Extension on the fuzzy integral based on ⊕‐decomposable measure

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.