An Interval-Valued Fuzzy Classifier Based on an Uncertainty-Aware Similarity Measure

  • Anna Stachowiak
  • Patryk Żywica
  • Krzysztof Dyczkowski
  • Andrzej Wójtowicz
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 322)

Abstract

In this paper we propose a new method for classifying uncertain data, modeled as interval-valued fuzzy sets. We develop the notion of an interval-valued prototype-based fuzzy classifier, with the idea of preserving full information including the uncertainty factor about data during the classification process. To this end, the classifier was based on the uncertainty-aware similarity measure, a new concept which we introduce and give an axiomatic definition for. Moreover, an algorithm for determining such a similarity value is proposed, and an application to supporting medical diagnosis is described.

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References

  1. 1.
    Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning–I. Information Sciences 8(3), 199–249 (1975)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20(1), 87–96 (1986)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Deschrijver, G., Kerre, E.: Advances and challenges in interval-valued fuzzy logic. Fuzzy Sets and Systems 157, 622–627 (2006)CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Bustince, H.: Indicator of inclusion grade for interval valued fuzzy sets. Application to approximate reasoning based on interval-valued fuzzy sets. International Journal of Approximate Reasoning 23, 137–209 (2000)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Wu, D.: On the fundamental differences between interval type-2 and type-1 fuzzy logic controllers. IEEE Transactions on Fuzzy Systems 20, 832–848 (2012)CrossRefGoogle Scholar
  6. 6.
    Yager, R.R.: Fuzzy subsets of type II in decisions. Journal of Cybernetics 10, 137–159 (1980)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Karnik, N.N., Mendel, J.M.: Applications of type-2 fuzzy logic systems to forecasting of time-series. Information Sciences 120, 89–111 (1999)CrossRefMATHGoogle Scholar
  8. 8.
    Bezdek, J., Keller, J., Krisnapuram, R., Pal, N.: Fuzzy Models and algorithms for pattern recognition and image processing. Springer (2005)Google Scholar
  9. 9.
    Kuncheva, L.: Fuzzy Classifier Design. STUDFUZZ, vol. 49. Springer, Heidelberg (2000)MATHGoogle Scholar
  10. 10.
    Höppner, F., Klawonn, F., Kruse, R., Runkler, T.: Fuzzy Cluster Analysis: Methods for Classification, Data Analysis and Image Recognition. Wiley (1999)Google Scholar
  11. 11.
    Duda, R., Hart, P., Stork, D.: Pattern Classification, 2nd edn. Wiley (2000)Google Scholar
  12. 12.
    Bishop, C.: Pattern Recognition and Machine Learning. Information Science and Statistics. Springer (2006)Google Scholar
  13. 13.
    Zeng, W., Li, H.: Relationship between similarity measure and entropy of interval valued fuzzy sets. Fuzzy Sets and Systems 157, 1477–1484 (2006)CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Wu, D., Mendel, J.M.: A comparative study of ranking methods, similarity measures and uncertainty measures for interval type-2 fuzzy sets. Information Sciences 179, 1169–1192 (2009)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Nguyen, H.T., Kreinovich, V.: Computing degrees of subsethood and similarity for interval-valued fuzzy sets: Fast algorithms. In: Proc. of the 9th International Conference on Intelligent Technologies, InTec 2008, pp. 47–55 (2008)Google Scholar
  16. 16.
    Wu, D., Mendel, J.: Efficient algorithms for computing a class of subsethood and similarity measures for interval type-2 fuzzy sets. In: FUZZ-IEEE, pp. 1–7 (2010)Google Scholar
  17. 17.
    Stachowiak, A., Dyczkowski, K.: A similarity measure with uncertainty for incompletely known fuzzy sets. In: Proceedings of the 2013 Joint IFSA World Congress NAFIPS Annual Meeting, pp. 390–394 (2013)Google Scholar
