A note on the convergence theorem of generalized fuzzy integrals
A convergence theorem in the framework of generalized fuzzy integrals is shown in its complete form (i.e., stating necessary and sufficient conditions to ensure the convergence of integrals for pointwisely convergent decreasing sequences of nonnegative measurable functions). Thus a series of several convergence theorems for the Sugeno and related integrals is completed, yielding mentioned convergence theorems as special corollaries (see, e.g., [\textit{C. Wu}, \textit{M. Ma}, \textit{S. Song} and \textit{S. Zhang}, Fuzzy Sets and Syst. 70, No. 1, 75-87 (1995; Zbl 0859.28013)]; [\textit{E. Pap}, ``Non-additive set functions'' (1995; Zbl 0856.28001)]; [\textit{Z. Wang} and \textit{G. J. Klir}, ``Fuzzy measure theory'' (1992; Zbl 0812.28010)]).
scientific article; zbMATH DE number 1766469