An extension of Sugeno integral

Abstract 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(μ),ρ(.,.)) 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.