Skip to main content
Top
Published in: Soft Computing 19/2019

13-03-2019 | Foundations

A theoretical study on the object (property) oriented concept lattices based on three-way decisions

Authors: Ting Qian, Ling Wei, Jianjun Qi

Published in: Soft Computing | Issue 19/2019

Log in

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

search-config
loading …

Abstract

The three-way object oriented lattice and the three-way property oriented lattice are extend researches of rough concept analysis by combining three-way decisions. In this paper, we investigate them more comprehensively and detailedly. Firstly, the relationship between the object (property) oriented concept lattice and the three-way object (property) oriented concept lattice is studied, respectively. In addition, approaches to construct two types of three-way concept lattices based on apposition and subposition of formal contexts are given based on these relationships. Finally, since the methods for constructing three-way concept lattices and three-way object oriented and property oriented concept lattices are similar, the connections among them are discussed.

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 "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!

Literature
go back to reference Belohlavek R, Sigmund E, Zacpal J (2011) Evaluation of IPAQ questionnaires supported by formal concept analysis. Inf Sci 181(10):1774–1786MathSciNetCrossRef Belohlavek R, Sigmund E, Zacpal J (2011) Evaluation of IPAQ questionnaires supported by formal concept analysis. Inf Sci 181(10):1774–1786MathSciNetCrossRef
go back to reference Burusco A, Fuentes-Gonzalez R (1994) The study of the L-fuzzy concept lattice. Mathw Soft Comput 3:209–218MathSciNetMATH Burusco A, Fuentes-Gonzalez R (1994) The study of the L-fuzzy concept lattice. Mathw Soft Comput 3:209–218MathSciNetMATH
go back to reference Cho WC, Richards W (2004) Improvement of precision and recall for information retrieval in a narrow domain: reuse of concepts by formal concept analysis. In: IEEE/WIC/ACM international conference on web intelligence, (WI04), pp 370–376 Cho WC, Richards W (2004) Improvement of precision and recall for information retrieval in a narrow domain: reuse of concepts by formal concept analysis. In: IEEE/WIC/ACM international conference on web intelligence, (WI04), pp 370–376
go back to reference Ciucci D, Dubois D, Lawry J (2014) Borderline vs. unknown: comparing three-valued representations of imperfect information. Int J Approx Reason 55:1866–1889MathSciNetCrossRefMATH Ciucci D, Dubois D, Lawry J (2014) Borderline vs. unknown: comparing three-valued representations of imperfect information. Int J Approx Reason 55:1866–1889MathSciNetCrossRefMATH
go back to reference Düntsch I, Gediga G (2002) Modal-style operators in qualitative data analysis. In: Proceedings of 2002 IEEE international conference on data mining, pp 155–162 Düntsch I, Gediga G (2002) Modal-style operators in qualitative data analysis. In: Proceedings of 2002 IEEE international conference on data mining, pp 155–162
go back to reference Ganapathy V, King D, Jaeger T, Jha S (2007) Mining security sensitive operations in legacy code using concept analysis. In: the 29th international conference on software engineering, pp 458–467 Ganapathy V, King D, Jaeger T, Jha S (2007) Mining security sensitive operations in legacy code using concept analysis. In: the 29th international conference on software engineering, pp 458–467
go back to reference Ganter B, Kuznetsov SO (2001) Pattern structures and their projections. In: Delugach HS, Stumme G (eds) Conceptual structures: broadening the base. ICCS 2001. Lecture Notes in Computer Science, vol 2120. Springer, Berlin, pp 129–142 Ganter B, Kuznetsov SO (2001) Pattern structures and their projections. In: Delugach HS, Stumme G (eds) Conceptual structures: broadening the base. ICCS 2001. Lecture Notes in Computer Science, vol 2120. Springer, Berlin, pp 129–142
