模糊测度的广义可加性、转化定理和可加性估计

J4 ›› 2010, Vol. 45 ›› Issue (10): 53-60.

模糊测度的广义可加性、转化定理和可加性估计

巩增泰,谢婷

西北师范大学数学与信息科学学院, 甘肃兰州 730070

收稿日期:2009-09-02 出版日期:2010-10-16 发布日期:2010-10-19
作者简介:巩增泰(1966-),男,教授,博士,博士生导师,主要从事模糊分析学的研究.Email:gongzt@nwnu.edu.cn
基金资助:
国家自然科学基金资助项目(10771171);甘肃省自然科学基金资助项目(0803RJZA108)

The generalized additivity，transformation theorem and the defect of additivity for fuzzy measures

GONG Zeng-tai, XIE Ting

College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, Gansu, China

Received:2009-09-02 Online:2010-10-16 Published:2010-10-19

摘要/Abstract

摘要：

基于广义可加的概念,研究了常见的两种非可加测度的广义可加性，同时给出了广义可加模糊测度的刻画定理,即给出了广义可加与普通可加之间的关系;最后讨论了广义可加性与普通可加性之间的误差估计。

关键词: 模糊测度;广义可加性;可加性的误差

Abstract:

Based on the concept of generalized additivity proposed in this paper, the generalized additivity for two popular types of non-additive measures are studied. Simultaneously, the characteristic theorem for generalized additivity fuzzy measures is given, that is, the relationship between generalized additivity and ordinary additivity is presented. Furthermore, the error estimates between generalized additivity and ordinary additivity are discussed.

Key words: fuzzy measures; generalized additivity; the defect of additivity

巩增泰,谢婷. 模糊测度的广义可加性、转化定理和可加性估计[J]. J4, 2010, 45(10): 53-60.

GONG Zeng-tai, XIE Ting. The generalized additivity，transformation theorem and the defect of additivity for fuzzy measures[J]. J4, 2010, 45(10): 53-60.

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