Skip to main content

Interval Type-2 Fuzzy Possibilistic C-Means Optimization Using Particle Swarm Optimization

  • Chapter
  • First Online:
Nature-Inspired Design of Hybrid Intelligent Systems

Part of the book series: Studies in Computational Intelligence ((SCI,volume 667))

Abstract

In this paper, we present optimization of the Interval Type-2 Fuzzy Possibilistic C-Means (IT2FPCM) algorithm using Particle Swarm Optimization (PSO), with the goal of automatically finding the optimal number of clusters and the optimal lower and upper limit of Fuzzy and Possibility exponents of weight of the of the IT2FPCM algorithm, and also the centroids of clusters of each dataset tested with the IT2FPCM algorithm optimized using PSO.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
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. J. Bezdek, “Pattern Recognition with Fuzzy Objective Function Algorithms”, Plenum, 1981.

    Google Scholar 

  2. D. E. Gustafson and W. C. Kessel, “Fuzzy clustering with a fuzzy covariance matrix,” in Proc. IEEE Conf. Decision Contr., San Diego, CA, pp. 761–766, 1979.

    Google Scholar 

  3. R. Krishnapuram and J. Keller, “A possibilistic approach to clustering,” IEEE Trans. Fuzzy Sys., vol. 1, no. 2, pp. 98-110, May 1993.

    Google Scholar 

  4. R. Krishnapuram and J. Keller, “The possibilistic c-Means algorithm: Insights and recommendations,” IEEE Trans. Fuzzy Sys., vol. 4, no. 3, pp. 385-393, August 1996.

    Google Scholar 

  5. N. R. Pal, K. Pal, J. M. Keller and J. C. Bezdek, “A Possibilistic Fuzzy c-Means Clustering Algorithm,” IEEE Trans. Fuzzy Sys., vol. 13, no. 4, pp. 517-530, August 2005.

    Google Scholar 

  6. J. Yen; R. Langari; “Fuzzy Logic: Intelligence, Control, and Information,” Upper Saddle River, New Jersey; Prentice Hall, 1999.

    Google Scholar 

  7. R. Kruse, C. Döring, M. J. Lesot; “Fundamentals of Fuzzy Clustering,” In: Advances in Fuzzy Clustering and its Applications; John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England, 2007, Pages 3-30

    Google Scholar 

  8. K. Hirota, W. Pedrycz, “Fuzzy Computing for data mining,” Proceeding of the IEEE, Vol 87(9), 1999, pp 1575-1600.

    Google Scholar 

  9. N. S. Iyer, A. Kendel, and M. Schneider, “Feature-based fuzzy classification for interpretation of mamograms,” Fuzzy Sets and Systems, Vol. 114, 2000, pp. 271-280.

    Google Scholar 

  10. W.E. Philips, R.P. Velthuinzen, S. Phuphanich, L.O. Hall, L.P Clark, and M. L Sibiger, “Aplication of fuzzy c-means segmentation technique for tissue deifferentation in MR images of hemorrhagic gliobastomamultifrome,” Magnetic Resonance Imaging, Vol 13(2), 1995, pp. 277-290.

    Google Scholar 

  11. Miin-Shen Yang, Yu-Jen Hu, Karen Chia-Ren Lin, and Charles Chia-Lee Lin, “Segmentation techniques for tissue differentiation in MRI of Ophthalmology using fuzzy clustering algorithms,” Magnetic Resonance Imaging, Vol. 20, 2002, pp. 173-179.

    Google Scholar 

  12. X. Chang, Wei Li, and J. Farrell, “A C-means clustering based fuzzy modeling method,” Fuzzy Systems, 2000. FUZZ IEEE 2000. The Ninth IEEE International Conference on, vol.2, 2000, pp. 937-940.

    Google Scholar 

  13. C. Hwang, F. Rhee, “Uncertain fuzzy clustering: interval type-2 fuzzy approach to C-means”, IEEE Transactions on Fuzzy Systems 15 (1) (2007) 107–120.

