Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
International Journal of Machine Learning and Cybernetics
Published in: International Journal of Machine Learning and Cybernetics 6/2013

01-12-2013 | Original Article

Two kinds of multi-level formal concepts and its application for sets approximations

Authors: Mingwen Shao, Hongzhi Yang

Published in: International Journal of Machine Learning and Cybernetics | Issue 6/2013

Log in

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

search-config
loading …

Abstract

In this paper, we introduce two pairs of operators in fuzzy formal contexts. Based on the proposed operators, we present two kinds of multi-level formal concepts. We also propose two pairs of rough approximation operators by employing the two kinds of multi-level formal concepts. By the proposed rough set approximation operators, we not only approximate a crisp set, but also approximate a fuzzy set. Finally, we discuss the properties of the proposed approximation operators in details.
previous article A variational Bayesian framework for group feature selection
next article Fuzzy rough set models over two universes

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!

inform now

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!

inform now

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!

inform now
Show more products
Literature
1.
2.
3.
Belohlavek R (2007) A note on variable threshold concept lattices: threshold-based operators are reducible to classical concept-forming operators. Inf Sci 177(15):3186–3191MathSciNetCrossRefMATH
4.
Burusco A, Fuentes-González R (2000) Concept lattices defined from implication operators. Fuzzy Sets Syst 114(3):431–436CrossRefMATH
5.
Carpineto C, Romano G (1996) A lattice conceptual clustering system and its application to browsing retrieval. Mach Learn 10:95–122
6.
7.
Chen DG, Zhao SY (2010) Local reduction of decision system with fuzzy rough sets. Fuzzy Sets Syst 161(13):1871–1883CrossRefMATH
8.
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 163:253–262MathSciNetCrossRefMATH
9.
Elloumi S, Jaoua A (2000) Automatic classification using fuzzy concepts. in: Proceedings of JCIS 2000, Atlantic City, vol 1, pp 276–279
10.
Faid M, Missaoi R, Godin R (1997) Mining complex structures using context concatenation in formal concept analysis. International KRUSE symposium, Vancouver
11.
Gediga G, Duntsch I (2002) Modal-style operators in qualitative data analysis. In: Proceedings of the 2002 IEEE international conference on data mining, pp 155–162
12.
Gediga B, Wille R (1999) Formal concept analysis. Mathematic foundations. Springer, Berlin
13.
14.
Godin R, Missaoi R (1994) An incremental concept formation approach for learning from databases. Theoret Comput Sci 133:387–419CrossRefMATH
15.
Harms SK, Deogum JS (2004) Sequential association rule mining with time lags. J Intell Inf Syst 22(1):7–22CrossRef
16.
Kwon O, Kim J (2009) Concept lattices for visualizing and generating user profiles for context-aware service recommendations. Expert Syst Appl 36:1893–1902CrossRef
17.
Jaoua A, Elloumi S (2002) Galois connection, formal concepts and Galois lattice in real relations: application in a real classifier. J Syst Softw 60:149–163CrossRef
18.
Lai HL, Zhang DX (2009) Concept lattices of fuzzy contexts: formal concept analysis vs. rough set theory. Int J Approx Reason 50:695–707MathSciNetCrossRefMATH
19.
Li LF, Zhang JK (2010) Attribute reduction in fuzzy concept lattices based on the T implication. Knowl Based Syst 23:497–503CrossRef
20.
Liu HW, Liu L, Zhang HJ (2011) A fast pruning redundant rule method using Galois connection. Appl Soft Comput 11:130–137CrossRef
21.
22.
Mi JS, Leung Y, Wu WZ (2010) Approaches to attribute reduction in concept lattices induced by axialities. Knowl Based Syst 23:504–511CrossRef
23.
24.
25.
Popescu A (2001) A general approach to fuzzy concept. Math Logic Q 50(3):1–17
26.
27.
Saquer J, Deogun JS (1999) Formal rough concept analysis, new directions in rough sets, data mining, and granular-soft. Lecture Notes in Computer science, vol 1711, Springer, pp 91–99
28.
Shao MW, Zhang WX (2005) The set approximation in formal contexts. Lecture Notes in Computer science, vol 3641, Springer, pp 43–53
29.
Wang X, Zhang WX (2008) Relations of attribute reduction between object and property oriented concept lattices. Knowl Based Syst 21(5):398–403CrossRef
30.
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):910–923MathSciNetCrossRef
31.
Wille R (1982) Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival (ed) Ordered sets, I. Reidel, Dordrecht, pp 445–470
32.
Wille R (1989) Knowledge acquisition by methods of formal concept analysis. In: Diday E (ed) Data analysis, learning symbolic and numeric knowledge. Nova Science, New York, pp 365–380
33.
Wolff KE (2001) A conceptual view of knowledge bases in rough set theory. Rough sets and current trends in computing, Second international Conference, RSCTC 2000. Lecture Notes in Computer Science, vol 2005, Springer, pp 220–228
34.
Wu WZ (2008) Attribute reduction based on evidence theory in incomplete decision systems. Inf Sci 178(5):1355–1371CrossRefMATH
35.
36.
Wu WZ, Leung Y, Mi JS (2009) Granular computing and knowledge reduction in formal contexts. IEEE Trans Knowl Data Eng 21(10):1461–1474CrossRef
37.
Xu WH, Zhang XY, Zhang WX (2009) Knowledge granulation, knowledge entropy and knowledge uncertainty measure in ordered information systems. Appl Soft Comput 9(4):1244–1251CrossRef
38.
39.
Yao YY (2004) Concept lattices in rough set theory. In: Proceedings of 2004 annual meeting of the North American Fuzzy Information Processing Society, pp 796–801
40.
Yao YY, Chen Y (2004) Rough set approximations in formal concept analysis. In: Proceedings of 2004 annual meeting of the North American Fuzzy Information Processing Society, pp 73–78
41.
42.
Zhang WX, Wei L, Qi JJ (2005) Attribute reduction theory and approach of concept lattices. Sci China Ser E Inf Sci 35(6):628–639MathSciNet
43.
Zhou L, Wu WZ (2008) On generalized intuitionistic fuzzy rough approximation operators. Inf Sci 178(11):2448–2465MathSciNetMATH
Metadata
Title
Two kinds of multi-level formal concepts and its application for sets approximations
Authors
Mingwen Shao
Hongzhi Yang
Publication date
01-12-2013
Publisher
Springer Berlin Heidelberg
Published in
International Journal of Machine Learning and Cybernetics / Issue 6/2013
Print ISSN: 1868-8071
Electronic ISSN: 1868-808X
DOI
https://doi.org/10.1007/s13042-012-0128-2

Other articles of this Issue 6/2013

International Journal of Machine Learning and Cybernetics 6/2013 Go to the issue

Original Article

On rule acquisition in decision formal contexts

Original Article

Properties of two types of covering-based rough sets

Original Article

An intuitionistic fuzzy weighted OWA operator and its application

Original Article

A fuzzy approach to multicriteria assignment problem using exponential membership functions

Original Article

Automatic non-interactive matting of dynamic targets in complex video using Graph Cuts

Original Article

A variational Bayesian framework for group feature selection