go back to reference Ganter B, Wille R (1999) Formal concept analysis. mathematical foundations. Springer, BerlinCrossRefMATH Ganter B, Wille R (1999) Formal concept analysis. mathematical foundations. Springer, BerlinCrossRefMATH
go back to reference Godin R (1995) Incremental concept formal algorithm based on Galois (concept) lattices. Comput Intell 11:246–267CrossRef Godin R (1995) Incremental concept formal algorithm based on Galois (concept) lattices. Comput Intell 11:246–267CrossRef
go back to reference 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 83:218–242MathSciNetCrossRefMATH 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 83:218–242MathSciNetCrossRefMATH
go back to reference Jaoua A, Elloumi S (2002) Galois connection, formal concepts and Galois lattice in real relations: application in a real classiffer. J Syst Softw 60:149–163CrossRef Jaoua A, Elloumi S (2002) Galois connection, formal concepts and Galois lattice in real relations: application in a real classiffer. J Syst Softw 60:149–163CrossRef
go back to reference Kent RE (1996) Rough concept analysis: a synthesis of rough sets and formal concept analysis. Fundam Inf 27:169–181MathSciNetMATH Kent RE (1996) Rough concept analysis: a synthesis of rough sets and formal concept analysis. Fundam Inf 27:169–181MathSciNetMATH
go back to reference Li JH, Mei CL, Lv YJ (2013) Incomplete decision contexts: approximate concept construction, rule acquisition and knowledge reduction. Int J Approx Reason 54(1):149–165MathSciNetCrossRefMATH Li JH, Mei CL, Lv YJ (2013) Incomplete decision contexts: approximate concept construction, rule acquisition and knowledge reduction. Int J Approx Reason 54(1):149–165MathSciNetCrossRefMATH
go back to reference Li JH, Mei CL, Wang JH (2015) On inference rules in decision formal contexts. Int J Comput Intell Syst 8(1):175–186MathSciNetCrossRef Li JH, Mei CL, Wang JH (2015) On inference rules in decision formal contexts. Int J Comput Intell Syst 8(1):175–186MathSciNetCrossRef
go back to reference Liang JY, Wang JH (2006) A new lattice structure and method for extracting association rules based on concept lattice. Int J Comput Sci Netw Secur 6(11):107–114 Liang JY, Wang JH (2006) A new lattice structure and method for extracting association rules based on concept lattice. Int J Comput Sci Netw Secur 6(11):107–114
go back to reference Ma JM, Cai MJ (2017) Concept acquisition approach of object-oriented concept lattices. Int J Mach Learn Cybern 8:123–134CrossRef Ma JM, Cai MJ (2017) Concept acquisition approach of object-oriented concept lattices. Int J Mach Learn Cybern 8:123–134CrossRef
go back to reference Mao H (2017) Representing attribute reduction and concepts in concept lattice using graphs. Soft Comput 21:7293–7311CrossRefMATH Mao H (2017) Representing attribute reduction and concepts in concept lattice using graphs. Soft Comput 21:7293–7311CrossRefMATH
go back to reference Mi JS, Leung Y, Wu WZ (2010) Approaches to attribute reduction in concept lattices induced by axialities. Knowl Based Syst 23(6):504–511CrossRef Mi JS, Leung Y, Wu WZ (2010) Approaches to attribute reduction in concept lattices induced by axialities. Knowl Based Syst 23(6):504–511CrossRef
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 185:114–127MathSciNetCrossRefMATH Outrata J, Vychodil V (2012) Fast algorithm for computing fixpoints of Galois connections induced by object-attribute relational data. Inf Sci 185:114–127MathSciNetCrossRefMATH
go back to reference Poelmans J, Ignatov DI, Kuznetsov SO, Dedene G (2014) Fuzzy and rough formal concept analysis: A survey. Int J Gen Syst 43:105–134MathSciNetCrossRefMATH Poelmans J, Ignatov DI, Kuznetsov SO, Dedene G (2014) Fuzzy and rough formal concept analysis: A survey. Int J Gen Syst 43:105–134MathSciNetCrossRefMATH
