| 集值函数的对偶半模模糊积分 |
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| 引用本文： | 郭彩梅,张德利.集值函数的对偶半模模糊积分[J].清华大学学报(自然科学版),2004,44(3):369-371. |
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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,应用理学院,长春,130022
2. 吉林省教育学院,数学系,长春,130022 |
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| 基金项目： | 国家自然科学基金 (10271035) |
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| 摘 要： | 为了将函数的对偶半模模糊积分推广到集值函数的情形,要建立一种新的非可加集值积分理论。仿照Aumann积分的方式,用集值函数的单值可测选择的对偶半模模糊积分,定义集值函数的对偶半模模糊积分,并给出了其性质及收敛定理。这些是函数的对偶半模模糊积分有关结果的推广,同时是一种新的集值积分。
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| 关 键 词： | 集值函数 对偶半模 对偶半模模糊积分 |
| 文章编号： | 1000-0054(2004)03-0369-03 |
| 修稿时间： | 2003年6月5日 |
Semi-conormed fuzzy integrals of set-valued functions |
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| GUO Caimei,ZHANG Deli.Semi-conormed fuzzy integrals of set-valued functions[J].Journal of Tsinghua University(Science and Technology),2004,44(3):369-371. |
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| Authors: | GUO Caimei ZHANG Deli |
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| Abstract: | The semi-conormed fuzzy integral of functions was extended to the case of set-valued functions to develop a new theory on non-additive set-valued integrals. The present paper uses a method similar to Aumann's integral to define the semi-conormed fuzzy integral of set-valued functions using the semi-conormed fuzzy integral of single-valued measurable selections of set-valued functions and to describe its properties and convergence theorems. These results extend the semi-conormed fuzzy integral of single-valued functions to a new kind of set-valued integrals. |
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| Keywords: | set-valued function semi-conormed semi-conormed fuzzy integral |
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