Comparing Fuzzy and Probability Calculus in Design

This technical report presents a comparison of two methodologies for representing and manipulating imprecision in engineering design: fuzzy calculus and probability calculus. The authors, Kristin L. Wood, Erik K. Antonsson, and James L. Beck, outline the necessity of these methods in the context of preliminary engineering design, where uncertainty in design parameters is prevalent. The report details the characteristics of design imprecision and stochastic uncertainty, emphasizing that fuzzy calculus is particularly effective for handling imprecision, while probability calculus is suited for stochastic uncertainty. Through examples, the report illustrates the application of both methods, progressing from simple operations to complex design equations. The findings indicate that while both methods have their merits, fuzzy calculus offers distinct advantages in managing imprecise design descriptions. The report aims to enhance decision-making processes in engineering design by providing tools that accommodate the inherent uncertainties faced during the design phase.