Fuzzy Aggregation Techniques in Situations Without Experts: Towards A New Justification

Fuzzy techniques have been originally invented as a methodology that transforms the knowledge of experts formulated in terms of natural language into a precise computer-implementable form. There are many successful applications of this methodology to situations in which expert knowledge exist, the must 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 another traditional approximation technique, researchers try to approximate it by guessing and tuning the expert rules. Surprisingly, this approximation often works fine. 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