combination of the base functions of a finite dimension linear space. Then inРspired by the wave-particle dualism from quantum mechanics, the wave-set dualism is firstly defined in the paper. So the relationship Рbetween Cantor sets and their characteristic functions is of wave-set dualism； the relationship between fuzzy sets and their membership Рfunctions is of wave-set dualism, too. Based on such wave-set dualism, the relationship between Riemann integral of continuous funcРtions and fuzzy sets is introduced.Р Keywords: Riemann integral ； Lebesgue integral ； linear normed space ； function approximation ； characteristic functions ； fuzzy Рsets； fuzzy reasoningР 2020 MSC：26A06Р （编辑郑月蓉）
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