We introduce two kinds of risk measures with respect to some reference probability measure, which both allow for a certain order structure and domination property. Analyzing their relation each other leads the question when minimax inequality is actually an equality. then provide conditions under corresponding robust measures, being defined as supremum over all induced by set can be represented...

Objective:This study aimed to differentiate illness anxiety and generalized anxiety by the role of metacognition and intolerance of uncertainty. Methods: This research was a descriptive-correlational study with an ex post facto design. The study population included all students of Yazd University, and the study sample comprised 400 healthy adult university students (Mean age=23....

Scientific approaches and methods are considered of the social-economic evaluation efficiency a set measures on improving road safety in conditions uncertainty considered. The risk levels for adopted indicators were determined with help expert presented as fuzzy number. In order to make decision be implemented, scenario method, linear programming, production rules used. An integral indicator is...

Engineering decisions are invariably made under substantial uncertainty about current and future system cost and response, including cost and response associated with low-probability, high-consequence events. A risk-neutral decision maker would rely on expected values when comparing designs, while a riskaverse decision maker might adopt nonlinear utility functions or failure probability criteri...

Multigranulation rough set theory is a relatively new mathematical tool for solving complex problems in the multigranulation or distributed circumstances which are characterized by vagueness and uncertainty. In this paper, we first introduce the multigranulation approximation space. According to the idea of fusing uncertain, imprecise information, we then present three uncertainty measures: fus...

We illustrate the correspondence between uncertainty sets in robust optimization and some popular risk measures in finance, and show how robust optimization can be used to generalize the concepts of these risk measures. We also show that by using properly defined uncertainty sets in robust optimization models, one can construct coherent risk measures, and address the issue of the computational ...