Abstract
A introduction to the basic concepts of fuzzy set theory is first provided. We next discuss some ideas from the theory of of approximate reasoning. As we shall see it is this theory, which uses fuzzy sets as its primary representational structure, that provides a formal mechanism for reasoning with uncertain information. Finally we discuss the technology of fuzzy systems modeling. This technology has provided the bases for most of the current generation of applications of fuzzy set theory.
Preview
Unable to display preview. Download preview PDF.
References
Zadeh, L. A., “Fuzzy sets,” Information and Control 8, 338–353, 1965.
Yager, R. R. and Filev, D. P., Essentials of Fuzzy Modeling and Control, John Wiley: New York, 1994.
Klir, G. J. and Bo, Y., Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall: Upper Saddle River, NJ, 1995.
Yager, R. R., “On a general class of fuzzy connectives,” Fuzzy Sets and Systems 4. 235–242, 235–242, 1980.
Klement, E. P., “Characterization of fuzzy measures constructed by means of triangular norms,” J. of Math. Anal. & Appl. 86, 345–358, 1982.
Weber, S., “A general concept of fuzzy connectives, negations and implications based on t-norms,” Fuzzy Sets and Systems 11, 115–134, 1983.
Zadeh, L. A., “Fuzzy sets as a basis for a theory of possibility,” Fuzzy Sets and Systems 1, 3–28, 1978.
Dubois, D. and Prade, H., Possibility Theory: An Approach to Computerized Processing of Uncertainty, Plenum Press: New York, 1988.
Zadeh, L. A., “A theory of approximate reasoning,” in Machine Intelligence, Vol. 9, Hayes, J., Michie, D., & Mikulich, L.I. (eds.), New York: Halstead Press, 149–194, 1979.
Yager, R. R., Ovchinnikov, S., Tong, R. and Nguyen, H., Fuzzy Sets and Applications: Selected Papers by L. A. Zadeh, John Wiley & Sons: New York, 1987.
Zadeh, L. A., “PRUF-a meaning representation language for natural languages,” International journal of Man-Machine Studies 10, 395–460, 1978.
Yager, R. R., “The entailment principle for Dempster-Shafer granules,” Int. J. of Intelligent Systems 1, 247–262, 1986.
Yager, R. R., Sugeno, M., Nguyen, H. T. and Tong, R. T., Theoretical Aspects of Fuzzy Control, John Wiley & Sons: New York, 1995.
Kosko, B., Neural Networks and Fuzzy Systems, Prentice Hall: Englewood Cliffs, NJ, 1991.
Zadeh, L., “Outline of a new approach to the analysis of complex systems and decision processes,” IEEE Trans. Systems, Man, and Cybernetics, SMC-3, 28–44, 1973.
Mamdani, E. H., “Application of fuzzy algorithms for control of simple dynamic plant,” Proc. IEEE 121, 1585–1588, 1974.
Mamdani, E. H. and Assilian, S., “An experiment in linguistic synthesis with a fuzzy logic controller,” Int. J. of Man-Machine Studies 7, 1–13, 1975.
Mamdani, E. H. and Baaklini, N., “Prescriptive method for deriving control policy in a fuzzy logic control,” Electronic Lett. Ii, 625–626, 1975.
Mamdani, E. H., “Advances in the linguistic synthesis of fuzzy controllers,” Int. J. of Man-Machine Studies 8, 669–678, 1976.
Sugeno, M., Industrial Applications of Fuzzy Control, North-Holland: Amsterdam, 1985.
Yen, J., Langari, R. and Zadeh, L. A., Industrial Applications of Fuzzy Logic and Intelligent Systems, IEEE Press: New York, 1995.
Yager, R. R. and Filev, D. P., “On a flexible structure for fuzzy systems models,” in Fuzzy Sets, Neural Networks and Soft Computing, edited by Yager, R. R. and Zadeh, L. A., Van Nostrand: New York, 1–28, 1994.
Takagi, T. and Sugeno, ML, “Fuzzy identification of systems and its application to modeling and control,” IEEE Transactions on Systems, Man and Cybernetics 15, 116–132, 1985.
Yager, R. R. and Filev, D. P., “Learning of fuzzy rules by mountain clustering,” SPIE Conference on Applications of Fuzzy Logic Technology, Boston, 246–254, 1993.
Yager, R. R. and Filev, D. P., “Approximate clustering via the mountain method,” IEEE Transactions on Systems, Man and Cybernetics 24, 1279–1284, 1994.
Yager, R. R. and Filev, D. P., “Generation of fuzzy rules by mountain clustering,” Journal of Intelligent and Fuzzy Systems 2, 209–219, 1994.
Chiu, S. L., “Fuzzy model identification based on cluster estimation,” Journal of Fuzzy and Intelligent Systems 2, 267–278, 1994.
Bezdek, J., Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum: New York, 1981.
Pedrycz, W., Fuzzy Sets Engineering, CRC Press: Boca Raton, FL, 1995.
Yager, R. R. and Filev, D. P., “Template based fuzzy systems modeling,” Journal of Intelligent and Fuzzy Systems 2, 39–54, 1994.
Tong, R. M., “Synthesis of fuzzy models for industrial processes-some recent results,” Int. J. of General Systems 4, 143–163, 1978.
Dubois, D., Prade, H. and Yager, R. R., Readings in Fuzzy Sets for Intelligent Systems, Morgan Kaufmann: San Mateo, CA, 1993.
Bezdek, J. C. and Pal, S. K., Fuzzy Models for Pattern Recognition, IEEE Publications: New York, 1992.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Yager, R.R. (1995). Fuzzy sets as a tool for modeling. In: van Leeuwen, J. (eds) Computer Science Today. Lecture Notes in Computer Science, vol 1000. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015265
Download citation
DOI: https://doi.org/10.1007/BFb0015265
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60105-0
Online ISBN: 978-3-540-49435-5
eBook Packages: Springer Book Archive