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In mathematics, the Sugeno integral, named after M. Sugeno, is a type of integral with respect to a fuzzy measure.
Let {\displaystyle } be a measurable space and let h : X → {\displaystyle h:X\to } be an Ω {\displaystyle \Omega } -measurable function.
The Sugeno integral over the crisp set A ⊆ X {\displaystyle A\subseteq X} of the function h {\displaystyle h} with respect to the fuzzy measure g {\displaystyle g} is defined by:
where F α = { x | h ≥ α } {\displaystyle F_{\alpha }=\left\{x|h\geq \alpha \right\}}.