A Fluctuation Theory of Systems by Fuzzy Mapping Concept and Its Applications

Kazuo HORIUCHI; Yasunori ENDO

A Fluctuation Theory of Systems by Fuzzy Mapping Concept and Its Applications

Kazuo HORIUCHI, Yasunori ENDO

Full Text Views

0

Cite this

Summary :

This paper proposes a methodology for fine evaluation of the uncertain behaviors of systems affected by any fluctuation of internal structures and internal parameters, by the use of a new concept on the fuzzy mapping. For a uniformly convex real Banach space X and Y, a fuzzy mapping G is introduced as the operator by which we can define a bounded closed compact fuzzy set G(x,y) for any (x,y)∈X×Y. An original system is represented by a completely continuous operator f defined on X, for instance, in a form xλ(f(x)) by a continuous operator λ: YX. The nondeterministic fluctuations induced into the original system are represented by a generalized form of the fuzzy mapping equation xG_β (x,f(x)) {ζX|µ_G(x,f(x))(ζ)β}, in order to give a fine evaluation of the solutions with respect to an arbitrarily–specified β–level. By establishing a useful fixed point theorem, the existence and evaluation problems of the "β–level-likely" solutions are discussed for this fuzzy mapping equaion. The theory developed here for the fluctuation problems is applied to the fine estimation of not only the uncertain behaviors of system–fluctuations but also the validity of system–models and -simulations with uncertain properties.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E77-A No.11 pp.1728-1735

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--

Cite this

Copy

Kazuo HORIUCHI, Yasunori ENDO, "A Fluctuation Theory of Systems by Fuzzy Mapping Concept and Its Applications" in IEICE TRANSACTIONS on Fundamentals, vol. E77-A, no. 11, pp. 1728-1735, November 1994, doi: .
Abstract: This paper proposes a methodology for fine evaluation of the uncertain behaviors of systems affected by any fluctuation of internal structures and internal parameters, by the use of a new concept on the fuzzy mapping. For a uniformly convex real Banach space X and Y, a fuzzy mapping G is introduced as the operator by which we can define a bounded closed compact fuzzy set G(x,y) for any (x,y)∈X×Y. An original system is represented by a completely continuous operator f defined on X, for instance, in a form xλ(f(x)) by a continuous operator λ: YX. The nondeterministic fluctuations induced into the original system are represented by a generalized form of the fuzzy mapping equation xG_β (x,f(x)) {ζX|µ_G(x,f(x))(ζ)β}, in order to give a fine evaluation of the solutions with respect to an arbitrarily–specified β–level. By establishing a useful fixed point theorem, the existence and evaluation problems of the "β–level-likely" solutions are discussed for this fuzzy mapping equaion. The theory developed here for the fluctuation problems is applied to the fine estimation of not only the uncertain behaviors of system–fluctuations but also the validity of system–models and -simulations with uncertain properties.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e77-a_11_1728/_p

Copy

@ARTICLE{e77-a_11_1728,
author={Kazuo HORIUCHI, Yasunori ENDO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Fluctuation Theory of Systems by Fuzzy Mapping Concept and Its Applications},
year={1994},
volume={E77-A},
number={11},
pages={1728-1735},
abstract={This paper proposes a methodology for fine evaluation of the uncertain behaviors of systems affected by any fluctuation of internal structures and internal parameters, by the use of a new concept on the fuzzy mapping. For a uniformly convex real Banach space X and Y, a fuzzy mapping G is introduced as the operator by which we can define a bounded closed compact fuzzy set G(x,y) for any (x,y)∈X×Y. An original system is represented by a completely continuous operator f defined on X, for instance, in a form xλ(f(x)) by a continuous operator λ: YX. The nondeterministic fluctuations induced into the original system are represented by a generalized form of the fuzzy mapping equation xG_β (x,f(x)) {ζX|µ_G(x,f(x))(ζ)β}, in order to give a fine evaluation of the solutions with respect to an arbitrarily–specified β–level. By establishing a useful fixed point theorem, the existence and evaluation problems of the "β–level-likely" solutions are discussed for this fuzzy mapping equaion. The theory developed here for the fluctuation problems is applied to the fine estimation of not only the uncertain behaviors of system–fluctuations but also the validity of system–models and -simulations with uncertain properties.},
keywords={},
doi={},
ISSN={},
month={November},}

Copy

TY - JOUR
TI - A Fluctuation Theory of Systems by Fuzzy Mapping Concept and Its Applications
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1728
EP - 1735
AU - Kazuo HORIUCHI
AU - Yasunori ENDO
PY - 1994
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E77-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 1994
AB - This paper proposes a methodology for fine evaluation of the uncertain behaviors of systems affected by any fluctuation of internal structures and internal parameters, by the use of a new concept on the fuzzy mapping. For a uniformly convex real Banach space X and Y, a fuzzy mapping G is introduced as the operator by which we can define a bounded closed compact fuzzy set G(x,y) for any (x,y)∈X×Y. An original system is represented by a completely continuous operator f defined on X, for instance, in a form xλ(f(x)) by a continuous operator λ: YX. The nondeterministic fluctuations induced into the original system are represented by a generalized form of the fuzzy mapping equation xG_β (x,f(x)) {ζX|µ_G(x,f(x))(ζ)β}, in order to give a fine evaluation of the solutions with respect to an arbitrarily–specified β–level. By establishing a useful fixed point theorem, the existence and evaluation problems of the "β–level-likely" solutions are discussed for this fuzzy mapping equaion. The theory developed here for the fluctuation problems is applied to the fine estimation of not only the uncertain behaviors of system–fluctuations but also the validity of system–models and -simulations with uncertain properties.
ER -