Abstract

We extend the concept of fuzzy integral based on ⊕-decomposable measure from nonnegative fuzzy measurable function to extended real-valued fuzzy measurable function. Further investigations of fuzzy integrals based on pseudo-additive decomposable measure are carried out. Meanwhile, the space (S(μ),σ(⋅,⋅)) of all fuzzy measurable function will be proved to be a pseudo-metric space. Finally, as an application of this extension the Pettis integral will be obtained for that kind of fuzzy integral.