The expected value models on Sugeno measure space
type: Item
instance of: scholarly article
title: The expected value models on Sugeno measure space
zbMATH Open document ID: 1198.28020
author: Ming-Hu Ha
author: Hong Zhang
author: Witold Pedrycz
author: Hong-Jie Xing
published in: International Journal of Approximate Reasoning
publication date: 2010-04-07T00:00:00Z
review text: Stochastic programming is the earliest and most familiar approach for optimization problems under uncertainty. Based on probability, possibility and credibility measures, [see \textit{B. Liu}, Uncertainty theory. Berlin: Springer (2004; Zbl 1072.28012)] other approaches for optimization under uncertainty are proposed. The authors especially discuss optimization problems where the uncertainty is modeled by the Sugeno measure \(g_\lambda\) which for \(\lambda = 0\) reduces to a probability measure. First they develop a probability-like theory in a so called Sugeno measure space, with \(g_\lambda\) random variables, their distribution functions, with the notions of independence and expectation, with laws of large numbers a.s.o. Then they discuss the so-called Sugeno expected value model (SEVM) where a given expected objective function is to be minimized subject to some expected constraints. To find an approximate solution of the SEVM ideas of Sugeno random number generation and Sugeno simulation are presented along with a hybrid approach.
reviewed by: Wolfgang Näther
Mathematics Subject Classification ID: 28E10
Mathematics Subject Classification ID: 90C15
Mathematics Subject Classification ID: 90C70
zbMATH DE Number: 5690182
zbMATH Keywords: Sugeno measure
zbMATH Keywords: \(g_\lambda\) random variable
zbMATH Keywords: Sugeno expected value model
zbMATH Keywords: optimization
MaRDI profile type: Publication
full work available at URL: j.ijar.2009.03.008
OpenAlex ID: W2046568540
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DOI: 10.1016/J.IJAR.2009.03.008
description: scientific article; zbMATH DE number 5690182