In the fuzzy finite element method uncertain geometrical, material and loading parameters are treated as fuzzy values. The modeling of uncertain parameters as fuzzy values is necessary when it is not possible to uniquely and reliably specify these parameters either deterministically or stochastically. Often in such cases, only a limited number of samples are available or the reproduction conditions for generating sample elements vary. The parameters possess informal or lexical uncertainty, which may be modeled as fuzziness.  

Physical parameters possessing fuzziness with regard to external loading or material, geometrical and model parameters may occur at all points of a structure. Depending on the dimensionality of the structure - ¹ bar structures , ² plane structures, ³ 3-D structures – it is proposed to describe fuzziness using fuzzy functions. The fuzzy function is approximated by means of fuzzy values at suitably distributed interpolation nodes in ⁿ. Fuzzy values at interpolation nodes are fuzzy numbers, which describe the fuzziness of the physical parameter concerned at discrete points i.  These discrete points may be (but not necessarily) identical to nodes in the finite element mesh.

The fundamental equations of the FE method are derived e.g. on the basis of the principle of virtual displacements, taking into consideration the fuzziness of the geometrical, material and loading parameters. Accounting for inertial and damping forces, a second-order system of fuzzy differential equations is obtained.

Closed solutions of this system of fuzzy equations already exist for simple special cases. In the case of a larger number of fuzzy parameters, also taking into account nonlinearities, the system of fuzzy equations can be solved numerically by the fuzzy finte element method. Solution strategies must take into consideration the interaction relationships between fuzzy values and the special properties of the mapping model.

Both in linear statical and dynamical analysis as well as in the case of geometrically and/or physically nonlinear analysis the fuzzy analysis may be applied, which involves the α-level discretization and the repeated solution of an optimization problem, e.g. by means of a modified evolution strategy.