Measure theory | Definitions of mathematical integration | Fuzzy logic

Sugeno integral

In mathematics, the Sugeno integral, named after M. Sugeno, is a type of integral with respect to a fuzzy measure. Let be a measurable space and let be an -measurable function. The Sugeno integral over the crisp set of the function with respect to the fuzzy measure is defined by: where . The Sugeno integral over the fuzzy set of the function with respect to the fuzzy measure is defined by: where is the membership function of the fuzzy set . (Wikipedia).

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Related pages

Fuzzy set | Journal of Mathematical Analysis and Applications | Fuzzy measure theory | Measurable function | Measurable space