A New Approach of Fuzzy Theory with Uncertainties in Geographic Information Systems

Until now, fuzzy logic has been extensively used to better analyze and design controllers for chemical processes. It has also been used for other applications like parameter estimation of nonlinear continuous-time systems but in general fuzzy logic has been intensively used for heuristics based system. Recently, fuzzy logic has been applied successfully in many areas where conventional model based approaches are difficult or not cost effective to implement. Mechanistic modeling of physical systems is often complicated by the presence of uncertainties. When models are used as purely predictive tools, uncertainty and variability lead to the need for assessment of the plausible range of model outcomes. A systematic uncertainty analysis provides insight into the level of confidence in model estimates, and can aid in assessing how various possible model estimates should be weighed. In this paper, generalized fuzzy α-cut is used to show the utility of fuzzy approach in uncertainty analysis of pollutant transport in ground water. Based on the concept of transformation method which is an extension of α-cuts, the approach shows superiority over conventional methods of uncertainty modeling. A 2-D groundwater transport model has been used to show the utility of this approach. Results are compared with commonly used probabilistic method and normal Fuzzy alpha-cut technique. In order to provide a basis for comparison between the two approaches, the shape of the membership functions used in the fuzzy methods are the same as the shape of the probability density function used in the Monte-Carlo method. The extended fuzzy α-cut technique presents a strong alternative to the conventional approach.