Proceedings of the International Conference of Cybernetics and Society, IEEE Systems, Man, and Cybernetics
Fuzzy Set Theory -- Systems, Fuzzy logic, Many-valued logic -- Mathematical models
In a recent short note, Flondor has alluded to a possible linkage of fuzzy set theory and catastrophe theory. We consider several features of catastrophe theory, namely the properties of discontinuous jumps, hysteresis, and divergence in the "cusp catastrophe," and the role of the bias factor in the "butterfly catastrophe," which have affinities to and suggest possible extensions of fuzzy set ideas. Certain functions extensively considered in catastrophe theory lend themselves in some cases to interpretation as membership functions. The use of such functions may be of interest for the characterization of linguistic descriptions which are time-varying and encompass both discrete and fuzzy distinctions.
This is the accepted manuscript version (post-print). The final version is copyrighted by IEEE Systems, Man, and Cybernetics.
Zwick, M., Schwartz, D.G., and Lendaris, G.G. (1978) "Fuzziness and Catastrophe." [Post-print] Proceedings of the International Conference of Cybernetics and Society, IEEE Systems, Man, and Cybernetics, 1237-1241, November 1978.