Fuzzy integrals and linearity

  • Authors:
  • Radko Mesiar;Andrea Mesiarová

  • Affiliations:
  • Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, SK-813 68 Bratislava, Slovakia and Institute for Research and Application of Fuzz ...;Mathematical Institute of SAS, Štefánikova 49, 81473 Bratislava, Slovakia

  • Venue:
  • International Journal of Approximate Reasoning
  • Year:
  • 2008

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Abstract

Linearity and generalized linearity of fuzzy integrals are studied. For continuous from below fuzzy integrals, linearity leads to the Lebesgue integral while the comonotone linearity results to the Choquet integral with respect to a selfdual fuzzy measure m. Similar results in the case of idempotent linearity are presented. Some open problems were stated, too. Finally, pseudo-linearity related to two types of semirings is discussed.