Fuzzy Membership Optimization
Cleveland State University
The membership functions of a fuzzy logic system can be optimized for a particular task in a variety of ways. In particular, derivative-based methods such as gradient descent, Kalman filtering, or H-infinity filtering can be used. This web page makes available various m-files that demonstrate fuzzy membership function optimization using gradient descent, Kalman filtering, and H-infinity filtering. The task which is considered by these m-files is an automotive cruise control system. M-files are run in the MATLAB environment. M-files are written in a very high-level language that can be easily read, almost like pseudo code. The data files and m-files are contained in the following zip file.
FuzzyOpt.zip - 16 kilobytes - gradient descent and Kalman filtering
HinfFuzz.zip - 14 kilobytes - Kalman filtering and H-infinity filtering
If you download one of the above zip files to your hard drive by clicking on the above link, then unzip the file (using, for example, WinZip), you can run fuzzy control experiments. When you unzip the file on your hard drive, look at the readme.txt file for more detailed information. If you don't have software to unzip the file, you can download a free evaluation version of WinZip from www.winzip.com.
Note that the above zip files have some duplicate files inside them, so if you download both zip files you should unzip them in separate directories.
Below are some references that discuss the work that I have done in the area of optimization of fuzzy logic systems. Reprints of the below references are available upon request.
1. D. Simon, “H-infinity Estimation for Fuzzy Membership Function Optimization,” International Journal of Approximate Reasoning, vol. 40, no. 3, pp. 224-242, November 2005 - pdf, 312 KB
2. D. Simon, “Training fuzzy systems with the extended Kalman filter,” Fuzzy Sets and Systems, vol. 132, pp. 189-199, December 2002 - pdf, 216 KB
3. D. Simon, “Sum normal optimization of fuzzy membership functions,” International Journal of Uncertainty, Fuzziness, and Knowledge-Based Systems, vol. 10, no. 4, pp. 363-384, August 2002 - pdf, 3.22 MB
4. D. Simon, “Design and rule base reduction of a fuzzy filter for the estimation of motor currents,” International Journal of Approximate Reasoning, vol. 25, pp. 145-167, October 2000 - pdf, 376 KB
5. D. Simon, “Fuzzy membership optimization via the extended Kalman filter,” North American Fuzzy Information Processing Society Conference, pp. 311-315, 2000 - pdf, 256 KB
6. D. Simon, “Fuzzy estimation of DC motor winding currents,” North American Fuzzy Information Processing Society Conference, pp. 859-863, 1999 - pdf, 224 KB
7. D. Simon and H. El-Sherief, “Fuzzy logic for digital phase-locked loop filter design,” IEEE Transactions on Fuzzy Systems, vol. 3, no. 2, pp. 211-218, 1995 – pdf, 637 KB
Last Revised: December 13, 2013