Numerical solute transport simulation using fuzzy sets approach

This paper applies fuzzy sets and fuzzy arithmetic to incorporate imprecise information into transport modeling of nonreactive solute materials in groundwater flow. The method is applied to both one- and two-dimensional uniform flow fields. Emphasis is on the solution methods of the fuzzy numerical model of solute transport, which is a function of fuzzy variables. The solution techniques, including the vertex method and the fuzzy-numerical simulation method (i.e. the single-value simulation method), are discussed in detail. The solute concentration outputs from the fuzzy finite-difference numerical models based on these two solution methods are compared with those from the fuzzy analytical models. The vertex method can avoid the widening of the fuzzy function value set, in this case, the fuzzy solute concentration function. This widening is due to multi-occurrence of variables in the function expression when using conventional interval analysis. However, in fuzzy finite-difference numerical simulation of solute transport, the vertex method may still overestimate the uncertainty in the concentration outputs since all the fuzzy variables in the fuzzy numerical model are taken to be independent. The fuzzy-numerical simulation method can control the growth of the imprecision in the solute concentration calculations by taking into account the interaction (dependence) of concentration variables in both space and time dimensions in the fuzzy finite-difference model of solute transport. It has the advantage of allowing the use of imprecise data for modeling and also processing the fuzzy information using generated crisp values of fuzzy variables. The adoption of fuzzy sets allows common-sense knowledge to be represented in defining values through the use of a membership function. This enables the subjective information to be incorporated in system modeling in a formal algorithm.