Sugeno integral

In mathematics, the Sugeno integral, named after M. Sugeno, is a type of integral with respect to a fuzzy measure.

Let ( X , Ω ) be a measurable space and let h : X → [ 0 , 1 ] be an Ω -measurable function.

The Sugeno integral over the crisp set A ⊆ X of the function h with respect to the fuzzy measure g is defined by:

where F α = { x | h ( x ) ≥ α } .

The Sugeno integral over the fuzzy set A ~ of the function h with respect to the fuzzy measure g is defined by:

where h A ( x ) is the membership function of the fuzzy set A ~ .