The expected value models on Sugeno measure space
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.
scientific article; zbMATH DE number 5690182
scientific article