A modification of Sugeno integral describes stability and smoothness of fuzzy control

Sugeno discovered a natural fuzzy analogue of the classical integral. The Sugeno integral has many interesting applications. It is reasonable to expect that the Sugeno integral 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, the classical integral is one of the main tools. It is even more surprising because fuzzy control is one of the main applications of fuzzy systems theory, probably its most deeply-researched and widely applied area. In the paper, we explain why the original Sugeno integral has not been used in fuzzy control, and how we can modify this notion so that it will lead to useful applications: namely, it will provide numerical characterization of stability and smoothness of fuzzy control strategies