An Equivalent Definition of Pan-Integral
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.
KeywordsPan-integral Sugeno integral Shilkret integral Support disjointness super-\(\oplus \)-additivity Positively super-\(\otimes \)-homogeneity
- 12.Sugeno, M.: Theory of fuzzy integrals and its applications. Ph.D. dissertation, Takyo Institute of Technology (1974)Google Scholar