Quantitative non-monotonic modeling of economic uncertainty by probability and possibility distributions

Two basic approaches to quantitative non-monotonic modeling of economic uncertainty are available today and have been applied to a number of real world uncertainty problems, such as investment analyses and budgeting of large infra structure projects. This paper further contributes to the understanding of similarities and differences of the two approaches as well as practical applications. The probability approach offers a good framework for representation of randomness and variability. Once the probability distributions of uncertain parameters and their correlations are known the resulting uncertainty can be calculated. The possibility approach is particular well suited for representation of uncertainty of a non-statistical nature due to lack of knowledge and requires less information than the probability approach. Based on the kind of uncertainty and knowledge present, these aspects are thoroughly discussed in the case of rectangular representation of uncertainty by the uniform probability distribution and the interval, respectively. Also triangular representations are dealt with and compared. Calculation of monotonic as well as non-monotonic functions of variables represented by probability distributions is readily done by means of Monte Carlo simulation. Calculation of non-monotonic functions of possibility distributions is done within the theoretical framework of fuzzy intervals, but straight forward application of fuzzy arithmetic in general results in overestimation of interval bounds and less specific fuzzy intervals. Correct results to an accuracy specified by the user are obtained by application of a global optimization algorithm. The paper further presents computational evidence of quantitative similarities and differences between probability and probability representations depending on the degree of correlation between probabilistic variables.