On the implementation of fuzzy arithmetical operations for engineering problems

Fuzzy arithmetic is a successful tool to solve engineering problems with uncertain parameters. The generalized mathematical operations for fuzzy numbers can theoretically be defined making use of Zadeh's extension principle. Practical real-world applications of fuzzy arithmetic, however require an appropriate form of implementation for the fuzzy numbers and the fuzzy arithmetical operations. For this mason, the often applied concept of triangular fuzzy numbers and the more promising approach of discretized fuzzy numbers are presented and rated with respect to their practical application to solve engineering problems with uncertain parameters. As an example, a rather simple but typical problem of mechanical engineering is considered, consisting of determining the displacements in a two-component massless rod under tensile load with uncertain elasticity parameters.