On the existence and uniqueness of solutions of fuzzy Volterra-Fredholm integral equations
type: Item
instance of: scholarly article
title: On the existence and uniqueness of solutions of fuzzy Volterra-Fredholm integral equations
zbMATH Open document ID: 0966.45001
DOI: 10.1016/S0165-0114(98)00341-8
author: Jae Ug Jeong
author: Jong Yeoul Park
published in: Fuzzy Sets and Systems
publication date: 2001-08-08T00:00:00Z
review text: Fuzzy integral equations were introduced by \textit{H. Y. Chen} [J. Math. Anal. Appl. 80, 19-30 (1981; Zbl 0506.45014)] as the method of solution of fuzzy differential equations [cf. also \textit{D. Dubois} and \textit{H. Prade}, Fuzzy Sets Syst. 8, 105-116 (1982; Zbl 0493.28003); \textit{R. Goetschel jun.} and \textit{W. Voxman}, ibid. 18, 31-43 (1986; Zbl 0626.26014); \textit{O. Kaleva}, ibid. 24, 301-317 (1987; Zbl 0646.34019)]. This paper contains the existence and uniqueness theorem for the fuzzy version of Volterra-Fredholm integral equation in \(\mathbb{R}^n\) [cf. \textit{P. V. Subrahmanyam} and \textit{S. K. Sudarsanam}, ibid. 81, No. 2, 237-240 (1996; Zbl 0884.45002); \textit{M. Friedman, M. Ming} and \textit{A. Kandel}, Fundam. Inform. 37, No. 1-2, 89-99 (1999; Zbl 0934.45011)]. A verification of its assumptions is difficult (two pages of assumptions without examples).
Mathematics Subject Classification ID: 45B05
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 46S40
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 1545761
zbMATH Keywords: compact fuzzy set
zbMATH Keywords: convex fuzzy set
zbMATH Keywords: fuzzy valued mapping
zbMATH Keywords: integrable mapping
zbMATH Keywords: fuzzy integral equation
zbMATH Keywords: fuzzy solution
zbMATH Keywords: Volterra-Fredholm equation
reviewed by: Józef Drewniak
MaRDI profile type: Publication
cites work: Towards fuzzy differential calculus. I: Integration of fuzzy mappings
cites work: Towards fuzzy differential calculus. II: Integration on fuzzy intervals
cites work: Fuzzy differential equations
cites work: Differentials of fuzzy functions
cites work: Fuzzy random variables
cites work: On the fuzzy initial value problem
full work available at URL: s0165-0114(98)00341-8
OpenAlex ID: W2001644846
description: scientific article; zbMATH DE number 1545761