A Modification of Sugeno Integral Describes Stability and Smoothness of Fuzzy Control

Authors

Hung T. Nguyen
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

1-1998

Comments

Technical Report: UTEP-CS-97-16a

Published in Proceedings of FUZZ-IEEE'98, Anchorage, Alaska, May 1998, Vol. 1, pp. 360-365.

Abstract

Sugeno integral was invented a few decades ago as a natural fuzzy analogue of the classical integral. Sugeno integral has many interesting applications. It is reasonable to expect that it can be used in all application areas where classical integrals are used, and in many such areas it is indeed useful. Surprisingly, however, it has never been used in fuzzy control, although in traditional control, classical integral is one of the main tools.

In this paper, we show that the appropriately modified Sugeno integral is indeed useful for fuzzy control: namely, it provides numerical characterization of stability and smoothness of fuzzy control strategies.