| Choquet积分的收敛定理 |
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| 引用本文： | 郭彩梅,张德利.Choquet积分的收敛定理[J].模糊系统与数学,2001,15(2):51-54. |
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| 作者姓名： | 郭彩梅 张德利 |
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| 作者单位： | 1. 长春大学基础部,
2. 吉林大学计算机科学系, |
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| 基金项目： | China Postdoctorl Science
Foundation in OSCKEL of SEC of Jilin University |
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| 摘 要： | Murofushi、Sugeno等学者已对关于模糊测度的Choquet积分进行了详细的研究，但关于积分的收敛理论是不够的。本文讨论这一问题，给出Choquet积分的一些收敛定理，包括广义单调收敛定理、Fatou引理等。从中可以看出，Choquet积分与Sugeno模糊积分具有相同的收敛定理。
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| 关 键 词： | 测度论 模糊测度 模糊积分 收敛定理 Choquet积分 Faton引理 Sugeno模糊积分 |
| 文章编号： | 1001-7402(2001)02-0051-04 |
| 修稿时间： | 1999年10月11 |
Convergence Theorems of
the Choquet Integral |
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| GUO Cai-mei,ZHANG De-Li.Convergence Theorems of
the Choquet Integral[J].Fuzzy Systems and Mathematics,2001,15(2):51-54. |
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| Authors: | GUO Cai-mei ZHANG De-Li |
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| Institution: | GUO Cai mei 1,ZHANG De li 2 |
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| Abstract: | So far, the Choquet integral with respect to a fuzzy measure has been studied much extensive by Dr.Murofushi,Sugeno and some others. But the convergence theory is not enough. The paper′s aim is just discussing this topic,and shows some convergence theorems for the Choquet integral. These include generalized monotone convergence theorem,Fatou′s lemmas,etc. We conclude that the Choquet integral has the same convergence theorems as Sugeno integral owns. |
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| Keywords: | Measure Theory Choquet Integral Fuzzy Measure Fuzzy Integral Convergence Theorem |
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