Fuzzy without fuzzy

why fuzzy-related aggregation techniques are often better even in situations without true fuzziness

Hung T. Nguyen

Vladik Kreinovich

François Modave

Martine Ceberio

pp. 27-51

in: Ajith Abraham, Francisco Herrera, Aboul-Ella Hassanien (eds), Foundations of computational intelligence volume 2, Berlin, Springer, 2009

Abstract

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 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 fine, especially in such application areas as control and multi-criteria decision making.In this chapter, we give a mathematical explanation for this phenomenon.