Adding Fuzzy Integral to Fuzzy Control

Authors

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

Publication Date

3-1998

Comments

Technical Report: UTEP-CS-97-26a

Published in the Proceedings of the International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU'98), Paris, France, July 6-10, 1998, pp. 657-664.

Abstract

Sugeno integral was invented a few decades ago as a natural fuzzy-number 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.