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Sugeno integral

From Wikipedia, the free encyclopedia

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

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Sugeno integral is related to h-index.[2]

References

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  1. ^ Sugeno, M. (1974) Theory of fuzzy integrals and its applications, Doctoral. Thesis, Tokyo Institute of Technology
  2. ^ 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.