FUZZY GOULD INTEGRABILITY ON ATOMS

In this paper we study the relationships existing between total measurability in variation and Gould type fuzzy integrability (introduced and studied in [۲۱]), giving a special interest on their behaviour on atoms and on finite unions of disjoint atoms. We also establish that any continuous real valued function defined on a compact metric space is totally measurable in the variation of a regular finitely purely atomic multisubmeasure and it is also Gould integrable with respect to regular finitely purely atomic multisubmeasures.

Keywords:

Fuzzy Gould integral , Totally measurability (in variation) , (Multi) (sub) measure , Atom , Finitely purely atomic , Regularity