K. Sakai et al., CHAOTIC RESPONSES IN A SELF-RECURRENT FUZZY INFERENCE WITH NONLINEAR RULES, IEICE transactions on fundamentals of electronics, communications and computer science, E77A(11), 1994, pp. 1736-1741
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Categorie Soggetti
Engineering, Eletrical & Electronic","Computer Science Hardware & Architecture","Computer Science Information Systems
It is shown that a self-recurrent fuzzy inference can cause chaotic re
sponses at least three membership functions, if the inference rules ar
e set to represent nonlinear relations such as pie-kneading transforma
tion. This system has single input and single output both with crisp v
alues, in which membership functions is taken to be triangular. Extens
ions to infinite memberships are proposed, so as to reproduce the cont
inuum case of one-dimensional logistic map f(x) = Ax(1-x). And bifurca
tion diagrams are calculated for number N of memberships of 3, 5, 9 an
d 17. It is found from bifurcation diagrams that different periodic st
ates, coexist at the same bifurcation parameter for N greater-than-or-
equal-to 9. This indicates multistability necessarily accompanied with
hysteresis effects. Therefore, it is concluded that the final states
are not uniquely determined by fuzzy inferences with sufficiently larg
e number of memberships.