Skip to main content
SpringerLink
Log in
Book cover

Interactions Between Computational Intelligence and Mathematics pp 105–119Cite as

Generating Fuzzy Attribute Rules Via Fuzzy Formal Concept Analysis

  • Chapter
  • First Online:

Part of the book series: Studies in Computational Intelligence ((SCI,volume 758))

Abstract

Extracting knowledge from databases is a procedure which interest has increased in a wide variety of areas like stock market, medicine or census data, to name a few. A compact representation of this knowledge is given by rules. Formal concept analysis plays an important role in this area. This paper introduces a new kind of attribute implications considering the fuzzy notions of support and confidence and is also focused on the particular case in which the set of attributes are intensions. Moreover, an application to clustering for size reduction of concept lattices is included.

Partially supported by the State Research Agency (AEI) and the European Regional Development Fund (ERDF) projects TIN2015-65845-C3-3-R and TIN2016-76653-P.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Agrawal, R., Imielinski, T., Swami, A.: Mining association rules between sets of items in large databases. In: ACM SIGMOD International Conference on Management of Data, pp. 207–216 (1993)

    Google Scholar 

  2. Antoni, L., Krajci, S., Kridlo, O., Macek, B., Pisková, L.: On heterogeneous formal contexts. Fuzzy Sets Syst. 234, 22–33 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bělohlávek, R.: Lattices of fixed points of fuzzy Galois connections. Math. Logic Q. 47(1), 111–116 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  4. Belohlavek, R., Cordero, P., Enciso, M., Mora, A., Vychodil, V.: Automated prover for attribute dependencies in data with grades. Int. J. Approx. Reasoning 70, 51–67 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  5. Belohlávek, R., Vychodil, V.: Attribute dependencies for data with grades ii. Int. J. Gen. Syst. 46(1), 66–92 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  6. Butka, P., Pócs, J.: Generalization of one-sided concept lattices. Comput. Inform. 32(2), 355–370 (2013)

    MathSciNet  Google Scholar 

  7. Chertov, O., Aleksandrova, M.: Using association rules for searching levers of influence in census data. Procedia Soc. Behav. Sci. 73(0), 475–478 (2013), In: Proceedings of the 2nd International Conference on Integrated Information (IC-ININFO 2012), Budapest, Hungary, 30 Aug–3 Sept 2012

    Google Scholar 

  8. Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations, Springer, New York (2012)

    Google Scholar 

  9. Ge, X., Wang, P., Yun, Z.: The rough membership functions on four types of covering-based rough sets and their applications. Inf. Sci. 390, 1–14 (2017)

    Article  MathSciNet  Google Scholar 

  10. Glodeanu, C.V.: Knowledge discovery in data sets with graded attributes. Int. J. Gen. Syst. 45(2), 232–249 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  11. Hill, J., Walkington, H., France, D.: Graduate attributes: implications for higher education practice and policy. J. Geogr. High. Educ. 40(2), 155–163 (2016)

    Article  Google Scholar 

  12. Ikram, A., Qamar, U.: Developing an expert system based on association rules and predicate logic for earthquake prediction. Knowl. Based Syst. 75, 87–103 (2015)

    Article  Google Scholar 

  13. Kianmehr, K., Alhajj, R.: Carsvm: a class association rule-based classification framework and its application to gene expression data. Artif. Intell. Med. 44(1), 7–25 (2008)

    Article  Google Scholar 

  14. Krajči, S.: A generalized concept lattice. Logic J. IGPL 13(5), 543–550 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  15. Kuhr, T., Vychodil, V.: Fuzzy logic programming reduced to reasoning with attribute implications. Fuzzy Sets Syst. 262, 1–20 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  16. Lu, H., Han, J., Feng, L.: Stock movement prediction and n-dimensional inter-transaction association rules. In: Proceedings of the ACM SIGMOD Workshop on Research Issues in Data Mining and Knowledge Discovery, p. 12 (1998)

    Google Scholar 

  17. Luxenburger, M.: Implications partielles dans un contexte. Mathématiques, Informatique et Sciences Humaines 29(113), 35–55 (1991)

