Sugeno integral

In mathematics, the Sugeno integral, named after M. Sugeno, is a type of integral with respect to a fuzzy measure.
Let formula_1 be a measurable space and let formula_2 be an formula_3-measurable function.
The Sugeno integral over the crisp set formula_4 of the function formula_5 with respect to the fuzzy measure formula_6 is defined by:
where formula_8.
The Sugeno integral over the fuzzy set formula_9 of the function formula_5 with respect to the fuzzy measure formula_6 is defined by:
where formula_13 is the membership function of the fuzzy set formula_9.