A Review of Developments from Fuzzy Rule Bases to Fuzzy Functions

Abstract

We first touch upon a Philosophical Grounding of fuzzy theory expressed by Pierce and Zadeh. Then we review briefly basic and well known fuzzy rule base models and their variations as well as our fuzzy functions with LSE and their enhanced version. We propose a potential future investigation for the basic structure of fuzzy function models generated with an additive effect of membership values and suggest future research for a multiplicative affect of membership values.

Keywords

• System structure identification,Fuzzy rule bases,Fuzzy functions with additive components,Future research for fuzzy functions with multiplicative components,2000 AMS Classification: 03 B 52

A REVIEW OF DEVELOPMENTS FROM FUZZY RULE BASES TO FUZZY FUNCTIONS

Abstract

References

1. Babuska, R. and Verbruggen, H. B. Constructing fuzzy models by product space clustering, in: H. Hellendoorn and D. Driankov(eds.), Fuzzy Model Identification: Selected Approaches (Springer, Berlin, 1997), 53-90. [2] Bezdek, J. C. Pattern recognition with fuzzy objective function algorithms ISBN-10: 0306406713|ISBN-13: 9780306406713 (1981).
2. Celikyilmaz, A. and Turksen, I. B. Enhanced fuzzy system models with improved fuzzy clus- tering algorithm, IEEE Trans. Fuzzy Systems 16, 779–794, 2008.
3. Delgado, M. Gomez-Skermata, A. F. and Martin, F. Rapid prototyping of fuzzy models, in: H. Hellendoorn and D. Driankov (Eds.), Fuzzy Model Identification: Selected Approaches (Springer, Berlin, 1997), 53-90. [5] Hathaway, R. J. and Bezdek, J. C. Switching regression models and fuzzy clustering, IEEE Transactions on Fuzzy Systems 1 (3), 195–204, 1993.
4. Hoppner, F. and Klawonn, F. Improved fuzzy partitions for fuzzy regression models, Inter- national Journal of Approximate Reasoning 32, 85–102, 2003.
5. Mamdani, E. M. Application of fuzzy logic to approximate reasoning using linguistic systems 26, 1182–1191, 1977.
6. Mizimoto, M. Method of fuzzy inference suitable for fuzzy control, J. Soc. Instrument Control Engineering 58, 959–963, 1989. [9] Ozkan, I. and Turksen, I. B. Upper and lower values for the level of fuzziness in FCM, Inf. Sci., 5143–5152, 2007.
7. Schweitzer, B. and Sklar, A. Probabilistic Metric Spaces (North-Holland, New York, 1983). [11] Sugeno, M. and Yasukawa, T. A fuzzy logic based approach to qualitative modelling, IEEE Trans on Fuzzy Systems 1 (1), 7–31, 1993.
8. Takagi, T. and Sugeno, M. Fuzzy identification of systems and its applications to modelling and control, IEEE Transactions on Systems, Man and Cybernetics, SMC-15 (1), 116–132, 1985.

9. Turksen, I. B. Interval valued fuzzy sets based on normal forms, Fuzzy Sets and Systems 20, 191–210, 1986.
10. Turksen, I. B. Four methods of approximate reasoning with interval-valued fuzzy sets, Int. J. Approximate Reasoning 3, 121–142, 1989.
11. Turksen, I. B. Interval-valued fuzzy sets and compensatory AND, Fuzzy Sets and Systems 51, 295–307, 1992.
12. Turksen, I. B. Interval valued fuzzy sets and fuzzy connectives, Interval Computations, 125– 142, 1993.
13. Turksen, I. B. Interval valued fuzzy sets and fuzzy measures, Proc. First Int. Conf. of NAFIPS, 317–321, 1994.
14. Turksen, I. B. Fuzzy normal forms, Fuzzy Sets and Systems 69, 319–346, 1995.
15. Turksen, I. B. Type I and “interval-valued” type II fuzzy sets and logics, in: P. Wang (Ed.), Advances in Fuzzy Set Theory and Technology, 1995.
16. Turksen, I. B. Non-specificity and interval-valued fuzzy sets, Fuzzy Sets and Systems 80, 87–100, 1996.
17. Turksen, I. B. Type I and type II fuzzy system modeling, Fuzzy Sets and Systems 106, 11–34, 1999.
18. Turksen, I. B. Type 2 representation and reasoning for CWW, Fuzzy Sets and Systems 127, 17–36, 2002.
19. Turksen, I. B. Fuzzy functions with LSE, Applied Soft Computing 8, 1178–1188, 2008.
20. Uncu, O. and Turksen, I. B. A novel fuzzy system modeling approach: Multidimensional structure identification and inference, Proc. Tenth IEEE, International Conference on Fuzzy Systems, (Melbourne, Australia, 2001), 557–562.
21. Vapnik, N. V. Statistical Learning Theory (John Wiley and Sons, New York, 1998).
22. Zadeh, L. A. Fuzzy sets, Information and Control 8, 338–353, 1965.
23. Zadeh, L. A. The concept of a linguistic variable and its application to approximate reason- ing, Information Sciences 8, 199–249, 1975.