Decomposable measures and nonlinear equations
type: Item
instance of: scholarly article
title: Decomposable measures and nonlinear equations
zbMATH Open document ID: 0934.28015
DOI: 10.1016/S0165-0114(97)00171-1
author: Endre Pap
published in: Fuzzy Sets and Systems
publication date: 2000-04-11T00:00:00Z
review text: A closed interval in the extended real line is considered with two binary operations \(\oplus\) and \(\odot\) (pseudo-addition and pseudo-multiplication) having some properties analogous to the properties of the usual addition and multiplication [see \textit{E. Pap}: ``Null-additive set functions'' (1995; Zbl 0856.28001)]. A \(\oplus\)-decomposable measure is characterized by the equality \(m(A\cup B)= m(A)+ m(B)\) for disjoint \(A\), \(B\). Then the pseudo-integral is defined and a special case of \(\oplus\) is considered, where \(u\oplus v= g^{-1}(g(u)+ g(v))\). In this case the so-called \(g\)-derivative is introduced and the apparatus is applied for solving ordinary differential equations and nonlinear difference equations. The pseudo-Laplace transform is used for optimization and the Burgers partial differential equation is solved.
reviewed by: Beloslav Riečan
Mathematics Subject Classification ID: 28E10
Mathematics Subject Classification ID: 26E50
zbMATH DE Number: 1320404
zbMATH Keywords: decomposable measures
zbMATH Keywords: fuzzy measures
zbMATH Keywords: \(g\)-derivative
zbMATH Keywords: ordinary differential equations
zbMATH Keywords: nonlinear difference equations
MaRDI profile type: Publication
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full work available at URL: s0165-0114(97)00171-1
OpenAlex ID: W1974100730
description: scientific article; zbMATH DE number 1320404