In this paper, we shall introduce a metric on the space of fuzzy-valued measurable functions by means of a kind of nonlinear integral — Choquet integral with respect to a capacity. We called it as Choquet integral norm. By using the metric between fuzzy-valued measurable functions, we discuss the mean approximation of regular fuzzy neural networks in the sense of Choquet integral. It is shown that any fuzzy-valued measurable function on can be approximated in mean by four-layer regular fuzzy neural networks in the sense of Choquet integral norm.
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