Skip to main content
SpringerLink
Log in

On the Use of Lattice OWA Operators in Image Reduction and the Importance of the Orness Measure

  • 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 610))

Abstract

In this work we investigate the use of OWA operators in color image reduction. Since the RGB color scheme can be seen as a Cartesian product of lattices, we use the generalization of OWA operators to any complete lattice. However, the behavior of lattice OWA operators in image processing is not easy to predict. Therefore, we propose an orness measure that generalizes the orness measure given by Yager for usual OWA operators. With the aid of this new measure, we are able to classify each OWA operator and to analyze how its properties affect the results of applying OWA operators in an algorithm for reducing color images.

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

References

  1. Beliakov, G., Bustince, H., Paternain, D.: Image reduction using means on discrete product lattice. IEEE Trans. Image Process. 21, 1070–1083 (2012)

    Article  MathSciNet  Google Scholar 

  2. Beliakov, G., Bustince, H., Calvo, T.: A Practical Guide to Averaging Functions. Springer, Heidelberg (2016)

    Book  Google Scholar 

  3. De Baets, B., Mesiar, R.: Triangular norms on product lattices. Fuzzy Sets Syst. 104, 61–75 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  4. Dujmović, J.J.: A generalization of some functions in continuous mathematical logic - evaluation functions and its applications (In Serbo-Croatian). In: Proceedings of the Informatica Conference, Bled, paper d27, Yugoslavia (1973)

    Google Scholar 

  5. Galar, M., Fernandez, J., Beliakov, G., Busince, R.: Interval-valued fuzzy sets applied to stereo matching of color images. IEEE Trans. Image Process. 20, 1949–1961 (2011)

    Article  MathSciNet  Google Scholar 

  6. Grätzer, G.: General Lattice Theory. Birkhäuser Verlag, Basel (1978)

    Book  MATH  Google Scholar 

  7. Kishor, A., Singh, A.K., Pal, N.R.: Orness measure of OWA operators: a new approach. IEEE Trans. Fuzzy Syst. 22, 1039–1045 (2014)

    Article  Google Scholar 

  8. Komorníková, M., Mesiar, R.: Aggregation functions on bounded partially ordered sets and their classification. Fuzzy Sets Syst. 175, 48–56 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. Lizasoain, I., Moreno, C.: OWA operators defined on complete lattices. Fuzzy Sets Syst. 224, 36–52 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  10. González-Hidalgo, M., Massanet, S.: A fuzzy mathematical morphology based on discrete t-norms: fundamentals and applications to image processing. Soft Comput. 18, 2297–2311 (2014)

    Article  MATH  Google Scholar 

  11. Paternain, D., Fernandez, J., Bustince, H., Mesiar, R., Beliakov, G.: Construction of image reduction operators using averaging aggregation functions. Fuzzy Sets Syst. 261, 87–111 (2015)

    Article  MathSciNet  Google Scholar 

  12. Perfilieva, I.: Fuzzy transforms: theory and applications. Fuzzy Sets Syst. 157, 993–1023 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  13. Perfilieva, I., Kreinovich, V.: F-transform in view of aggregation functions. In: Bustince, H., Fernandez, J., Mesiar, R., Calvo, T. (eds.) Aggregation Functions in Theory and in Practise. AISC, vol. 228, pp. 393–400. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  14. Yager, R.R.: On ordered weighting averaging aggregation operators in multicriteria decision-making. IEEE Trans. Syst. Man Cybern. 18, 183–190 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  15. Yager, R.R.: Families of OWA operators. Fuzzy Sets Syst. 59, 125–148 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  16. Zhou, W., Boviz, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13, 600–612 (2004)

    Article  Google Scholar 

Download references

Acknowledgments

D. Paternain and H. Bustince have been partially supported by Spanish project TIN2013-40765-P. R. Mesiar has been partially supported by grant APVV-14-0013.

Author information

Authors and Affiliations

  1. Departamento de Automatica Y Computacion, Universidad Publica de Navarra, Campus Arrosadia Sn, 31006, Pamplona, Spain

    Daniel Paternain, Edurne Barrenechea & Humberto Bustince

  2. Institute of Smart Cities, Universidad Publica de Navarra, Campus Arrosadia Sn, 31006, Pamplona, Spain

    Daniel Paternain, Edurne Barrenechea & Humberto Bustince

  3. Departamento de Matemáticas, Universidad Publica de Navarra, Campus Arrosadia Sn, 31006, Pamplona, Spain

    Gustavo Ochoa & Inmaculada Lizasoain

  4. Institute for Advanced Materials, Universidad Publica de Navarra, Campus Arrosadia Sn, 31006, Pamplona, Spain

    Inmaculada Lizasoain

  5. Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Radlinskho 11, 813 68, Bratislava, Slovakia

    Radko Mesiar

Authors
  1. Daniel Paternain
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gustavo Ochoa
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Inmaculada Lizasoain
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Edurne Barrenechea
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Humberto Bustince
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Radko Mesiar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Daniel Paternain .

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. Machine Intelligence Institute, Iona College, 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

Paternain, D., Ochoa, G., Lizasoain, I., Barrenechea, E., Bustince, H., Mesiar, R. (2016). On the Use of Lattice OWA Operators in Image Reduction and the Importance of the Orness Measure. 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 610. Springer, Cham. https://doi.org/10.1007/978-3-319-40596-4_52

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-40596-4_52

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40595-7

  • Online ISBN: 978-3-319-40596-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation