ABSTRACT
As mentioned earlier, every system possesses uncertainties and they occur due to partial knowledge and truth. In general, partial knowledge–based uncertainties may be handled by probability theory and truth-based uncertainties are operated through possibility theory. In practical problems, we may have the combined effect of both the uncertainties. As such, this chapter comprises hybridization of the concept of stochasticity with fuzzy theory. Here, we have the modelled SDE, which includes the essence of fuzziness, and we call it the fuzzy stochastic differential equation (FSDE). Two well-known methods, viz. Euler–Maruyama method (EMM) and Milstein method (MM), are extended to the fuzzy form, and these are named fuzzy Euler–Maruyama method (FEMM) and fuzzy Milstein method (FMM). These methods have been used to investigate various diffusion problems.
