A note on the interval-valued generalized fuzzy integral by means of an interval-representable pseudo-multiplication and their convergence properties

In this paper, we consider the generalized fuzzy integral which is a fuzzy integral based on the idempotent pseudo-addition (supremum) and a pseudo-multiplication studied by Xie and Fang in 2006. The purpose of this study is to define the interval-valued generalized fuzzy integral with respect to a fuzzy measure by means of an interval-representable pseudo-multiplication of measurable interval-valued functions and to investigate some characterizations and convergence properties of them.