go back to reference Qi JJ, Wei L, Yao YY (2014) Three-way formal concept analysis. In: Miao D, Pedrycz W, Ślȩzak D, Peters G, Hu Q, Wang R (eds) Rough set and knowledge technology, volume 8818, Lecture Notes in Computer Science. Spring, Cham, pp 732–741 Qi JJ, Wei L, Yao YY (2014) Three-way formal concept analysis. In: Miao D, Pedrycz W, Ślȩzak D, Peters G, Hu Q, Wang R (eds) Rough set and knowledge technology, volume 8818, Lecture Notes in Computer Science. Spring, Cham, pp 732–741
go back to reference Qi JJ, Qian T, Wei L (2016) The connections between three-way and classical concept lattices. Knowl Based Syst 91:143–151CrossRef Qi JJ, Qian T, Wei L (2016) The connections between three-way and classical concept lattices. Knowl Based Syst 91:143–151CrossRef
go back to reference Qian T, Wei L, Qi JJ (2017) Constructing three-way concept lattices based on apposition andsubposition of formal contexts. Knowl Based Syst 116:39–48CrossRef Qian T, Wei L, Qi JJ (2017) Constructing three-way concept lattices based on apposition andsubposition of formal contexts. Knowl Based Syst 116:39–48CrossRef
go back to reference Qian T, Wei L (2014) A novel concept acquisition approach based on formal contexts. Sci World J 1:1–7CrossRef Qian T, Wei L (2014) A novel concept acquisition approach based on formal contexts. Sci World J 1:1–7CrossRef
go back to reference Rodriguez-Jimenez JM, Cordero P, Enciso M, Mora A (2014) Negative attributes and implications in formal concept analysis. Procedia Comput Sci 31:758–765CrossRef Rodriguez-Jimenez JM, Cordero P, Enciso M, Mora A (2014) Negative attributes and implications in formal concept analysis. Procedia Comput Sci 31:758–765CrossRef
go back to reference Shao MW, Leung Y (2014) Relations between granular reduct and dominance reduct in formal contexts. Knowl Based Syst 65:1–11CrossRef Shao MW, Leung Y (2014) Relations between granular reduct and dominance reduct in formal contexts. Knowl Based Syst 65:1–11CrossRef
go back to reference Shao MW, Leung Y, Wu WZ (2014) Rule acquisition and complexity reduction in formal decision contexts. Int J Approx Reason 55:259–274MathSciNetCrossRefMATH Shao MW, Leung Y, Wu WZ (2014) Rule acquisition and complexity reduction in formal decision contexts. Int J Approx Reason 55:259–274MathSciNetCrossRefMATH
go back to reference Shao MW, Yang HZ, Wu WZ (2015) Knowledge reduction in formal fuzzy contexts. Knowl Based Syst 3:265–275CrossRef Shao MW, Yang HZ, Wu WZ (2015) Knowledge reduction in formal fuzzy contexts. Knowl Based Syst 3:265–275CrossRef
go back to reference Shivhare R, Cherukuri AK (2017) Three-way conceptual approach for cognitive memory functionalities. Int J Mach Learn Cybern 8(1):21–34CrossRef Shivhare R, Cherukuri AK (2017) Three-way conceptual approach for cognitive memory functionalities. Int J Mach Learn Cybern 8(1):21–34CrossRef
go back to reference Tang YQ, Fan M, Li JH (2016) An information fusion technology for triadic decision contexts. Int J Mach Learn Cybern 1(7):13–24CrossRef Tang YQ, Fan M, Li JH (2016) An information fusion technology for triadic decision contexts. Int J Mach Learn Cybern 1(7):13–24CrossRef
go back to reference Tonella P (2003) Using a concept lattice of decomposition slices for program understanding and impact analysis. IEEE Trans Softw Eng 29:495–509CrossRef Tonella P (2003) Using a concept lattice of decomposition slices for program understanding and impact analysis. IEEE Trans Softw Eng 29:495–509CrossRef
go back to reference Wei L, Qian T (2015) The three-way object oriented concept lattice and three-way property oriented concept lattice. In: Proceedings of the 2015 international conference on machine learning and cybernetics, pp 854–859 Wei L, Qian T (2015) The three-way object oriented concept lattice and three-way property oriented concept lattice. In: Proceedings of the 2015 international conference on machine learning and cybernetics, pp 854–859
