Fuzzy finite element

The fuzzy finite element method combines the well-established finite element method with the concept of fuzzy numbers, the latter being a special case of a fuzzy set. The advantage of using fuzzy numbers instead of real numbers lies in the incorporation of uncertainty in the finite element analysis.
One way to establish a fuzzy finite element analysis is to use existing FE software as an inner-level module to compute a deterministic result, and to add an outer-level loop to handle the fuzziness. This outer-level loop comes down to solving an optimization problem. If the inner-level deterministic module produces monotonic behavior with respect to the input variables, then the outer-level optimization problem is greatly simplified, since in this case the extrema will be located at the vertices of the domain.