–1 Zhao HM, Liu HD, Xu JJ, Deng W (2019) Performance prediction using high-order differential mathematical morphology gradient spectrum entropy and extreme learning machine. IEEE Trans Instrum Meas 1–1
Zurück zum Zitat Zhang WX, Wei L, Qi JJ (2005) Attribute reduction in concept lattice based on discernibility matrix. International workshop on rough sets, fuzzy sets, data mining, and granular-soft computing. Springer, Berlin, pp 157–165MATH Zhang WX, Wei L, Qi JJ (2005) Attribute reduction in concept lattice based on discernibility matrix. International workshop on rough sets, fuzzy sets, data mining, and granular-soft computing. Springer, Berlin, pp 157–165MATH
Zurück zum Zitat Zhang WX, Wei L, Qi JJ (2005) Attribute reduction theory and approach to concept lattice. Sci China Ser F Inf Sci 48(6):713–726MathSciNetMATH Zhang WX, Wei L, Qi JJ (2005) Attribute reduction theory and approach to concept lattice. Sci China Ser F Inf Sci 48(6):713–726MathSciNetMATH
Metadaten
Titel
Granular matrix method of attribute reduction in formal contexts
verfasst von
Yidong Lin
Jinjin Li
Hongkun Wang
Publikationsdatum
28.04.2020
Verlag
Springer Berlin Heidelberg
Erschienen in
Soft Computing / Ausgabe 21/2020
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-020-04941-5

Weitere Artikel der Ausgabe 21/2020

Soft Computing 21/2020 Zur Ausgabe

Methodologies and Application

Perturbation-based classifier

Premium Partner