Sugeno integral

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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[edit]

  • Gunther Schmidt Relational Mathematics, Encyclopedia of Mathematics and its Applications, vol. 132, Cambridge University Press, 2011, ISBN 978-0-521-76268-7
  • Gunther Schmidt Relational Measures and Integration. pp. 343{357 in Schmidt, R. A., Ed. RelMiCS '9 | Relations and Kleene-Algebra in Computer Science (2006), no. 4136 in Lect. Notes in Comput. Sci., Springer-Verlag
  1. ^ Sugeno, M., Theory of fuzzy integrals and its applications, Doctoral. Thesis, Tokyo Institute of Technology, 1974