NUMERICAL SOLUTE TRANSPORT SIMULATION USING FUZZY-SETS APPROACH

This paper applies fuzzy sets and fuzzy arithmetic to incorporate impr ecise information into transport modeling of nonreactive solute materi als in groundwater flow. The method is applied to both one- and two-di mensional 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 simul ation method), are discussed in detail. The solute concentration outpu ts from the fuzzy finite-difference numerical models based on these tw o solution methods are compared with those from the fuzzy analytical m odels. 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 expr ession when using conventional interval analysis. However, in fuzzy fi nite-difference numerical simulation of solute transport. the vertex m ethod may still overestimate the uncertainty in the concentration outp uts since all the fuzzy variables in the fuzzy numerical model are tak en to be independent. The fuzzy-numerical simulation method can contro l the growth of the imprecision in the solute concentration calculatio ns by taking into account the interaction (dependence) of concentratio n variables in both space and time dimensions in the fuzzy finite-diff erence model of solute transport. It has the advantage of allowing the use of imprecise data for modeling and also processing the fuzzy info rmation using generated crisp values of fuzzy variables. The adoption of fuzzy sets allows common-sense knowledge to be represented in defin ing values through the use of a membership function. This enables the subjective information to be incorporated in system modeling in a form al algorithm. (C) 1997 Elsevier Science B.V.