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The transformation method for the simulation and analysis of systems with uncertain parameters. (English) Zbl 1015.65005

Summary: The transformation method is introduced as a powerful approach for both the simulation and the analysis of systems with uncertain model parameters. Based on the concept of $\alpha$-cuts, the method represents a special implementation of fuzzy arithmetic that avoids the well-known effect of overestimation which usually arises when fuzzy arithmetic is reduced to interval computation. Systems with uncertain model parameters can thus be simulated without any artificial widening of the simulation results.

As a by-product of the implementation scheme, the transformation method also provides a measure of influence to quantitatively analyze the uncertain system with respect to the effect of each uncertain model parameter on the overall uncertainty of the model output. By this, a special kind of sensitivity analysis can be defined on the basis of fuzzy arithmetic.

Finally, to show the efficiency of the transformation method, the method is applied to the simulation and analysis of a model for the friction interface between the sliding surfaces of a bolted joint connection.

##### MSC:
 65C60 Computational problems in statistics 93B35 Sensitivity (robustness) of control systems 26E50 Fuzzy real analysis