Representation and calculation of economic uncertainties: Intervals, fuzzy numbers, and probabilities

Management and decision making when certain information is available may be a matter of rationally choosing the optimal alternative by calculation of the utility function. When only uncertain information is available (which is most often the case) decision-making calls for more complex methods of representation and calculation and the basis for choosing the optimal alternative may become obscured by uncertainties of the utility function. In practice, several sources of uncertainties of the required information impede optimal decision making in the classical sense. In order to be able to better handle the economic uncertainties involved, different procedures have been suggested. This paper discusses the representation of economic uncertainties by intervals,fuzzy numbers and probabilities, including double, triple and quadruple estimates and the problems of applying the four basic arithmetical operations to uncertain economic numbers are discussed. When solving economic models for decision-making purposes calculation of uncertain functions will have to be carried out in addition to the basic arithmetical operations. This is a challenging numerical problem since improper methods of calculation may introduce additional uncertainties not present in the original economic problem. The paper will finally discuss the applicability and limitations of a few computational procedures based on available computer programs used for practical economic calculations with uncertain values. (C) 2002 Elsevier Science B.V. All rights reserved.