赵汝怀.(N)模糊积分[J].数学研究及应用,1981,1(2):55~72
(N)模糊积分
(N) Fuzzy Integral
投稿时间:1981-01-06  
DOI:10.3770/j.issn:1000-341X.1981.02.006
中文关键词:  
英文关键词:
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作者单位
赵汝怀 西安交通大学数学系 
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中文摘要:
      本文定义了一种新的模糊积分,它较[2]所定义的模糊积分与Lebesgue积分有更多的相似之处。特别是作为人类思维过程的模拟,较[2]更切近于实际。文中研究了这种积分的性质,证明了类似Lebesgue积分中Levi定理、Fatou定理等关于积分序列的收敛性定理,给出了把一般的模糊测度空间上的(N)模糊积分转化为R1上以Lebesgue测度为模糊测度的(N)模糊积分的公式。§4中引进了一类特殊的所谓λ次可加模糊测度空间,给出了这种测度空间上收敛性的Егоров定理和Riesz定理并得到了该空间上的(N)模糊积分在积分号下取极限的一些充分条件。
英文摘要:
      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.
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