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Kazuo HORIUCHI, "A Fixed Point Theorem for Recurrent System of Fuzzy-Set-Valued Nonlinear Mapping Equations" in IEICE TRANSACTIONS on Fundamentals,
vol. E86-A, no. 9, pp. 2256-2261, September 2003, doi: .
Abstract: Let us introduce n ( 2) nonlinear mappings fi (i = 1,2,,n) defined on complete linear metric spaces (Xi-1,ρ) (i = 1,2,,n), respectively, and let fi: Xi-1 Xi be completely continuous on bounded convex closed subsets Xi-1,(i = 1,2,,n 0), such that fi() . Moreover, let us introduce n fuzzy-set-valued nonlinear mappings Fi: Xi-1 Xi {a family of all non-empty closed compact fuzzy subsets of Xi}. Here, we have a fixed point theorem on the recurrent system of β-level fuzzy-set-valued mapping equations: xi Fiβ(xi-1,fi(xi-1)), (i = 1,2,,n 0), where the fuzzy set Fi is characterized by a membership function µFi(xi): Xi [0,1], and the β-level set Fiβ of the fuzzy set Fi is defined as Fiβ {ξi Xi | µFi(ξi) β}, for any constant β (0,1]. This theorem can be applied immediately to discussion for characteristics of ring nonlinear network systems disturbed by undesirable uncertain fluctuations and to fine estimation of available behaviors of those disturbed systems. In this paper, its mathematical situation and proof are discussed, in detail.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e86-a_9_2256/_p
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@ARTICLE{e86-a_9_2256,
author={Kazuo HORIUCHI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Fixed Point Theorem for Recurrent System of Fuzzy-Set-Valued Nonlinear Mapping Equations},
year={2003},
volume={E86-A},
number={9},
pages={2256-2261},
abstract={Let us introduce n ( 2) nonlinear mappings fi (i = 1,2,,n) defined on complete linear metric spaces (Xi-1,ρ) (i = 1,2,,n), respectively, and let fi: Xi-1 Xi be completely continuous on bounded convex closed subsets Xi-1,(i = 1,2,,n 0), such that fi() . Moreover, let us introduce n fuzzy-set-valued nonlinear mappings Fi: Xi-1 Xi {a family of all non-empty closed compact fuzzy subsets of Xi}. Here, we have a fixed point theorem on the recurrent system of β-level fuzzy-set-valued mapping equations: xi Fiβ(xi-1,fi(xi-1)), (i = 1,2,,n 0), where the fuzzy set Fi is characterized by a membership function µFi(xi): Xi [0,1], and the β-level set Fiβ of the fuzzy set Fi is defined as Fiβ {ξi Xi | µFi(ξi) β}, for any constant β (0,1]. This theorem can be applied immediately to discussion for characteristics of ring nonlinear network systems disturbed by undesirable uncertain fluctuations and to fine estimation of available behaviors of those disturbed systems. In this paper, its mathematical situation and proof are discussed, in detail.},
keywords={},
doi={},
ISSN={},
month={September},}
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TY - JOUR
TI - A Fixed Point Theorem for Recurrent System of Fuzzy-Set-Valued Nonlinear Mapping Equations
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2256
EP - 2261
AU - Kazuo HORIUCHI
PY - 2003
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E86-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2003
AB - Let us introduce n ( 2) nonlinear mappings fi (i = 1,2,,n) defined on complete linear metric spaces (Xi-1,ρ) (i = 1,2,,n), respectively, and let fi: Xi-1 Xi be completely continuous on bounded convex closed subsets Xi-1,(i = 1,2,,n 0), such that fi() . Moreover, let us introduce n fuzzy-set-valued nonlinear mappings Fi: Xi-1 Xi {a family of all non-empty closed compact fuzzy subsets of Xi}. Here, we have a fixed point theorem on the recurrent system of β-level fuzzy-set-valued mapping equations: xi Fiβ(xi-1,fi(xi-1)), (i = 1,2,,n 0), where the fuzzy set Fi is characterized by a membership function µFi(xi): Xi [0,1], and the β-level set Fiβ of the fuzzy set Fi is defined as Fiβ {ξi Xi | µFi(ξi) β}, for any constant β (0,1]. This theorem can be applied immediately to discussion for characteristics of ring nonlinear network systems disturbed by undesirable uncertain fluctuations and to fine estimation of available behaviors of those disturbed systems. In this paper, its mathematical situation and proof are discussed, in detail.
ER -
English
