Compound Distance Function for Similarity Measurement Between Fuzzy Sets

László Kovács

doi:10.20965/jaciii.2011.p0299

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JACIII Vol.15 No.3 pp. 299-303

doi: 10.20965/jaciii.2011.p0299

(2011)

Paper:

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Compound Distance Function for Similarity Measurement Between Fuzzy Sets

László Kovács

Department of Information Technology, University of Miskolc, H-3515 Miskolc-Egyetemváros, Hungary

Received:

December 21, 2010

Accepted:

March 29, 2011

Published:

May 20, 2011

Keywords:

distance function, similarity of fuzzy sets, Hausdorff metric, Hamilton metric

Abstract

Distance is usually used to measure the similarity of different objects. The distance function has a key role in clustering, pattern recognition, in information retrieval. The compound real valued distance function on fuzzy sets we propose considers both key aspects of fuzzy sets – membership function and support set.

Cite this article as:

L. Kovács, “Compound Distance Function for Similarity Measurement Between Fuzzy Sets,” J. Adv. Comput. Intell. Intell. Inform., Vol.15 No.3, pp. 299-303, 2011.

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References

[1] L. A. Zadeh, “Fuzzy Sets,” Information and Control, Vol.8, pp. 338-353, 1965.
[2] V. G. Adelson and E. Landis, “An algorithm for the organisation of information,” Doklady Akademii Nauk, SSR, pp. 146-263, 1962.
[3] P.-N. Yianilos, “Data structures and algorithms for nearest neighbor search in general metric spaces,” Proc. of SODA, pp. 311-321, 1993.
[4] A. Anderson, “General Balanded Tree,” J. of Algorithms, 30, pp. 1-18, 1999.
[5] Z. C. Johanyák, “Fuzzy Rule Interpolation based on Subsethood Values,” Proc. of 2010 IEEE Int. Conf. on Systems Man and Cybernetics, pp. 2387-2393, 2010.
[6] L. T. Kóczy and K. Hirota, “Approximate reasoning by linear rule interpolation and general approximation,” Int. J. of Approximative Reasoning, pp. 197-225, 1993.
[7] P. Baranyi, L. T. Kóczy, and T. D. Gedeon, “A Generalized Concept for Fuzzy Rule Interpolation,” IEEE Trans. on Fuzzy Systems, Vol.12, No.6, pp. 820-837, 2004.
[8] D. Huttenlocher, G. Klanderman, A. Gregory, and W. Rucklidge, “Comparing Images Using the Hausdorff Distance,” IEEE Trans. on Pattern Analysis and Machine Intelligence, pp. 850-863, 1993.
[9] B. Huffaker, M. Fomenkov, D. Plummer, and D. Moore, “Distance Metrics in the Internet,” IEEE Int. Telecommunications Symposium, pp. 200-212, 2002.
[10] D. Dubois and H. Prade, “Operations on fuzzy numbers,” Int. J. of Systems Science, Vol.9, No.6, pp. 613-626, 1978.
[11] B. Sridevi and R. Nadarajan, “Fuzzy similarity Measure for Generalized Fuzzy Members,” Int. J. Open Problems Compt.Math., Vol.2, No.2, pp. 240-254, June 2009.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] L. A. Zadeh, “Fuzzy Sets,” Information and Control, Vol.8, pp. 338-353, 1965.

[2] [2] V. G. Adelson and E. Landis, “An algorithm for the organisation of information,” Doklady Akademii Nauk, SSR, pp. 146-263, 1962.

[3] [3] P.-N. Yianilos, “Data structures and algorithms for nearest neighbor search in general metric spaces,” Proc. of SODA, pp. 311-321, 1993.

[4] [4] A. Anderson, “General Balanded Tree,” J. of Algorithms, 30, pp. 1-18, 1999.

[5] [5] Z. C. Johanyák, “Fuzzy Rule Interpolation based on Subsethood Values,” Proc. of 2010 IEEE Int. Conf. on Systems Man and Cybernetics, pp. 2387-2393, 2010.

[6] [6] L. T. Kóczy and K. Hirota, “Approximate reasoning by linear rule interpolation and general approximation,” Int. J. of Approximative Reasoning, pp. 197-225, 1993.

[7] [7] P. Baranyi, L. T. Kóczy, and T. D. Gedeon, “A Generalized Concept for Fuzzy Rule Interpolation,” IEEE Trans. on Fuzzy Systems, Vol.12, No.6, pp. 820-837, 2004.

[8] [8] D. Huttenlocher, G. Klanderman, A. Gregory, and W. Rucklidge, “Comparing Images Using the Hausdorff Distance,” IEEE Trans. on Pattern Analysis and Machine Intelligence, pp. 850-863, 1993.

[9] [9] B. Huffaker, M. Fomenkov, D. Plummer, and D. Moore, “Distance Metrics in the Internet,” IEEE Int. Telecommunications Symposium, pp. 200-212, 2002.

[10] [10] D. Dubois and H. Prade, “Operations on fuzzy numbers,” Int. J. of Systems Science, Vol.9, No.6, pp. 613-626, 1978.

[11] [11] B. Sridevi and R. Nadarajan, “Fuzzy similarity Measure for Generalized Fuzzy Members,” Int. J. Open Problems Compt.Math., Vol.2, No.2, pp. 240-254, June 2009.