On some optimization problems under uncertainty (Q1094334)

The first part of the paper is devoted to the problem of inexact mathematical programming: Maximize \(f(c,x)\), subject to \(g_ i(a_ i,x)\leq 0\) \((i=1,\dots,m)\), where \(x\in R^ n\), \(c,a_ i\) are unknown parameters being supposed to lie in prescribed sets \(C\), \(A_ i\), respectively. Several strategies for solving such problems, e.g. Wald's criterion, Savage-Niehans, Hurwitz and Laplace criteria are discussed for the convex case of \(f,g_ i\), \(C\) and \(A_ i.\) The results obtained are applied to nonlinear multiobjective optimization problems and an application to capital budgeting of interrelated projects under uncertainty is also presented. The last part deals with nonlinear fuzzy mathematical programming. An extended Bellman-Zadeh's approach to the optimal decision in a fuzzy environment is presented.