Soil water management problems using fuzzy arithmetic

Drainage management problems are usually very hard to simulate due to the uncertainty of
the hydraulic parameters involved. Fuzzy analysis is one of the available tools that can be
used for such problems, involving uncertain data. A fuzzy analysis approach usually involves
the consideration of several α-level cuts and an analytical approach or an explicit scheme
approach for the PDE's discretization. Several application examples of this approach are
listed in the literature, including uncertainty in hydraulic conductivity, specific yield,
transmissivities, porosities, dispersivities, and deoxygenation rate coefficient.
A methodology for the simulation of drainage problem having vague values of hydraulic
parameters is introduced in this paper, and an analytical solution for a two-dimensional
drainage application is presented. The two-dimensional problem of drainage is handled using
fuzzy analysis by defining the hydraulic conductivity K as a triangular fuzzy number (TFN).
The method of interval analysis is used in all the α-level cut examples. A solution is obtained
using eleven α-level cuts and also solutions for two, three, and five α-level cuts are presented.
Trials for different values of effective porosity are also performed. Finally conclusions on the
necessary number of α-cuts utilized for drainage problems are drawn.