    MathSciNet  MATH  Google Scholar 

  18. Malerba, D., Lisi, F.A., Sblendorio, F.: Mining spatial association rules in census data: a relational approach. In: Proceeding of the ECML/PKDD?02 workshop on Mining Official Data, University Printing House, Helsinki, Citeseer (2002)

    Google Scholar 

  19. Medina, J., Ojeda-Aciego, M., Ruiz-Calviño, J.: Formal concept analysis via multi-adjoint concept lattices. Fuzzy Sets Syst. 160(2), 130–144 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  20. Nahar, J., Imam, T., Tickle, K.S., Chen, Y.-P.P.: Association rule mining to detect factors which contribute to heart disease in males and females. Expert Syst. Appl. 40(4), 1086–1093 (2013)

    Article  Google Scholar 

  21. Ordonez, C., Santana, C., de Braal, L.: Discovering interesting association rules in medical data. In: Proceedings of ACM SIGMOD Workshop on Research Issues on Data Mining and Knowledge Discovery, pp. 78–85 (2000)

    Google Scholar 

  22. Paranjape-Voditel, P., Deshpande, U.: An association rule mining based stock market recommender system. In: 2011 Second International Conference on Emerging Applications of Information Technology (EAIT), pp. 21–24, Feb 2011

    Google Scholar 

  23. Popescu, A.: A general approach to fuzzy concepts. Math. Logic Q. 50(3), 265–280 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  24. Rai, S., Sharma, S.: Determining minimum spanning tree in an undirected weighted graph. In: 2015 International Conference on Advances in Computer Engineering and Applications (ICACEA), pp. 637–642, Mar 2015

    Google Scholar 

  25. Rudin, C., Letham, B., Salleb-Aouissi, A., Kogan, E., Madigan, D.: Sequential event prediction with association rules. In: 24th Annual Conference on Learning Theory (COLT 2011), pp. 615–634, July 2011

    Google Scholar 

  26. Vychodil, V.: Computing sets of graded attribute implications with witnessed non-redundancy (2015). arxiv: CoRRabs/1511.01640

  27. Vychodil, V.: Rational fuzzy attribute logic (2015). arxiv: CoRRabs/1502.07326

  28. Vychodil, V.: Computing sets of graded attribute implications with witnessed non-redundancy. Inf. Sci. 351, 90–100 (2016)

    Article  MathSciNet  Google Scholar 

  29. Wang, W., Wang, Y., Bañares-Alcántara, R., Cui, Z., Coenen, F.: Application of classification association rule mining for mammalian mesenchymal stem cell differentiation. In: Perner, P. (ed.) Advances in Data Mining. Applications and Theoretical Aspects, Volume 5633 of Lecture Notes in Computer Science, pp. 51–61. Springer, Berlin Heidelberg (2009)

    Google Scholar 

  30. Yang, B., Hu, B.O.: On some types of fuzzy covering-based rough sets. Fuzzy Sets Syst. 312, 36–65 (2017) (Theme: Fuzzy Rough Sets)

    Google Scholar 

  31. Zadeh, L.A.: Fuzzy logic. Computer 21(4), 83–93 (1988)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Cádiz, Cadiz, Spain

    Valentín Liñeiro-Barea & Jesús Medina

  2. Department of Computer Engineering, University of Cádiz, Cadiz, Spain

    Inmaculada Medina-Bulo

Authors
  1. Valentín Liñeiro-Barea
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jesús Medina
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Inmaculada Medina-Bulo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jesús Medina .

Editor information

Editors and Affiliations

  1. Faculty of Engineering Sciences, Széchenyi István University, Gyõr, Hungary

    László T. Kóczy

  2. Departamento de Matemáticas, Facultad de Ciencias, Universidad de Cádiz, Puerto Real, Cádiz, Spain

    Jesús Medina

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Liñeiro-Barea, V., Medina, J., Medina-Bulo, I. (2018). Generating Fuzzy Attribute Rules Via Fuzzy Formal Concept Analysis. In: Kóczy, L., Medina, J. (eds) Interactions Between Computational Intelligence and Mathematics. Studies in Computational Intelligence, vol 758. Springer, Cham. https://doi.org/10.1007/978-3-319-74681-4_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-74681-4_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-74680-7

  • Online ISBN: 978-3-319-74681-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation