Abstract
In this chapter, we present basic theoretical foundations of uncertain variables — as a comparatively new tool for analysis and decision problems in uncertain systems [44, 46, 54]. The uncertain variable is described by a certainty distribution given by an expert and characterizing his or her knowledge on approximate values of the variable. The uncertain variables are related to random and fuzzy variables, but there are also essential differences. The comparison with random and fuzzy variables will be presented in Chapter 6. The definitions of the uncertain variables are based on uncertain logics described in Sects. 4.1 and 4.2. It is worth noting that the uncertain logics and variables are defined for any metric space X (the set of values). Starting from Sect. 4.4, the considerations are concerned with a real number vector space X.
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