Extension on the fuzzy integral based on \(\oplus\)-decomposable measure (Q1607762)

Summary: We extend the concept of fuzzy integral based on \(\oplus\)-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 \((S(\mu),\sigma(\cdot,\cdot))\) of all fuzzy measurable functions is proved to be a pseudo-metric space. Finally, as an application of this extension the Pettis integral is obtained for that kind of fuzzy integral.