Skip to main content
SpringerLink
Log in

How to Incorporate Excluding Features in Fuzzy Relational Compositions and What for

  • Conference paper
  • First Online:
Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 611))

Abstract

The aim of this paper is, first, to recall fuzzy relational compositions (products) and, to introduce an idea, how the so-called excluding features could be incorporated into the theoretical background. Apart from rather natural definitions, we provide readers with a theoretical investigation that provides and answer to a rather natural question, under which conditions, in terms of the underlying algebraic structures, the proposed incorporation of excluding features preserves the same properties as the incorporation in the classical relational compositions. The positive impact of the incorporation on reducing the suspicions provided by the basic “circlet” composition without losing the possibly correct suspicion, as in the case of the use of the Bandler-Kohout products, is demonstrated on an example.

M. Štěpnička—This research was partially supported by the NPU II project LQ1602 “IT4Innovations excellence in science” provided by the MŠMT.

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

Access this chapter

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

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Instead of the term composition, one may often encounter the term “product” denoting the same mappings or objects. This terminology naturally comes from the product-like matrix calculation of the compositions.

References

  1. Pedrycz, W.: Applications of fuzzy relational equations for methods of reasoning in presence of fuzzy data. Fuzzy Sets Syst. 16, 163–175 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  2. Štěpnička, M., Jayaram, B.: On the suitability of the Bandler-Kohout subproduct as an inference mechanism. IEEE Trans. Fuzzy Syst. 18(2), 285–298 (2010)

    Article  Google Scholar 

  3. Bandler, W., Kohout, L.: Semantics of implication operators and fuzzy relational products. Int. J. Man-Mach. Stud. 12(1), 89–116 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bandler, W., Kohout, L.: Relational-product architectures for information processing. Inf. Sci. 37, 25–37 (1985)

    Article  Google Scholar 

  5. Dubois, D., Prade, H.: Semantics of quotient operators in fuzzy relational databases. Fuzzy Sets Syst. 78, 89–93 (1996)

    Article  MathSciNet  Google Scholar 

  6. De Baets, B., Kerre, E.: Fuzzy relational compositions. Fuzzy Sets Syst. 60, 109–120 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  7. Běhounek, L., Daňková, M.: Relational compositions in fuzzy class theory. Fuzzy Sets Syst. 160(8), 1005–1036 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Novák, V., Perfilieva, I., Močkoř, J.: Mathematical Principles of Fuzzy Logic. Kluwer Academic Publishers, Boston (1999)

    Book  MATH  Google Scholar 

  9. Bandler, W., Kohout, L.: Fuzzy power sets and fuzzy implication operators. Fuzzy Sets Syst. 4, 183–190 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  10. Pedrycz, W.: Fuzzy relational equations with generalized connectives and their applications. Fuzzy Sets Syst. 10, 185–201 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  11. Chung, F., Lee, T.: Analytical resolution and numerical identification of fuzzy relational systems. IEEE Trans. Syst. Man Cybern. 28, 919–924 (1998)

    Article  Google Scholar 

  12. Štěpnička, M., Holčapek, M.: Fuzzy relational compositions based on generalized quantifiers. In: Laurent, A., Strauss, O., Bouchon-Meunier, B., Yager, R.R. (eds.) IPMU 2014, Part II. CCIS, vol. 443, pp. 224–233. Springer, Heidelberg (2014)

    Google Scholar 

  13. Cao, N., Štěpnička, M.: An existence of fuzzy relational compositions using generalized quantifiers. In: Proceedings of the 16th World Congress of the International Fuzzy Systems Association (IFSA), 9th Conference of the European Society for Fuzzy-Logic, Technology (EUSFLAT). Advances in Intelligent Systems Research, vol. 89, pp. 49–58. Atlantis press, Gijón (2015)

    Google Scholar 

  14. Murinová, P., Novák, V.: A formal theory of generalized intermediate syllogisms. Fuzzy Sets Syst. 186(1), 47–80 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  15. Dvořák, A., Holčapek, M.: L-fuzzy quantifiers of type \(\langle 1\rangle \) determined by fuzzy measures. Fuzzy Sets Syst. 160(23), 3425–3452 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. Lim, C., Chan, C.: A weighted inference engine based on interval-valued fuzzy relational theory. Expert Syst. with Appl. 42, 3410–3419 (2015)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre of Excellence IT4Innovations, Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. dubna 22, 701 03, Ostrava 1, Czech Republic

    Nhung Cao & Martin Štěpnička

Authors
  1. Nhung Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Martin Štěpnička
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nhung Cao .

Editor information

Editors and Affiliations

  1. INESC-ID,Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Joao Paulo Carvalho

  2. LIP 6, Université Pierre et Marie Curie, Paris, France

    Marie-Jeanne Lesot

  3. School of Industrial Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

    Uzay Kaymak

  4. IDMEC,Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Susana Vieira

  5. LIP6, Université Pierre et Marie Curie, CNRS, Paris, France

    Bernadette Bouchon-Meunier

  6. Iona College, Machine Intelligence Institute, New Rochelle, New York, USA

    Ronald R. Yager

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Cao, N., Štěpnička, M. (2016). How to Incorporate Excluding Features in Fuzzy Relational Compositions and What for. In: Carvalho, J., Lesot, MJ., Kaymak, U., Vieira, S., Bouchon-Meunier, B., Yager, R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2016. Communications in Computer and Information Science, vol 611. Springer, Cham. https://doi.org/10.1007/978-3-319-40581-0_38

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-40581-0_38

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40580-3

  • Online ISBN: 978-3-319-40581-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation