Uncertain variables and their applications for a class of uncertain systems

Abstract

This paper presents definitions and basic properties of uncertain variables and shows how they may be applied to the analysis and decision making in static systems with unknown parameters in their mathematical models. The unknown parameters are assumed to be uncertain variables described by certainty distributions given by an expert. Two versions of the uncertain variables are described. The uncertain variable in the first version may be considered as a special case of the fuzzy number with a specific interpretation. Two forms of systems are considered in the paper: a system described by a function (functional system) and a system described by a relation (relational system). In both cases the statements and general solutions of the analysis and decision problems are presented. Simple examples illustrating the application of the uncertain variables are included.