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.

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