| In this paper a new type of fuzzy integral is defined, which is more similar to Lebesgue's integral than the integral defined by Sugeno [2]. Especially, as an imitation for process of men's thinking, it is closer to circumstances than [2]. In the paper the properties of this type of integral are studied. There are proved the theorems on convergence of sequences of the integral, which are similar to Levi's theorem, Fatou's theorem and so on in Lebesgue's integral. The formula is given. which trnsform a (N)Fuzzy Integral in general measure space into a (N)Fuzzy Integral with Lebesgue measure in R1. In §4 a special type of so-called λ-semiadditive Fuzzy measure space is led in. The Egorov's theorem and Riesz's theorem on convergence in this measure space are given. Some of sufficient conditions on obtaining limit under the signal of integral has been got. |
