On the convergence and representation of random fuzzy number integrals
type: Item
instance of: scholarly article
title: On the convergence and representation of random fuzzy number integrals
zbMATH Open document ID: 0960.28015
DOI: 10.1016/S0165-0114(97)00150-4
author: Lizhong Wu
author: Xiaoping Xue
author: Xiaomin Wang
published in: Fuzzy Sets and Systems
publication date: 2000-11-26T00:00:00Z
review text: Let \(X\) be a separable reflexive Banach space. A function \(u: X\to[0,1]\) is said to be a Lipschitz fuzzy number if \(u^\alpha:= \{x\in X: u(x)\geq \alpha\}\) is a nonempty closed bounded convex subset of \(X\) for \(\alpha\in ]0,1]\) and there is a constant \(L> 0\) such that \(H(u^\alpha, u^\beta)\leq L|\alpha- \beta|\) for all \(\alpha, \beta\in [0,1]\), where \(H\) denotes the Hausdorff metric. The authors introduce in the space \({\mathcal F}_L(X)\) of all Lipschitz fuzzy numbers on \(X\) the concept of w-s-convergence: \(u_n@>\text{w-s}>> u\) means that \(H(x^* (u^\alpha_n), x^*(u^\alpha))\to 0\) \((n\to\infty)\) for any \(x^*\in X^*\) and \(\alpha\in [0,1]\). w-s-convergence is investigated for sequences in \({\mathcal F}_L(X)\) and for sequences of integrals with values in \({\mathcal F}_L(X)\). Moreover, it is studied the relationship between integration and differentiation for functions \(F: [a,b]\to {\mathcal F}_L(X)\).
reviewed by: Hans Weber
Mathematics Subject Classification ID: 28E10
Mathematics Subject Classification ID: 46S40
zbMATH DE Number: 1339548
zbMATH Keywords: random fuzzy number integral
zbMATH Keywords: Banach space
zbMATH Keywords: Lipschitz fuzzy number
zbMATH Keywords: w-s-convergence
MaRDI profile type: Publication
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full work available at URL: s0165-0114(97)00150-4
OpenAlex ID: W2063055081
description: scientific article; zbMATH DE number 1339548