Copy
Kazuo HORIUCHI, "A Refined Fixed Point Theorem for Recurrent System of Fuzzy-Set-Valued Nonlinear Mapping Equations and Its Application to Ring Nonlinear Network Systems" in IEICE TRANSACTIONS on Fundamentals,
vol. E87-A, no. 9, pp. 2308-2313, September 2004, 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-1Xi {a family of all non-empty closed compact fuzzy subsets of Xi}. Here, by introducing arbitrary constant βi (0,1], for every integer i (i = 1,2,,n 0), separately, we have a fixed point theorem on the recurrent system of βi -level fuzzy-set-valued mapping equations: xi Fiβi(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 βi -level set Fiβi of the fuzzy set Fi is defined as Fiβi {ξi Xi |µFi (ξi) βi}, for any constant βi (0,1]. This theorem can be applied immediately to discussion for characteristics of ring nonlinear network systems disturbed by undesirable uncertain fluctuations and to extremely 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/e87-a_9_2308/_p
Copy
@ARTICLE{e87-a_9_2308,
author={Kazuo HORIUCHI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Refined Fixed Point Theorem for Recurrent System of Fuzzy-Set-Valued Nonlinear Mapping Equations and Its Application to Ring Nonlinear Network Systems},
year={2004},
volume={E87-A},
number={9},
pages={2308-2313},
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-1Xi {a family of all non-empty closed compact fuzzy subsets of Xi}. Here, by introducing arbitrary constant βi (0,1], for every integer i (i = 1,2,,n 0), separately, we have a fixed point theorem on the recurrent system of βi -level fuzzy-set-valued mapping equations: xi Fiβi(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 βi -level set Fiβi of the fuzzy set Fi is defined as Fiβi {ξi Xi |µFi (ξi) βi}, for any constant βi (0,1]. This theorem can be applied immediately to discussion for characteristics of ring nonlinear network systems disturbed by undesirable uncertain fluctuations and to extremely 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},}
Copy
TY - JOUR
TI - A Refined Fixed Point Theorem for Recurrent System of Fuzzy-Set-Valued Nonlinear Mapping Equations and Its Application to Ring Nonlinear Network Systems
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2308
EP - 2313
AU - Kazuo HORIUCHI
PY - 2004
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E87-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2004
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-1Xi {a family of all non-empty closed compact fuzzy subsets of Xi}. Here, by introducing arbitrary constant βi (0,1], for every integer i (i = 1,2,,n 0), separately, we have a fixed point theorem on the recurrent system of βi -level fuzzy-set-valued mapping equations: xi Fiβi(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 βi -level set Fiβi of the fuzzy set Fi is defined as Fiβi {ξi Xi |µFi (ξi) βi}, for any constant βi (0,1]. This theorem can be applied immediately to discussion for characteristics of ring nonlinear network systems disturbed by undesirable uncertain fluctuations and to extremely fine estimation of available behaviors of those disturbed systems. In this paper, its mathematical situation and proof are discussed, in detail.
ER -
English
