Uncertainty Modeling Using Expert’s Knowledge as Evidence

Abstract

In this paper we discuss the uncertainty modeling using evidence theory. In practice, very often availability of data is incomplete in the sense that sufficient amount of data which is required may not be possible to collect. Therefore, uncertainty modeling in that case with this incomplete data set is not possible to carry out using probability theory or Monte Carlo method. Fuzzy set theory or any other imprecision based theory is applicable in this case. With a view to this expert’s knowledge is represented as the input data set. Belief and plausibility are the two bounds (lower and upper) of the uncertainty of this imprecision based system. The fundamental definitions and the mathematical structures of the belief and plausibility fuzzy measures are discussed in this chapter. Uncertainty modeling using this technique is illustrated with a simple example of contaminant transport through groundwater.