An extension of Sugeno integral
In this paper, we extend the concept of Sugeno fuzzy integral from nonnegative fuzzy measurable functions to extended real-valued fuzzy measurable functions and discuss the lost genuine properties for this extension; several necessary and sufficient conditions of absolute (S)-integrability for extended real-valued fuzzy measurable functions are given. Moreover, the space (S(mu), rho(.,.)) of all fuzzy measurable functions will be proved to be a pseudo-metric space under a necessary and sufficient condition. Finally, as an application of this extension the Pettis integral will be established for this kind of fuzzy integral. (C) 2002 Published by Elsevier B.V.
fuzzy measure fuzzy measurable function pseudo-metric space (s)fuzzy integral absolute (s)integrability