where the future cost f depends both on the decision u ∈ U as well as the outcome of uncertain events, represented by a random variable X ∈ X . Here the random variable X follows a distribution P which is assumed to be known in order to form the expectation in problem (1). Examples includes making an inventory decision with uncertainty future demand, purchasing stocks with uncertain information...

A complex structure has many uncertain factors and how to make a more accurate analysis on the structure reliability by a method is the key in engineering calculation. Rough set theory is utilized to analyze the fuzzy, random and uncertain factors and upper and lower approximation set relation is used to calculate the value taking interval of reliability index to make reliability index analysis...

Abstract: Uncertain information about a system variable described by a random set or an equivalent Dempster-Shafer structure on a finite space of singletons determines an infinite convex set of probability distributions, given by the convex hull of a finite set of extreme distributions. Extreme distributions allow one to evaluate (through the Choquet integral) exact upper/lower bounds of the ex...

Based on the chance theory, which is founded for modeling complex systems with not only uncertainty but also randomness, this paper is devoted to studying a new kind of multiobjective programming problem where randomness and uncertainty exist simultaneously, called uncertain random multiobjective programming (URMOP) problem. Since an uncertain random variable does not admit an order relationshi...

This paper discusses the uncertain portfolio selection problem when security returns cannot be well reflected by historical data. It is proposed that uncertain variable should be used to reflect the experts’ subjective estimation of security returns. Regarding the security returns as uncertain variables, the paper introduces a risk curve and develops a mean-risk model. In addition, the crisp fo...

This paper investigates the single period inventory Newsboy problem in a general uncertain environment. Here it is assumed that the uncertainty appears in the market demand of the product. Uncertain demand is used to describe a subjective estimate (not estimated by random/fuzzy demand), linguistically expressed by ‘‘demand is about n’’. Using identification functions of the uncertain variable w...

Most natural variables assume values at points within a spatiotemporal continuum. Each point in this continuum is represented by its space and time coordinates p = (s,t). Randomness of a natural variable manifests itself as an ensemble of possible realizations over the space/time continuum. This leads to the concept of the spatiotemporal random field (S/TRF) X(p), which is a collection of reali...