Abstract
We continue the investigation into the dynamics and evolution of fuzzy rules, obtained by the fuzzification of the disjunctive normal form, and initiated for rule 90 in [2], for rule 110 in [10] and for rule 30 in [3]. We present general methods for detecting the evolution and dynamics of any one of the 255 fuzzy rules and apply this theory to fuzzy rules 30, 110, 18, 45, and 184, each of which has a Boolean counterpart with interesting features. Finally, it is deduced that (except for at most nine cases) no fuzzy cellular automaton admits chaotic behavior in the sense that no sensitive dependence on the initial string can occur.
This research is partially supported by an NSERC Canada Discovery Grant and by a grant from the Office of the Vice-President Research and International, Carleton University.
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Mingarelli, A.B. (2005). The Dynamics of General Fuzzy Cellular Automata. In: Sunderam, V.S., van Albada, G.D., Sloot, P.M.A., Dongarra, J.J. (eds) Computational Science – ICCS 2005. ICCS 2005. Lecture Notes in Computer Science, vol 3515. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11428848_47
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DOI: https://doi.org/10.1007/11428848_47
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