On a Kleenean extension of fuzzy measure

The authors attempts to translate the vagueness of fuzzy set theory and fuzzy logic to the ambiguity of fuzzy measure by considering the fact that the Sugeno integral in fuzzy measure theory can be represented in fuzzy switching functions with constants in fuzzy logic. Then, we attempt to apply the facts clarified in fuzzy logic to fuzzy measure. We propose two new concepts: “Extended fuzzy measure” and “Kleene-Sugeno integral”