Hierarchical Imprecise Design with Weights

Manuscript prepared for submission to the International Joint Conference of the Fourth IEEE International Conference on Fuzzy Systems and the Second International Fuzzy Engineering Symposium.

William S. Law
Engineering Design Research Laboratory
California Institute of Technology
Pasadena, California 91125
law@design.caltech.edu

Erik K. Antonsson
Engineering Design Research Laboratory
Division of Engineering and Applied Science
California Institute of Technology
Pasadena, California 91125

An extension to the method of imprecision that allows the decomposition or aggregation of imprecise design problems with weighted attributes is presented. The method of imprecision uses the preferences of the designer and customer to define fuzzy sets that quantify the imprecision associated with a design attribute. These fuzzy sets, weighted by relative importance, are combined to produce an overall design measure. This paper introduces aggregation operators that can be hierarchically applied to combine weighted design attributes so that the structure of the design problem is appropriately modeled.