In mathematics, the Sugeno integral, introduced by Michio Sugeno as a fuzzy integral in work on fuzzy measures at the Tokyo Institute of Technology, 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 .
Usage and Relationships
Sugeno integral is related to h-index.
References
Gunther Schmidt (2006) Relational measures and integration, Lecture Notes in Computer Science # 4136, pages 343−57, Springer books M. Sugeno & T. Murofushi (1987) "Pseudo-additive measures and integrals", Journal of Mathematical Analysis and Applications 122: 197−222