Integral with Respect to a Non Additive Measure: An Overview

  • Yasuo Narukawa
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 310)

Abstract

This chapter surveys the fundamental aspect of non-additive measures and integral with respect to a non additive measure. Several basic definitions of non additive measure.

Sugeno integral and Choquet integral are presented. The basic properties of the generalized fuzzy integral which is a generalization of both Sugeno and Choquet integral are shown. The generalized Möbius transform and the representation of Choquet integral are also shown.

Keywords

non additive measure fuzzy measure Choquet integral Sugeno integral Möbius transform 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Yasuo Narukawa
    • 1
    • 2
  1. 1.Toho GakuenKunitchiJapan
  2. 2.Department of Computational Intelligence and Systems ScienceTokyo Institute of TechnologyYokohama 226Japan

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