Granular approximation of solutions of partial differential equations with fuzzy parameter

Fuzzy graph formed by a collection of fuzzy rules approximate solutions of partial differential equations with imprecise parameters in the form of fuzzy numbers. The fuzzy rules can be constructed by a judicious discretization of the variables domains, and using the extension principle on the fuzzy parameter. A detailed algorithm is developed, and numerical examples are offered using the heat, wave, and Poisson equations with triangular fuzzy numbers.