Fuzzy Aggregation Techniques in Situations Without Experts: Towards A New Justi cation

— Fuzzy techniques have been originally invented as a methodology that transforms the knowledge of experts formulated in terms of natural language into a precise computerimplementable form. There are many successful applications of this methodology to situations in which expert knowledge exist, the most well known is an application to fuzzy control. In some cases, fuzzy methodology is applied even when no expert knowledge exists: instead of trying to approximate the unknown control function by splines, polynomials, or by any other traditional approximation technique, researchers try to approximate it by guessing and tuning the expert rules. Surprisingly, this approximation often works ne. In this paper, we give a mathematical explanation for this phenomenon, and show that approximation by using fuzzy methodology is indeed (in some reasonable sense) the best.