Uncertainty quantification under hybrid structure of probability-fuzzy parameters in Gaussian plume model

Abstract

In almost all the realistic circumstances, such as atmospheric dispersion and health risk assessment analysis, it is very essential to include all the information into modelling. The parameters associated with a particular model may include different kinds of variability, imprecision and uncertainty. More often, it is seen that available information is interpreted in probabilistic sense. Probability theory is a well-established theory to measure such kind of variability. However, not all available information, data or model parameters affected by variability, imprecision and uncertainty can be handled by traditional probability theory. Uncertainty or imprecision may occur due to incomplete information or data, measurement error or data obtained from expert judgment or subjective interpretation of available data or information. Thus, model parameters’ data may be affected by subjective uncertainty. Traditional probability theory is inappropriate to represent subjective uncertainty. Possibility theory is another branch of mathematics which is used as a tool to describe the parameters with insufficient knowledge. It may also happen that the probabilistic information about the parameters may be imprecise; that is, it might be associated with some probability bounds. Such types of uncertainty are incorporated into imprecise probability, a theory that extends traditional probability theory by allowing for intervals or sets of probabilities. In this paper, an attempt has been made to combine imprecise probability knowledge and possibility knowledge and draw the uncertainty. The article describes a combination of imprecise probability and fuzzy knowledge and applied to atmospheric dispersion with a case study. Further, fuzziness measure has been utilized in quantifying the uncertainty.