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On Using Fuzzy Arithmetic to Solve Problems with Uncertain Model Parameters

Fuzzy arithmetic, based on Zadeh’s extension principle, is presented as a tool to solve engineering problems with uncertain model parameters. Fuzzy numbers are introduced, and different concepts to practically implement the uncertainty of the parameters are discussed. As an example, a rather simple but typical problem of engineering mechanics is considered. It consists of determining the displacements in a two-component massless rod under tensile load with uncertain elasticity parameters. The application of fuzzy arithmetic directly to the traditional techniques for the numerical solution of the engineering problem, however, turns out to be impracticable in all circumstances. In contrast to the use of exclusively crisp numbers, the results for the calculations including fuzzy numbers usually differ to a large extent depending on the solution technique applied. The uncertainties expressed in the different calculation results are then basically twofold. On the one hand, uncertainty is caused by the presence of parameters with fuzzy value, on the other hand, an additional, undesirable uncertainty is artificially created by the solution technique itself. This fuzzy-specific effect of artificial uncertainties is discussed and some concepts for its reduction are presented.