模糊值函数序列依⊙-模糊积分平均收敛

The mean converges of the sequence of fuzzy valued functions in ⊙-fuzzy integral

针对由乘法算子定义的⊙-模糊值积分,给出了模糊值函数序列依⊙-模糊积分平均收敛的概念,讨论了模糊值函数序列依⊙-模糊积分平均收敛和依模糊测度收敛、几乎处处收敛的蕴涵关系,并获得了可测模糊值函数序列依⊙-模糊积分平均收敛的必要条件.

Aim at the ⊙-fuzzy valued integral defined by the multiplaication operation,we give the concepts of the mean convergence in ⊙-fuzzy integral discuss the connected relationships among the mean convergence in ⊙-fuzzy integral,convergence in fuzzy measure and almost everywhere.Finally,as for the sequences of measurable fuzzy valued functions,a necessary condition of the mean convergence in ⊙-fuzzy integral is obtained.