go back to reference Wille R (1982) Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival I (ed) Ordered sets. Reidel, Dordrecht, pp 445–470CrossRef Wille R (1982) Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival I (ed) Ordered sets. Reidel, Dordrecht, pp 445–470CrossRef
go back to reference Yang HL, Guo ZL (2015) Multigranulation decision-theoretic rough sets in incomplete information systems. Int J Mach Learn Cybern 6(6):1005–1018CrossRef Yang HL, Guo ZL (2015) Multigranulation decision-theoretic rough sets in incomplete information systems. Int J Mach Learn Cybern 6(6):1005–1018CrossRef
go back to reference Yao YY (2004) A comparative study of formal concept analysis and rough set theory in data analysis. In: Tsumoto S, Słowiński R, Komorowski J, Grzymała-Busse JW (eds) Rough sets and current trends in computing RSCTC 2004 Lecture Notes in Artificial Intelligence, vol 3066. Springer, Berlin, pp 59–68 Yao YY (2004) A comparative study of formal concept analysis and rough set theory in data analysis. In: Tsumoto S, Słowiński R, Komorowski J, Grzymała-Busse JW (eds) Rough sets and current trends in computing RSCTC 2004 Lecture Notes in Artificial Intelligence, vol 3066. Springer, Berlin, pp 59–68
go back to reference Yao YY (2012) An outline of a theory of three-way decisions. In: Yao J et al (eds) Rough set and knowledge technology, volume 7413, Lecture Notes in Computer Science. Springer, Berlin, pp 1–17 Yao YY (2012) An outline of a theory of three-way decisions. In: Yao J et al (eds) Rough set and knowledge technology, volume 7413, Lecture Notes in Computer Science. Springer, Berlin, pp 1–17
go back to reference Yao YY (2017) Interval sets and three-way concept analysis in incomplete contexts. Int J Mach Learn Cybern 8:3–20CrossRef Yao YY (2017) Interval sets and three-way concept analysis in incomplete contexts. Int J Mach Learn Cybern 8:3–20CrossRef
go back to reference Yu H, Liu ZG, Wang GY (2014) An automatic method to determine the number of clusters using decision-theretic rough sets. Int J Approx Reason 55(1):101–115CrossRefMATH Yu H, Liu ZG, Wang GY (2014) An automatic method to determine the number of clusters using decision-theretic rough sets. Int J Approx Reason 55(1):101–115CrossRefMATH
go back to reference Zhang HR, Min F (2016) Three-way recommender systems based on random forests. Knowl Based Syst 91:275–286CrossRef Zhang HR, Min F (2016) Three-way recommender systems based on random forests. Knowl Based Syst 91:275–286CrossRef
go back to reference Zhang WX, Yao YY, Leung Y (2006) Rough set and concept lattice. Xi’an Jiaotong University Press, Xi’an Zhang WX, Yao YY, Leung Y (2006) Rough set and concept lattice. Xi’an Jiaotong University Press, Xi’an
go back to reference Zhao SY, Chen H, Li CP, Du XY, Sun H (2015) A novel approach to building a robust fuzzy rough classifie. IEEE Trans Fuzzy Syst 4(23):769–786CrossRef Zhao SY, Chen H, Li CP, Du XY, Sun H (2015) A novel approach to building a robust fuzzy rough classifie. IEEE Trans Fuzzy Syst 4(23):769–786CrossRef
go back to reference Zou L, Zhang Z, Long J (2015) A fast incremental algorithm for constructing concept lattices. Expert Syst Appl 42:4474–4481CrossRef Zou L, Zhang Z, Long J (2015) A fast incremental algorithm for constructing concept lattices. Expert Syst Appl 42:4474–4481CrossRef
Metadata
Title
A theoretical study on the object (property) oriented concept lattices based on three-way decisions
Authors
Ting Qian
Ling Wei
Jianjun Qi
Publication date
13-03-2019
Publisher
Springer Berlin Heidelberg
Published in
Soft Computing / Issue 19/2019
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-019-03799-6

Other articles of this Issue 19/2019

Soft Computing 19/2019 Go to the issue

Premium Partner