Abstract
Although defuzzification is an essential functional part of all fuzzy systems, it is not firmly embedded in fuzzy theory yet.
Proceeding from fuzzy decision theory we define defuzzification as crisp decision under fuzzy constraints and achieve a new theoretical foundation of the defuzzification process. From these theoretical considerations we develop a new class of lucidly customizable defuzzification procedures (constrained decision defuzzification CDD). We develop powerful examples of CDD customization and show that CDD is superior to the standard defuzzification algorithms center of gravity and mean of maxima, represented by the parametric basic defuzzification distribution (BADD), concerning static, dynamic and statistical properties.
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References
H. Bandemer and S. Gottwald. Einführung in Fuzzy Methoden. Akademie Verlag, Berlin, third edition, 1992.
D. Dubois and H. Prade. Fuzzy Sets and Systems. Academic Press, London, 1980.
D. P. Filev and R. R. Yager. A generalized de-fuzzification method via bad distributions. International Journal of Intelligent Systems, 6:687–697, 1991.
N. Pfluger, J. Yen, and R. Langari. A defuzzification strategy for a fuzzy logic controller employing prohibitive information in command formulation. In IEEE International Conference on Fuzzy Systems, pages 717–723, 1992.
T. A. Runkler and M. Glesner. Approximative Synthese von Fuzzy-Controllern. In B. Reusch, editor, Fuzzy Logic — Theorie und Praxis, pages 22–31. Springer, Berlin, 1993.
T. A. Runkler and M. Glesner. Defuzzification with improved static and dynamic behavior: Extended center of area. In European Congress on Fuzzy and Intelligent Technologies, pages 845–851, Aachen, September 1993.
T. A. Runkler and M. Glesner. A set of axioms for defuzzification strategies — towards a theory of rational defuzzification operators. In IEEE International Conference on Fuzzy Systems, San Francisco, pages 1161–1166, March/April 1993.
T. A. Runkler, H.-J. Herpel, and M. Glesner. Einsatz von Fuzzy Logic in einer intelligenten Kupplung. In VDE-Fachtagung “Technische Anwendungen von Fuzzy-Systemen”, pages 120–126, Dortmund, November 1992.
R. R. Yager. Fuzzy sets and approximate reasoning in decision and control. In IEEE International Conference on Fuzzy Systems, pages 418–428, 1992.
L. A. Zadeh. Fuzzy sets. In Information and Control 8, pages 338–353, 1965.
H. J. Zimmermann. Fuzzy Sets, Decision Making, and Expert Systems. Kluwer Academic Publishers, Boston, 1987.
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© 1994 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
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Runkler, T.A., Glesner, M. (1994). Defuzzification As Crisp Decision Under Fuzzy Constraints — New Aspects of Theory and Improved Defuzzification Algorithms. In: Kruse, R., Gebhardt, J., Palm, R. (eds) Fuzzy-Systems in Computer Science. Artificial Intelligence / Künstliche Intelligenz. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-86825-1_20
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DOI: https://doi.org/10.1007/978-3-322-86825-1_20
Publisher Name: Vieweg+Teubner Verlag
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