Sugeno integral
Appearance
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 .
Usage and Relationships
[edit]Sugeno integral is related to h-index.[2]
References
[edit]- ^ Sugeno, M. (1974) Theory of fuzzy integrals and its applications, Doctoral. Thesis, Tokyo Institute of Technology
- ^ Mesiar, Radko; Gagolewski, Marek (December 2016). "H-Index and Other Sugeno Integrals: Some Defects and Their Compensation". IEEE Transactions on Fuzzy Systems. 24 (6): 1668–1672. doi:10.1109/TFUZZ.2016.2516579. ISSN 1941-0034.
- 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