IEICE TRANSACTIONS on Fundamentals
Chaotic Responses in a Self–Recurrent Fuzzy Inference with Nonlinear Rules
Summary :
It is shown that a self–recurrent fuzzy inference can cause chaotic responses at least three membership functions, if the inference rules are set to represent nonlinear relations such as pie–kneading transformation. This system has single input and single output both with crisp values, in which membership functions is taken to be triangular. Extensions to infinite memberships are proposed, so as to reproduce the continuum case of one–dimensional logistic map f(x)=Ax(1–x). And bifurcation diagrams are calculated for number N of memberships of 3, 5, 9 and 17. It is found from bifurcation diagrams that different periodic states coexist at the same bifurcation parameter for N
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E77-A No.11 pp.1736-1741
- Publication Date
- 1994/11/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- Special Section PAPER (Special Section on Nonlinear Theory and Its Applications)
- Category
- Fuzzy System--Theory and Applications--
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Kazuo SAKAI, Tomio MACHIDA, Masao MUKAIDONO, "Chaotic Responses in a Self–Recurrent Fuzzy Inference with Nonlinear Rules" in IEICE TRANSACTIONS on Fundamentals,
vol. E77-A, no. 11, pp. 1736-1741, November 1994, doi: .
Abstract: It is shown that a self–recurrent fuzzy inference can cause chaotic responses at least three membership functions, if the inference rules are set to represent nonlinear relations such as pie–kneading transformation. This system has single input and single output both with crisp values, in which membership functions is taken to be triangular. Extensions to infinite memberships are proposed, so as to reproduce the continuum case of one–dimensional logistic map f(x)=Ax(1–x). And bifurcation diagrams are calculated for number N of memberships of 3, 5, 9 and 17. It is found from bifurcation diagrams that different periodic states coexist at the same bifurcation parameter for N
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e77-a_11_1736/_p
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@ARTICLE{e77-a_11_1736,
author={Kazuo SAKAI, Tomio MACHIDA, Masao MUKAIDONO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Chaotic Responses in a Self–Recurrent Fuzzy Inference with Nonlinear Rules},
year={1994},
volume={E77-A},
number={11},
pages={1736-1741},
abstract={It is shown that a self–recurrent fuzzy inference can cause chaotic responses at least three membership functions, if the inference rules are set to represent nonlinear relations such as pie–kneading transformation. This system has single input and single output both with crisp values, in which membership functions is taken to be triangular. Extensions to infinite memberships are proposed, so as to reproduce the continuum case of one–dimensional logistic map f(x)=Ax(1–x). And bifurcation diagrams are calculated for number N of memberships of 3, 5, 9 and 17. It is found from bifurcation diagrams that different periodic states coexist at the same bifurcation parameter for N
keywords={},
doi={},
ISSN={},
month={November},}
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TY - JOUR
TI - Chaotic Responses in a Self–Recurrent Fuzzy Inference with Nonlinear Rules
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1736
EP - 1741
AU - Kazuo SAKAI
AU - Tomio MACHIDA
AU - Masao MUKAIDONO
PY - 1994
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E77-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 1994
AB - It is shown that a self–recurrent fuzzy inference can cause chaotic responses at least three membership functions, if the inference rules are set to represent nonlinear relations such as pie–kneading transformation. This system has single input and single output both with crisp values, in which membership functions is taken to be triangular. Extensions to infinite memberships are proposed, so as to reproduce the continuum case of one–dimensional logistic map f(x)=Ax(1–x). And bifurcation diagrams are calculated for number N of memberships of 3, 5, 9 and 17. It is found from bifurcation diagrams that different periodic states coexist at the same bifurcation parameter for N
ER -
English
