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Fuzziness And Catastrophe, Martin Zwick, Daniel Guy Schwartz, George G. Lendaris

Systems Science Faculty Publications and Presentations

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 …