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*Proceedings of the Fourth IEEE International Conference on Fuzzy Systems*

(FUZZ-IEEE/IFES 95) (Mar. 1995), Volume 1, IEEE, pages 375 382.

## Abstract

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.