single-jc.php

JACIII Vol.4 No.1 pp. 95-101
doi: 10.20965/jaciii.2000.p0095
(2000)

Paper:

Fuzzy Rule Interpolation by the Conservation of Relative Fuzziness

Laszlo T. Koczy*, Kaoru Hirota** and Tamas D. Gedeon***

*International Education Center, Budapest University of Technology and Economics Building Z. 1F. 102, Bertalan L str 2, Budapest, H-1111, Hungary

**Department of Computational Intelligence and Systems Sciences Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology 4259 Nagatsuta, Midori-ku, Yokohama 226, Japan

***School of Information Technology, Murdoch University Perth WA, 6150, Australia

Received:
October 4, 1997
Accepted:
November 5, 1999
Published:
January 20, 2000
Keywords:
Fuzzy inference, Interpolation
Abstract

If the number of variables is growing the size of fuzzy rule bases increase exponentially. To reduce size and inference/control time, it is often necessary to deal with sparse rule bases. In such bases, classic algorithms such as the CRI of Zadeh and the Mamdani-method do not function. In such rule bases, rule interpolation techniques are necessary. The linear rule interpolation (KHinterpolation) based on the Fundamental Equation of Interpolation introduced by Koczy and Hirota is suitable for dealing with sparse bases, but this method often results in conclusions which are not directly interpretable, and need some further transformations. One of the possible ways to avoid this problem is the interpolation method based on the conservation of fuzziness, proposed recently by Gedeon and Koczy for trapezoidal fuzzy sets. In this paper, a refined version of that method will be presented that is fully in accordance with the Fundamental Equation, with extensions to multiple dimensions, and then to arbitrarily shaped membership functions. Several possibilities for the latter will be shown.

Cite this article as:
L. Koczy, K. Hirota, and T. Gedeon, “Fuzzy Rule Interpolation by the Conservation of Relative Fuzziness,” J. Adv. Comput. Intell. Intell. Inform., Vol.4, No.1, pp. 95-101, 2000.
Data files:

*This site is desgined based on HTML5 and CSS3 for modern browsers, e.g. Chrome, Firefox, Safari, Edge, IE9,10,11, Opera.

Last updated on Jul. 12, 2019