“There is a fairly wide gap between what might be regarded as ‘animate’ system theorists and ‘inanimate’ system theorists at the present time, and it is not at all certain that this gap will be narrowed, much less closed, in the near future. There are some who feel that this gap reflects the fundamental inadequacy of conventional mathematics -the mathematics of precisely- defined points, functions, sets, probability measures, etc.- for coping with the analysis of biological systems, and that to deal effectively with such systems, which are generally orders of magnitude more complex than man-made systems, we need a radically different kind of mathematics, the mathematics of fuzzy or cloudy quantities which are not describable in terms of probability distributions. Indeed, the need for such mathematics is becoming increasingly apparent even in the realm of inanimate systems, for in most practical cases the a priori data as well as the criteria by which the performance of a man-made system are judged are far from being precisely specified or having accurately-known probability distributions”.
KeywordsMembership Function Fuzzy Logic Fuzzy System Fuzzy Rule Fuzzy Controller
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- Dubois D., Prade H. and Yager R.R. (Eds.) (1997). Fuzzy Information Engineering: A Guided Tour of Applications, Wiley, New York.Google Scholar
- Haack S. (1996). Deviant Logic, Fuzzy Logic — Beyond the Formalism, The University of Chicago Press.Google Scholar
- Höhle U. and Rodabaugh S. (Eds.) (1998). Mathematics of Fuzzy sets: Logic, Topology and Measure Theory, The Handbooks of Fuzzy Sets Series, Kluwer Academic Publishers, Dordrecht, The Netherlands.Google Scholar
- Kaiman R.E., and Zadeh L.A. (1974). Discussion, Man and Computer (Marois M., ed.), North-Holland, 93–94.Google Scholar
- Mordeson J.N. and Nair P.S. (1998). Fuzzy Mathematics, Physica-Verlag.Google Scholar
- Patyra M.J. (Ed.) (1996). Fuzzy Logic Hardware Implementations, Special issue, IEEE Trans, on Fuzzy Systems, 4(4), 401–505.Google Scholar
- Patyra M.J. and Mlynek D.M., Eds. (1996). Fuzzy Logic — Implementation and Applications, John Wiley & Sons, Chichester and B.G. Teubner, Stuttgart.Google Scholar
- Verbruggen H.B., Zimmermann H.-J. and Babushka R. (Eds.) (1999). Fuzzy Algorithms for Control, Kluwer Academic, Dordrecht, The Netherlands.Google Scholar
- Zadeh L.A. (1963). Optimality and non-scalar-valued performance criteria, IEEE trans. on Automatic Control, 8 (1), 59–60.Google Scholar
- Zadeh L.A. (1969). Biological application of the theory of fuzzy sets and systems, Proc. of the Symp. on the Biocybernetics of the Higher Nervous System (Proctor L.D., ed.) Little, Brown and Co., Boston, 199–206.Google Scholar
- Zadeh L.A. (1981). Possibility theory and soft data analysis, Mathematical Frontiers of Social and Policy Sciences (Cobb L. and Thrall R.M., eds.), Westview Press, Boulder, Colo. 69–129.Google Scholar
- Zadeh L.A. (1984). Making computers think like people, IEEE Spectrum, 21, 26–32.Google Scholar
- Zadeh L.A. (1999). From computing with numbers to computing with words — From manipulation of measurements to manipulation of perceptions, IEEE Trans, on Circuits and Systems-I: Fundamental Theory and Applications, 45(1), 105–119.Google Scholar