Skip to main content
SpringerLink
Log in

Construction of Interval Type-2 Fuzzy Sets From Fuzzy Sets: Methods and Applications

  • Chapter
  • First Online:
Book cover Advances in Type-2 Fuzzy Sets and Systems

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 301))

Abstract

In this chapter, we present some methods to construct interval type-2 membership functions from fuzzy membership functions and their applications in image processing, classification, and decision making. First, we review some basic concepts of interval type-2 fuzzy sets (IT2FSs). Next, we analyze three different approaches to construct IT2FSs starting from fuzzy sets and their applications in different fields.

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 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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

Institutional subscriptions

References

  1. Aisbett, J., Rickard, J.T., Morgenthaler, D.G.: Type-2 fuzzy sets as functions on spaces. IEEE Trans. Fuzzy Syst. 18(4), 841–844 (2010)

    Article  Google Scholar 

  2. Barrenechea, E., Fernández, A., Herrera, F., Bustince, H.: Construction of Interval-valued fuzzy preference relations using ignorance functions. Interval-valued Non Dominance Criterion, Advances in Intelligent and Soft Computing 107, Eurofuse : Workshop on Fuzzy Models and. Knowledge-Based Systems, 243–257 (2011)

    Google Scholar 

  3. Bustince, H., Kacpryzk, J., Mohedano, V.: Intuitionistic fuzzy generators—application to intuitionistic fuzzy complementation. Fuzzy Sets Syst. 114, 485–504 (2000)

    Article  MATH  Google Scholar 

  4. Bustince, H., Barrenechea, E., Pagola, M.: Image thresholding using restricted equivalence functions and maximizing the measures of similarity. Fuzzy Sets Syst. 158, 496–516 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bustince, H., Pagola, M., Barrenechea, E., Orduna, R.: Representation of uncertainty associated with the fuzzification of an image by means of interval type 2 fuzzy sets. Application to threshold computing. In Proceedings of Eurofuse Workshop: New Trends in Preference Modelling, Eurofuse, (Spain) 73–78 (2007)

    Google Scholar 

  6. Bustince, H., Pagola, M., Barrenechea, E., Fernandez, J., Melo-Pinto, P., Couto, P., Tizhoosh, H.R., Montero, J.: Ignorance functions. An application to the calculation of the threshold in prostate ultrasound images. Fuzzy Sets Syst. 161(1), 20–36 (2010)

    Article  MathSciNet  Google Scholar 

  7. Bustince, H., Barrenechea, E., Pagola, M., Fernandez, J., Sanz, J.: Comment on: image thresholding using type II fuzzy sets. Importance of this method. Pattern Recognit. 43(9), 3188–3192 (2010)

    Article  MATH  Google Scholar 

  8. Cordón, O., del Jesus, M.J., Herrera, F.: A proposal on reasoning methods in fuzzy rule-based classification systems. Int. J. Approximate. Reasoning. 20(1), 21–45 (1999)

    Google Scholar 

  9. Chi, Z., Yan, H., Pham, T.: Fuzzy Algorithms with Applications to Image Processing and Pattern Recognition. World Scientific, singapore (1996)

    Google Scholar 

  10. Deschrijver, G., Kerre, E.E.: On the relationship between some extensions of fuzzy set theory. Fuzzy Sets Syst. 133(2), 227–235 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  11. Isibuchi, H., Yamamoto, T., Nakashima, T.: Hybridization of fuzzy GBML approaches for pattern classification problems. IEEE Trans. Syst. Man Cybern. B 35(2), 359–365 (2005)

    Google Scholar 

  12. Galar, M., Fernandez, J., Beliakov, G., Bustince, H.: Interval-Valued fuzzy sets applied to stereo matching of color Images. IEEE Trans. Image Process. 20, 1949–1961 (2011)

    Article  MathSciNet  Google Scholar 

  13. Grattan-Guinness I.:Fuzzy membership mapped onto interval and many-valued quantities. Z. Math. Logik Grundlag. Mathe. 22, 149–160 (1976)

    Google Scholar 

  14. Hidalgo, D., Melin, P., Castillo, O.: An optimization method for designing type-2 fuzzy inference systems based on the footprint of uncertainty using genetic algorithms. Expert Syst. Appl. 39(4), 4590–4598 (2012)

    Article  Google Scholar 

  15. Huang, L.K., Wang, M.J.: Image thresholding by minimimizing the measure of fuzziness. Pattern recognit. 28(1), 41–51 (1995)

    Article  Google Scholar 

  16. Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice-Hall, New York (1995)

    Google Scholar 

  17. Liu, F., Mendel, J.M.: Encoding words into interval type-2 fuzzy sets using an interval approach. IEEE Trans. Fuzzy Syst. 16(6), 1503–1521 (2008)