  18. 18.
    Luca, A.D., Termini, S.: A definition of nonprobabilistic entropy in the setting of fuzzy sets theory. Information and Computation 20, 301–312 (1972)MATHMathSciNetGoogle Scholar
  19. 19.
    Szmidt, E., Kacprzyk, J.: Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems 118, 467–477 (2001)CrossRefMATHMathSciNetGoogle Scholar
  20. 20.
    Żywica, P., Stachowiak, A.: A new method for computing relative cardinality of intuitionistic fuzzy sets. In: Atanassov, K., et al. (eds.) New Developments in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics. IBS PAN – SRI PAS, Warsaw (to appear, 2014)Google Scholar
  21. 21.
    Chen, S., Tan, J.M.: Handling multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems 67, 163–172 (1994)CrossRefMATHMathSciNetGoogle Scholar
  22. 22.
    Siegel, R., Ma, J., Zou, Z., Jemal, A.: Cancer statistics, 2014. CA: A Cancer Journal for Clinicians 64(1), 9–29 (2014)CrossRefGoogle Scholar
  23. 23.
    Alcázar, J.L., Mercé, L.T., Laparte, C., Jurado, M., López-Garcia, G.: A new scoring system to differentiate benign from malignant adnexal masses. Obstetrical & Gynecological Survey 58(7), 462–463 (2003)CrossRefGoogle Scholar
  24. 24.
    Szpurek, D., Moszyński, R., Ziętkowiak, W., Spaczyński, M., Sajdak, S.: An ultrasonographic morphological index for prediction of ovarian tumor malignancy. European Journal of Gynaecological Oncology 26(1), 51–54 (2005)Google Scholar
  25. 25.
    Timmerman, D., Testa, A.C., Bourne, T., Ameye, L., Jurkovic, D., Van Holsbeke, C., Paladini, D., Van Calster, B., Vergote, I., Van Huffel, S., et al.: Simple ultrasound-based rules for the diagnosis of ovarian cancer. Ultrasound in Obstetrics & Gynecology 31(6), 681–690 (2008)CrossRefGoogle Scholar
  26. 26.
    Timmerman, D., Testa, A.C., Bourne, T., Ferrazzi, E., Ameye, L., Konstantinovic, M.L., Van Calster, B., Collins, W.P., Vergote, I., Van Huffel, S., et al.: Logistic regression model to distinguish between the benign and malignant adnexal mass before surgery: a multicenter study by the International Ovarian Tumor Analysis Group. Journal of Clinical Oncology 23(34), 8794–8801 (2005)CrossRefGoogle Scholar
  27. 27.
    Van Calster, B., Timmerman, D., Nabney, I.T., Valentin, L., Testa, A.C., Van Holsbeke, C., Vergote, I., Van Huffel, S.: Using Bayesian neural networks with ARD input selection to detect malignant ovarian masses prior to surgery. Neural Computing and Applications 17(5-6), 489–500 (2008)CrossRefGoogle Scholar
  28. 28.
    Valentin, L., Hagen, B., Tingulstad, S., Eik-Nes, S.: Comparison of ’pattern recognition’ and logistic regression models for discrimination between benign and malignant pelvic masses: a prospective cross validation. Ultrasound in Obstetrics & Gynecology 18(4), 357–365 (2001)CrossRefGoogle Scholar
  29. 29.
    Van Holsbeke, C., Van Calster, B., Valentin, L., Testa, A.C., Ferrazzi, E., Dimou, I., Lu, C., Moerman, P., Van Huffel, S., Vergote, I., et al.: External validation of mathematical models to distinguish between benign and malignant adnexal tumors: a multicenter study by the International Ovarian Tumor Analysis Group. Clinical Cancer Research 13(15), 4440–4447 (2007)CrossRefGoogle Scholar
  30. 30.
    Wójtowicz, A., Żywica, P., Szarzyński, K., Moszyński, R., Szubert, S., Dyczkowski, K., Stachowiak, A., Szpurek, D., Wygralak, M.: Dealing with Uncertainty in Ovarian Tumor Diagnosis. In: Atanassov, K., et al. (eds.) New Developments in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics. IBS PAN – SRI PAS, Warsaw (to appear, 2014)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Anna Stachowiak
    • 1
  • Patryk Żywica
    • 1
  • Krzysztof Dyczkowski
    • 1
  • Andrzej Wójtowicz
    • 1
  1. 1.Faculty of Mathematics and Computer ScienceAdam Mickiewicz UniversityPoznańPoland

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