Abstract
We introduce definitions of fuzzy Orlicz class L Φ ( μ) and fuzzy Φ-mean convergence. We show that fuzzy Φ-mean convergence is equivalent to convergence in fuzzy measure and L Φ ( μ)= L 1( μ) for any Orlicz function Φ. This conclusion refines a result of D. Ralescu (Toward a general theory of fuzzy variable, J. Math. Anal. Appl. 86 (1982) 176–193). Moreover a necessary and sufficient condition for L 1( μ)= S( μ) is given. It also improves a result of D. Ralescu and G. Adams (The fuzzy integral, J. Math. Anal. Appl. 75 (1980) 562–570.)
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