    Google Scholar 

  14. B. Choi, F. Rhee, “Interval type-2 fuzzy membership function generation methods for pattern recognition,” Information Sciences, Volume 179, Issue 13, 13 June 2009, Pages 2102-2122,

    Google Scholar 

  15. L. A. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning-I,” Inform. Sci., vol. 8, no. 3, pp. 199-249, 1975.

    Google Scholar 

  16. J. Mendel, “Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions,” Prentice Hall, 2001.

    Google Scholar 

  17. K. L. Wu, M. S. Yang; A cluster validity index for fuzzy clustering, Pattern Recognition Letters, Volume 26, Issue 9, 1 July 2005, Pages 1275-1291.

    Google Scholar 

  18. M. K. Pakhira, S. Bandyopadhyay, U. Maulik, A study of some fuzzy cluster validity indices, genetic clustering and application to pixel classification, Fuzzy Sets and Systems, Volume 155, Issue 2, 16 October 2005, Pages 191-214.

    Google Scholar 

  19. W. Wang, Y. Zhang; On fuzzy cluster validity indices, Fuzzy Sets and Systems, Volume 158, Issue 19, Theme: Data Analysis, 1 October 2007, Pages 2095-2117, ISSN 0165-0114.

    Google Scholar 

  20. E. Rubio and O. Castillo; “Optimization of the Interval Type-2 Fuzzy C-Means using Particle Swarm Optimization”. Nabic 2013, pages 10-15.

    Google Scholar 

  21. R. Eberhart, J. Kennedy, “A new optimizer using particle swarm theory”, in proc. 6th Int. Symp. Micro Machine and Human Science (MHS), Oct. 1995, pages: 39-43.

    Google Scholar 

  22. R. Eberhart, Y. Shi, “Particle swarm optimization: Developments, applications and resources”, in Procceding of the IEEE Congress on Evolutionary Computation, May 2001, vol. 1, pages: 81–86.

    Google Scholar 

  23. J. Kennedy, R. Eberhart, “Particle Swam Optimization”, in Proc. IEEE Int. Conf. Neural Network (ICNN), Nov. 1995, vol. 4, pages: 1942-1948.

    Google Scholar 

  24. Y. del Valle, G.K. Venayagamoorthy, S. Mohagheghi a J.-C. Hernandez and Harley R.G., “Particle Swarm Optimization: Basic Concepts, Variants and Applications in Power Systems”, Evolutionary Computation, IEEE Transactions on, Apr 2008, pages: 171-195.

    Google Scholar 

  25. R. Eberhart, Y. Shi and J. Kennedy, “Swam Intelligence”, San Mateo, California. Morgan Kaufmann, 2001.

    Google Scholar 

  26. A. P. Engelbrecht, “Fundamentals of Computational Swarm Intelligence”, John Wiley & Sons, 2006.

    Google Scholar 

  27. Escalante H. J., Montes M., Sucar L. E., “Particle Swarm Model Selection”, Journal of Machine Learning Research 10, 2009, pages: 405-440.

    Google Scholar 

  28. K. L. Wu, M. S. Yang, “A cluster validity index for fuzzy clustering”, Pattern Recognition Letters, Volume 26, Issue 9, 1 July 2005, Pages 1275-1291.

    Google Scholar 

  29. Y. Zhang, W. Wang, X. Zhang, Y. Li, “A cluster validity index for fuzzy clustering”, Information Sciences, Volume 178, Issue 4, 15 February 2008, Pages 1205-1218.

    Google Scholar 

  30. E. Rubio, O. Castillo, and P. Melin; “A new validation index for fuzzy clustering and its comparisons with other methods”. SMC 2011, pages 301-306.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Elid Rubio .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Rubio, E., Castillo, O. (2017). Interval Type-2 Fuzzy Possibilistic C-Means Optimization Using Particle Swarm Optimization. In: Melin, P., Castillo, O., Kacprzyk, J. (eds) Nature-Inspired Design of Hybrid Intelligent Systems. Studies in Computational Intelligence, vol 667. Springer, Cham. https://doi.org/10.1007/978-3-319-47054-2_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-47054-2_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-47053-5

  • Online ISBN: 978-3-319-47054-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics