New Similarity Measure Between Two Fuzzy Sets

Hassan Rezaei; Masashi Emoto; Masao Mukaidono

doi:10.20965/jaciii.2006.p0946

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JACIII Vol.10 No.6 pp. 946-953

doi: 10.20965/jaciii.2006.p0946

(2006)

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New Similarity Measure Between Two Fuzzy Sets

Hassan Rezaei, Masashi Emoto, and Masao Mukaidono

Department of Computer Science, Meiji University, 1-1-1 Higashi-Mita, Tama-ku, Kawasaki-shi 214-8571, Japan

Received:

January 18, 2006

Accepted:

April 2, 2006

Published:

November 20, 2006

Keywords:

fuzzy sets, similarity measure, relative sigma count, proximity relation

Abstract

We propose a new similarity measure between two fuzzy sets based on their relative sigma count and extend it to define two other measures, one a similarity measure between elements in fuzzy sets and the second a similarity measure between fuzzy sets in which all elements in the universe of discourse are weighted. We compare our proposal to several previous measures proposed in [1-6].

Cite this article as:

H. Rezaei, M. Emoto, and M. Mukaidono, “New Similarity Measure Between Two Fuzzy Sets,” J. Adv. Comput. Intell. Intell. Inform., Vol.10 No.6, pp. 946-953, 2006.

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References

[1] C. P. Pappis and N. I. Karacapilidis, “A Comparative Assessment of Measures of Similarity of Fuzzy Values,” Fuzzy Sets and Systems 56, pp. 171-174, 1993.
[2] L. K. Hyung, Y. S. Song, and K. M. Lee, “Similarity Measures Between Fuzzy Sets and Between Elements,” Fuzzy Sets and Systems 62, pp. 291-293, 1994.
[3] S. M. Chen, M. S. Yeh, and P. Y. Hsiao, “A Comparison of Similarity Measures of Fuzzy Values,” Fuzzy Sets and Systems 72, pp. 79-89, 1995.
[4] W. J. Wang, “New Similarity Measures on Fuzzy Sets and on Elements,” Fuzzy Sets and Systems 85, pp. 305-309, 1997.
[5] R. Zwick, E. Carlstein, and D. Budescu, “Measures of Similarity Among Fuzzy Sets: A Comparative Analysis,” Int. J. Approximate Reasoning 1, pp. 221-242, 1987.
[6] T. Gerstenkorn and I. Man’ko, “Correlation of Intuitionistic Fuzzy Sets,” Fuzzy Sets and Systems 44, pp. 39-43, 1991.
[7] L. Xuecheng, “Entropy, Distance Measure and Similarity Measure of Fuzzy Sets and Their Relations,” Fuzzy Sets and Systems 52, pp. 305-318, 1992.
[8] G. J. Klir and B. Yuan, “Fuzzy Sets and Fuzzy Logic Theory and Applications,” Prentice Hall, New Jersey, 1995.
[9] D. Dubios and H. Prade, “Fuzzy Sets and Systems: Theory and Applications,” Academic Press, New York, 1980.
[10] S. M. Chen, “A New Approach to Handling Fuzzy Decision Making Problems,” IEEE Trans. Systems, Man Cybernet. 18, pp. 1012-1016, 1988.
[11] R. Intan and M. Mukaidono, “Degree of Similarity in Fuzzy Partition,” Proceedings of AFSS’02, pp. 20-26, 2000.
[12] L. A. Zadeh, “A Computational Theory of Dispositions,” Proceedings of the 22nd Annual Meeting on Association for Computational Linguistics, Stanford, California, pp. 312-318, 1984.

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

[1] [1] C. P. Pappis and N. I. Karacapilidis, “A Comparative Assessment of Measures of Similarity of Fuzzy Values,” Fuzzy Sets and Systems 56, pp. 171-174, 1993.

[2] [2] L. K. Hyung, Y. S. Song, and K. M. Lee, “Similarity Measures Between Fuzzy Sets and Between Elements,” Fuzzy Sets and Systems 62, pp. 291-293, 1994.

[3] [3] S. M. Chen, M. S. Yeh, and P. Y. Hsiao, “A Comparison of Similarity Measures of Fuzzy Values,” Fuzzy Sets and Systems 72, pp. 79-89, 1995.

[4] [4] W. J. Wang, “New Similarity Measures on Fuzzy Sets and on Elements,” Fuzzy Sets and Systems 85, pp. 305-309, 1997.

[5] [5] R. Zwick, E. Carlstein, and D. Budescu, “Measures of Similarity Among Fuzzy Sets: A Comparative Analysis,” Int. J. Approximate Reasoning 1, pp. 221-242, 1987.

[6] [6] T. Gerstenkorn and I. Man’ko, “Correlation of Intuitionistic Fuzzy Sets,” Fuzzy Sets and Systems 44, pp. 39-43, 1991.

[7] [7] L. Xuecheng, “Entropy, Distance Measure and Similarity Measure of Fuzzy Sets and Their Relations,” Fuzzy Sets and Systems 52, pp. 305-318, 1992.

[8] [8] G. J. Klir and B. Yuan, “Fuzzy Sets and Fuzzy Logic Theory and Applications,” Prentice Hall, New Jersey, 1995.

[9] [9] D. Dubios and H. Prade, “Fuzzy Sets and Systems: Theory and Applications,” Academic Press, New York, 1980.

[10] [10] S. M. Chen, “A New Approach to Handling Fuzzy Decision Making Problems,” IEEE Trans. Systems, Man Cybernet. 18, pp. 1012-1016, 1988.

[11] [11] R. Intan and M. Mukaidono, “Degree of Similarity in Fuzzy Partition,” Proceedings of AFSS’02, pp. 20-26, 2000.

[12] [12] L. A. Zadeh, “A Computational Theory of Dispositions,” Proceedings of the 22nd Annual Meeting on Association for Computational Linguistics, Stanford, California, pp. 312-318, 1984.