Engineering Design Calculations with Fuzzy Parameters.

Kristin L. Wood, Kevin N. Otto and Erik K. Antonsson

Fuzzy Sets and Systems
Volume 52, Number 1 (Nov. 1992), Pages 1-20.


Uncertainty in engineering analysis usually pertains to {\em stochastic} uncertainty, i.e., variance in product or process parameters characterized by probability (uncertainty in truth). Methods for calculating under stochastic uncertainty are well documented. It has been proposed by the authors that other forms of uncertainty exist in engineering design. Imprecision, or the concept of uncertainty in choice, is one such form. This paper considers real-time techniques for calculating with imprecise parameters. These techniques utilize interval mathematics and the notion of $\alpha$-cuts from the fuzzy calculus. The extremes or anomalies of the techniques are also investigated, particularly the evaluation of singular or multi-valued functions. It will be shown that realistic engineering functions can be used in imprecision calculations, with reasonable computational performance.