An Equivalent Definition of Pan-Integral

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9880)


In this note, we introduce the concepts of support disjointness super-\(\oplus \)-additivity and positively super-\(\otimes \)-homogeneity of a functional (with respect to pan-addition \(\oplus \) and pan-multiplication \(\otimes \), respectively). By means of these two properties of functionals, we discuss the characteristics of pan-integrals and present an equivalent definition of the pan-integral. As special cases, we obtain the equivalent definitions of the Shilkret integral, the \(+,\cdot \)-based pan-integral, and the Sugeno integral.


Pan-integral Sugeno integral Shilkret integral Support disjointness super-\(\oplus \)-additivity Positively super-\(\otimes \)-homogeneity 


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Faculty of ScienceHuzhou UniversityHuzhouChina
  2. 2.School of SciencesCommunication University of ChinaBeijingChina

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