A Mathematical Theory of System Fluctuations Using Fuzzy Mapping

Kazuo HORIUCHI; Yasunori ENDO

A Mathematical Theory of System Fluctuations Using Fuzzy Mapping

Kazuo HORIUCHI, Yasunori ENDO

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In the direct product space of a complete metric linear space X and its related space Y, a fuzzy mapping G is introduced as an operator by which we can define a projective fuzzy set G(x,y) for any xX and yY. An original system is represented by a completely continuous operator f(x)Y, e.g., in the form x=λ(f(x)), (λ is a linear operator), and a nondeterministic or fuzzy fluctuation induced into the original system is represented by a generalized form of system equation x_βG(x,f(x)). By establishing a new fixed point theorem for the fuzzy mapping G, the existence and evaluation problems of solution are discussed for this generalized equation. The analysis developed here for the fluctuation problem goes beyond the scope of the perturbation theory.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E76-A No.5 pp.678-682

Publication Date: 1993/05/25

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Type of Manuscript: Special Section PAPER (Special Section on Neural Nets,Chaos and Numerics)

Category: Mathematical Theory

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Kazuo HORIUCHI, Yasunori ENDO, "A Mathematical Theory of System Fluctuations Using Fuzzy Mapping" in IEICE TRANSACTIONS on Fundamentals, vol. E76-A, no. 5, pp. 678-682, May 1993, doi: .
Abstract: In the direct product space of a complete metric linear space X and its related space Y, a fuzzy mapping G is introduced as an operator by which we can define a projective fuzzy set G(x,y) for any xX and yY. An original system is represented by a completely continuous operator f(x)Y, e.g., in the form x=λ(f(x)), (λ is a linear operator), and a nondeterministic or fuzzy fluctuation induced into the original system is represented by a generalized form of system equation x_βG(x,f(x)). By establishing a new fixed point theorem for the fuzzy mapping G, the existence and evaluation problems of solution are discussed for this generalized equation. The analysis developed here for the fluctuation problem goes beyond the scope of the perturbation theory.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e76-a_5_678/_p

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@ARTICLE{e76-a_5_678,
author={Kazuo HORIUCHI, Yasunori ENDO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Mathematical Theory of System Fluctuations Using Fuzzy Mapping},
year={1993},
volume={E76-A},
number={5},
pages={678-682},
abstract={In the direct product space of a complete metric linear space X and its related space Y, a fuzzy mapping G is introduced as an operator by which we can define a projective fuzzy set G(x,y) for any xX and yY. An original system is represented by a completely continuous operator f(x)Y, e.g., in the form x=λ(f(x)), (λ is a linear operator), and a nondeterministic or fuzzy fluctuation induced into the original system is represented by a generalized form of system equation x_βG(x,f(x)). By establishing a new fixed point theorem for the fuzzy mapping G, the existence and evaluation problems of solution are discussed for this generalized equation. The analysis developed here for the fluctuation problem goes beyond the scope of the perturbation theory.},
keywords={},
doi={},
ISSN={},
month={May},}

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TY - JOUR
TI - A Mathematical Theory of System Fluctuations Using Fuzzy Mapping
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 678
EP - 682
AU - Kazuo HORIUCHI
AU - Yasunori ENDO
PY - 1993
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E76-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 1993
AB - In the direct product space of a complete metric linear space X and its related space Y, a fuzzy mapping G is introduced as an operator by which we can define a projective fuzzy set G(x,y) for any xX and yY. An original system is represented by a completely continuous operator f(x)Y, e.g., in the form x=λ(f(x)), (λ is a linear operator), and a nondeterministic or fuzzy fluctuation induced into the original system is represented by a generalized form of system equation x_βG(x,f(x)). By establishing a new fixed point theorem for the fuzzy mapping G, the existence and evaluation problems of solution are discussed for this generalized equation. The analysis developed here for the fluctuation problem goes beyond the scope of the perturbation theory.
ER -