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Two fuzziness indexes proposed by Kaufmann: observations about them
Keywords:
entropy, fuzziness, uncertainty indexes, uncertainty measure, fuzzy setsAbstract
Professor Arnold Kaufmann did propose at least two types of indexes for estimating fuzziness in finite standard fuzzy sets. First one has an analogue formulation to that stated by Claude Shannon for measuring uncertainty in a given system. Shannon formulation estimates one type of uncertainty classified as conflict. The present paper will reveal the inconvenience of such an index for measuring fuzziness phenomena. In addition, it is proved algebraic equivalence between another index posed by Kaufmann and a fuzziness index proposed by Ronald Yager.
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References
[1] C. Shannon, “The mathematical theory of communications”, The Bell System Technical Journal, 27, 1948, pp. 379-423, 623-658.
[2] A. Kaufmann, Introduction to the Theory of Fuzzy Subsets. vol. I Fundamental Theoretical Elements., New York: Academic Press, 1975, pp. 25-27.
[3] Ch. Huang, and Y. Shi. Towards Efficient Fuzzy Information Processing. Using the Principle of Information Diffusion, Heidelberg: Physica-Verlag, 2002.
[4] S. Al-sharhan, F. Karray, W. Gueaieb and O. Basir, “Fuzzy Entropy: a Brief survey”, in IEEE International Fuzzy Systems Conference, 2001.
[5] C. Isaza, J. Aguilar-Martin, M. V. Le Lann, J. Aguilar and A. Rios-Bolivar, “An Optimization Method for Data Space Partition Obtained by Classification Techniques for the Monitoring of Dynamic Processes”, in Artificial Intelligence and Development, vol. 146 , M. Polit et al. Eds, Amsterdam: IOS Press, 2006, pp 80-87.
[6] G. J. Klir, and T. A. Folger, Fuzzy sets, Uncertainty and Information, Prentice Hall, Englewood Cliffs, NJ, 1988.
[7] A. DeLuca, and S. Termini, “A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory”, Information and Control, vol. 20, Nº 4, 1972, pp. 301-312.
[8] A. DeLuca, and S. Termini, “Entropy of L-fuzzy sets”, Information and Control, vol. 24, Nº 1, 1974, pp. 55-73.
[9] A. DeLuca, and S. Termini, “On Convergence of entropy measures of a fuzzy set”, Kybernetes, vol. 6, 1977, pp. 219 – 222.
[10] R. R., Yager, “On the Measure of Fuzziness and Negation. Part I: Membership in the Unit Interval”. Int. J. General Systems. Vol. 5, 1979, pp 221-229.
[2] A. Kaufmann, Introduction to the Theory of Fuzzy Subsets. vol. I Fundamental Theoretical Elements., New York: Academic Press, 1975, pp. 25-27.
[3] Ch. Huang, and Y. Shi. Towards Efficient Fuzzy Information Processing. Using the Principle of Information Diffusion, Heidelberg: Physica-Verlag, 2002.
[4] S. Al-sharhan, F. Karray, W. Gueaieb and O. Basir, “Fuzzy Entropy: a Brief survey”, in IEEE International Fuzzy Systems Conference, 2001.
[5] C. Isaza, J. Aguilar-Martin, M. V. Le Lann, J. Aguilar and A. Rios-Bolivar, “An Optimization Method for Data Space Partition Obtained by Classification Techniques for the Monitoring of Dynamic Processes”, in Artificial Intelligence and Development, vol. 146 , M. Polit et al. Eds, Amsterdam: IOS Press, 2006, pp 80-87.
[6] G. J. Klir, and T. A. Folger, Fuzzy sets, Uncertainty and Information, Prentice Hall, Englewood Cliffs, NJ, 1988.
[7] A. DeLuca, and S. Termini, “A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory”, Information and Control, vol. 20, Nº 4, 1972, pp. 301-312.
[8] A. DeLuca, and S. Termini, “Entropy of L-fuzzy sets”, Information and Control, vol. 24, Nº 1, 1974, pp. 55-73.
[9] A. DeLuca, and S. Termini, “On Convergence of entropy measures of a fuzzy set”, Kybernetes, vol. 6, 1977, pp. 219 – 222.
[10] R. R., Yager, “On the Measure of Fuzziness and Negation. Part I: Membership in the Unit Interval”. Int. J. General Systems. Vol. 5, 1979, pp 221-229.
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Published
2009-04-01
How to Cite
Sierra Duque, C. M., & Álvarez, H. (2009). Two fuzziness indexes proposed by Kaufmann: observations about them. Journal of Computer Science and Technology, 9(01), p. 17–20. Retrieved from https://journal.info.unlp.edu.ar/JCST/article/view/737
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