Propagating imprecise engineering design constraints

Constraint based CAD systems are used to manipulate input and output variables by allowing a user to adjust the variables' crisp values. The different variables are iteratively specified and relaxed until a final configuration of variable values is accepted. This paper introduces a method for propagating imprecise (fuzzy) constraints to reduce the number of exploratory iterations required to obtain an acceptable set of values. An imprecision transformation is defined to induce imprecise specifications from specified variables to unspecified variables, either of which can be of the independent input or dependent output type. When the imprecise specifications are placed on the dependent variables exclusively, the transformation reduces to composition. When the imprecise specifications are placed on the input variables exclusively, the transformation becomes Zadeh's extension principle. In a traditional non-fuzzy use of constraint based CAD systems, an over-constrained system of relations must be relaxed by the user. With a fuzzy formulation, however, it is shown that imprecise constraints allow calculations to be made: the values which simultaneously satisfy all of the imprecise constraints can be calculated. Thus, using imprecise quantities in constraint based CAD systems allows much of the iterative user specifications to be calculated by the computing platform instead, reducing the iterative tasks of the designer.