Sugeno integral
In mathematics, the Sugeno integral, named after M. Sugeno,[1] 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 .
References[]
- ^ Sugeno, M. (1974) Theory of fuzzy integrals and its applications, Doctoral. Thesis, Tokyo Institute of Technology
- 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 MR0874969
Categories:
- Fuzzy logic
- Measure theory
- Definitions of mathematical integration