The structural analysis of fuzzy measures

被引：0
作者：
ZHANG Ling1
2State Key Lab of Intelligent Technology & Systems
Tsinghua National Lab for Information Science & Technology
Information Science & Technology College
机构：
来源：
ScienceChina(InformationSciences) | 2011年 / 54卷 / 01期
基金：
中国国家自然科学基金;
关键词：
quotient space; fuzzy set; fuzzy measure; rough set; structural analysis;
D O I：
暂无
中图分类号：
O159 [模糊数学];
学科分类号：
070104 ;
摘要：
From quotient space based granular computing theory we explore the fuzzy measures of fuzzy sets. Based on the structural analysis of fuzzy sets,we present an"isotropism"assumption.Under this assumption we achieved the following insights:(1)the uniqueness of a fuzzy measure being isotropic on a finite complete semi-ordered set;(2)the necessary and suffcient condition of the isomorphism for fuzzy measure functions in fuzzy mathematics;(3)the necessary and suffcient condition that fuzzy measures have fuzzy and granular monotonicity;(4)under a certain assumption,the analytic expression for fuzzy measures.The results clarify the relationship between fuzzy measures and granular computing,reveal the essence of fuzzy measures,and provide a simple way of constructing fuzzy measures.
引用
收藏
页码：38 / 50
页数：13
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