Uncertain variables and their application to decision making problems

This paper describes a concept and basic theory of uncertain variables, an effective tool for dealing with the analysis and decision making in systems with unknown parameters in their mathematical models. To define the uncertain variable it is necessary to introduce an uncertain logic which deals with soft predicates introduced in the paper. Four versions of the uncertain logic and then two versions of the uncertain variables are presented and analyzed. The uncertain variables are defined by certainty distributions given by an expert and are related to random variables and fuzzy numbers. The comparison with probabilistic and fuzzy approaches is discussed. In the second part of the paper we show how the uncertain variables may be applied to the formulation and solving of the decision making problems for the static system described by a function (functional system) and described by a relation (relation system).