Skip to main content
Log in

A definition for I-fuzzy partitions

  • Original Paper
  • Published:
Soft Computing Aims and scope Submit manuscript

An Erratum to this article was published on 29 July 2010

An Erratum to this article was published on 29 July 2010

Abstract

In this paper, we define I-fuzzy partitions (or intuitionistic fuzzy partitions as called by Atanassov or interval-valued fuzzy partitions). As our ultimate goal is to compare the results of standard fuzzy clustering algorithms (e.g. fuzzy c-means), we define a method to construct them from a set of fuzzy clusters obtained from several executions of fuzzy c-means. From a practical point of view, the approach presented here tries to solve the difficulty of comparing the results of fuzzy clustering methods and, in particular, the difficulty of finding the global optimal.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  • Atanassov KT (1983) Intuitionistic fuzzy sets. VII ITKR’s session, Sofia (deposed in Central Science-Technical Library of Bulgarian Academy of Science, 1697/84) (in Bulgarian)

  • Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96

    Article  MATH  MathSciNet  Google Scholar 

  • Atanassov KT (1999) Intuitionistic fuzzy sets. Physica-Verlag, Heidelberg

    MATH  Google Scholar 

  • Atanassov K (2005) Answer to Dubois D, Gottwald S, Hajek P, Kacprzyk J, Prade H’s paper Terminological difficulties in fuzzy set theory: the case of Intuitionistic fuzzy sets. Fuzzy Sets Syst 156(3):496–499

    Google Scholar 

  • Bezdek JC (1981) Pattern recognition with fuzzy objective function algorithms. Plenum Press, New York

    MATH  Google Scholar 

  • Bhutani KR, Chaudhuri BB, Rosenfeld A (2002) Corrigendum to “A modified Hausdorff distance between fuzzy sets”. Inf Sci 148:233–234

    Article  MATH  MathSciNet  Google Scholar 

  • Burillo P, Bustince H (1996) Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets Syst 78(3):305–316

    Article  MATH  MathSciNet  Google Scholar 

  • Bustince H, Pagola M, Barrenechea E (2007) Construction of fuzzy indices from fuzzy DI-subsethood measures: application to the global comparison of images. Inf Sci 177(3):906–929

    Article  MATH  MathSciNet  Google Scholar 

  • Chaudhuri BB, Rosenfeld A (1999) A modified Hausdorff distance between fuzzy sets. Inf Sci 118:159–171

    Article  MATH  MathSciNet  Google Scholar 

  • Domingo-Ferrer J, Torra V (2001) Disclosure control methods and information loss for microdata. In: Doyle P, Lane JI, Theeuwes JJM, Zayatz LM (eds) Confidentiality, disclosure, and data access: theory and practical applications for statistical agencies. Elsevier, pp 91–110

  • Dubois D, Gottwald S, Hajek P, Kacprzyk J, Prade H (2005) Terminological difficulties in fuzzy set theory—the case of intuitionistic fuzzy sets. Fuzzy Sets Syst 156(3): 485–491

    Article  MATH  MathSciNet  Google Scholar 

  • Hasegawa Y, Endo Y, Hamasuna Y, Miyamoto S (2007) Fuzzy c-means for data with tolerance defined as hyper-rectangle. In: Proceedings of MDAI 2007, lecture notes in artificial intelligence, vol 4617, pp 237–248

  • Hastie T, Tibshirani R, Friedman J, (2001) The elements of statistical learning. Springer, Berlin

    MATH  Google Scholar 

  • Höppner F, Klawonn F, Kruse R, Runkler T (1999) Fuzzy cluster analysis. Wiley

  • Ladra S, Torra V (2008) On the comparison of generic information loss measures and cluster-specific ones. Int J Unc Fuzzy Knowl Based Syst 16(1):107–120

    Article  Google Scholar 

  • Ladra S, Torra V (2010) Information loss for synthetic data through fuzzy clustering. Int J Unc Fuzzy Knowl Based Syst 18(1):25–37

    Google Scholar 

  • Lane J, Heus P, Mulcahy T (2008) Data access in a cyber world: making use of cyberinfrastructure. Trans Data Priv 1(1):2–16

    MathSciNet  Google Scholar 

  • Lopez de Mantaras R (1991) A distance-based attribute selection. Measure for decision tree induction. Mach Learn 6: 81–92

    Google Scholar 

  • Miyamoto S (1999) Introduction to fuzzy clustering (in Japanese). Ed. Morikita, Tokyo

  • Miyamoto S, Umayahara K (2000) Methods in hard and fuzzy clustering. In: Liu Z-Q, Miyamoto S (eds) Soft computing and human-centered machines. Springer, Tokyo, pp 85–129

    Google Scholar 

  • Murata R, Endo Y, Haruyama H, Miyamoto S (2006) On fuzzy c-means for data with tolerance. J Adv Comput Intell Intell Inform 10(5):673–681

    Google Scholar 

  • Pappis CP, Karacapilidis NI (1993) A comparative assessment of measures of similarity of fuzzy values. Fuzzy Sets Syst 56:171–174

    Article  MATH  MathSciNet  Google Scholar 

  • Szmidt E, Kacprzyk J (2000) Distances between intuitionistic fuzzy sets. Fuzzy Sets and Syst 114(3):505–518

    Article  MATH  MathSciNet  Google Scholar 

  • Templ M, Petelin T (2009) A graphical user interface for microdata protection which provides reproducibility and interactions: the sdcMicro GUI. Trans Data Priv 2(3):207–224

    Google Scholar 

  • Torra V, Endo Y, Miyamoto S (2009) On the comparison of some fuzzy clustering methods for privacy preserving data mining: towards the development of specific information loss measures. Kybernetika 45(3):548–560

    MATH  MathSciNet  Google Scholar 

  • Torra V, Endo Y, Miyamoto S (2009) Computationally intensive parameter selection for clustering algorithms: the case of fuzzy c-means with tolerance (submitted)

Download references

Acknowledgments

Partial support by the Spanish MEC (projects ARES – CONSOLIDER INGENIO 2010 CSD2007-00004 – and eAEGIS – TSI2007-65406-C03-02) is acknowledged.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vicenç Torra.

Additional information

An erratum to this article can be found at http://dx.doi.org/10.1007/s00500-010-0635-6

Rights and permissions

Reprints and permissions

About this article

Cite this article

Torra, V., Miyamoto, S. A definition for I-fuzzy partitions. Soft Comput 15, 363–369 (2011). https://doi.org/10.1007/s00500-010-0605-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-010-0605-z

Keywords

Navigation