CONSTRUCTING MEMBERSHIP FUNCTIONS USING INTERPOLATION AND MEASUREMENTTHEORY

Imprecision is well suited for representing uncertainty in choice duri ng an engineering design process, and in particular for computer-aided engineering design and analysis tools. To propagate imprecise underst anding through engineering tools, however, first the membership functi ons must be constructed based on the understandings of the design engi neer. For this purpose, measurement theory offers an axiomatically bas ed, easy to use method. For any given variable, the best and worst val ues are determined, and the remaining values are assigned a degree of membership by comparison with the best and the worst. On real variable s, however, this would require an infinite number of questions. Instea d, a continuity assumption can be made, and the remaining membership v alues determined through interpolation. Traditional interpolation sche mes, however, fail to satisfy the restrictions of a membership functio n. The [0,1] boundedness condition and the fuzzy-convex property in pa rticular present difficulty. A simple and efficient constrained interp olation scheme is developed for fitting a membership function to a fin ite number of known membership values. Thus, a simple method enabling design engineers to construct membership functions is presented.