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The Calculus of Imprecision for the Analysis and Evaluation of Engineering Models



Ronald Giachetti


Engineering design is characterized by a high level of imprecision, vague parameters, and ill-defined relationships. In design, imprecision reduction must occur to arrive at a final product specification. Few design systems exist for adequately representing design imprecision, and formally reducing it to precise values. Fuzzy set theory has considerable potential for addressing the imprecision in design. However, it lacks a formal methodology for system development and operation. One repercussion of this is that imprecision reduction is, at present, implemented in a relatively ad-hoc manner. The main contribution of this paper is to introduce a methodology called precision convergence for making the transition from imprecise goals and requirements to the precise specifications needed to manufacture the product. A hierarchy of fuzzy constraint networks is presented along with a methodology for creating transitional links between different levels of the hierarchy. The solution methodology is illustrated with an example within which an imprecision reduction of 98% is achieved in only three stages of the design process. The imprecision reduction is measured using the coefficient of imprecision, a new metric introduced to quantify imprecision.


coefficient of imprecision, concurrent engineering, constraint processing, decision making, design, Engineering design, fuzzy set theory, hierarchical modeling, precision convergence


Giachetti, R. (1997), The Calculus of Imprecision for the Analysis and Evaluation of Engineering Models, NIST IR, [online], (Accessed April 24, 2024)
Created January 1, 1997, Updated February 17, 2017