    Article  Google Scholar 

  18. Mendel, J.M., John, R.I.: Type-2 fuzzy sets made simple. IEEE Trans. Fuzzy Syst. 10(2), 117–127 (2002)

    Article  Google Scholar 

  19. Mendel, J.M.: Uncertain Rule-Based Fuzzy Logic Systems. Prentice-Hall, Upper Saddle River (2001)

    Google Scholar 

  20. Mizumoto, M., Tanaka, K.: Some properties of fuzzy sets of type 2. Inform. Control 31, 312–340 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  21. Pagola, M.: Representation of uncertainty by interval-valued fuzzy sets. Application to image thresholding. Ph.D. dissertation, Departamento de Automática y Computacin, Universidad Pública de Navarra, Pamplona ( 2008)

    Google Scholar 

  22. Orlovsky, S.A.: Decision-making with a fuzzy preference relation. Fuzzy Sets Syst. 1(3), 155–167 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  23. Pal, S.K., King, R.A., Hashim, A.A.: Automatic grey level thresholding through index of fuzziness and entropy. Pattern Recognit. Lett. 1(3), 141–146 (1983)

    Article  Google Scholar 

  24. Sambuc, R.: Function \(\Phi \)- Flous. Application a l’aide au Diagnostic en Pathologie Thyroidienne. These de Doctorat en Medicine, University of Marseille (1975)

    Google Scholar 

  25. Sanz, J., Fernandez, A., Bustince, H., Herrera, F.: Improving the performance of fuzzy rule-based classification systems with interval-valued fuzzy sets and genetic amplitude tuning. Inf. Sci. 180, 3674–3685 (2010)

    Article  Google Scholar 

  26. Sanz, J., Fernandez, A., Bustince, H., Herrera, F.: A genetic tuning to improve the performance of fuzzy rule-based classification systems with interval-valued fuzzy sets: degree of ignorance and lateral position. Int. J. Approximate Reasoning 52(6), 751–766 (2011)

    Article  Google Scholar 

  27. Tehami, S., Bigand, A., Colot, O.: Color image segmentation based on type-2 fuzzy sets and region merging. Lect. Notes Comput. Sci. 4678, 943–954 (2007)

    Article  Google Scholar 

  28. Tizhoosh, H.R.: Image thresholding using type-2 fuzzy sets. Pattern Recognit. 38, 2363–2372 (2005)

    Article  MATH  Google Scholar 

  29. Yuksel, M.E., Borlu, M: Accurate segmentation of dermoscopic images by image thresholding based on type-2 fuzzy logi. IEEE Trans. Fuzzy Syst. 976–982 (2009)

    Google Scholar 

  30. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  31. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning-I. Inf. Sci. 8, 199–249 (1975)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

This research was partially supported by grant TIN2010-15505 from the Government of Spain.

Author information

Authors and Affiliations

  1. Universidad Pública de Navarra, Campus Arrosadia sn, 31006, Pamplona, Spain

    Miguel Pagola, Edurne Barrenechea, Javier Fernández, Aranzazu Jurio, Mikel Galar, Jose Antonio Sanz, Daniel Paternain, Carlos Lopez-Molina, Juan Cerrón & Humberto Bustince

Authors
  1. Miguel Pagola
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Edurne Barrenechea
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Javier Fernández
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Aranzazu Jurio
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Mikel Galar
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Jose Antonio Sanz
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Daniel Paternain
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Carlos Lopez-Molina
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Juan Cerrón
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Humberto Bustince
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Miguel Pagola .

Editor information

Editors and Affiliations

  1. Ryerson University, Victoria Street 350, Toronto, M5B 2K3, Ontario, Canada

    Alireza Sadeghian

  2. Hughes Aircraft Electrical Engineering B, Department of Electrical Engineering - S, University of Southern California, 3740 McClintock Ave., Los Angeles, 90089-2564, California, USA

    Jerry M. Mendel

  3. Ryerson University, Victoria Street 350, Toronto, M5B 2K3, Ontario, Canada

    Hooman Tahayori

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this chapter

Cite this chapter

Pagola, M. et al. (2013). Construction of Interval Type-2 Fuzzy Sets From Fuzzy Sets: Methods and Applications. In: Sadeghian, A., Mendel, J., Tahayori, H. (eds) Advances in Type-2 Fuzzy Sets and Systems. Studies in Fuzziness and Soft Computing, vol 301. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6666-6_10

Download citation

  • DOI: https://doi.org/10.1007/978-1-4614-6666-6_10

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-6665-9

  • Online ISBN: 978-1-4614-6666-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation