摘要
从商空间的粒度计算理论出发,本文讨论模糊集的模糊度量问题,即模糊度的定义.根据模糊集的结构分析,我们提出"各向同性"的假设,在这个假设下得出以下结果:(1)在有限完备半序集上具有各向同性的模糊度是唯一的.(2)得出模糊数学中的模糊度函数同构的充分必要条件.(3)得出模糊度具有模糊单调性和粒度单调性的充分必要条件.(4)在一定的假设下,给出模糊度的解析表达式.这些结果阐明了模糊度与粒计算的关系,揭示了模糊度的本质,同时提供一种构造模糊度的简易方法.
From the 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 the assumption we have the following results,（1） the uniqueness of the fuzzy measure having isotropic on a finite complete semi-order set;（2） the necessary and sufficient condition of the isomorphism of fuzzy measure functions in fuzzy mathematics;（3） the necessary and sufficient condition that fuzzy measures have fuzzy and granular monotony; （4） under a certain assumption,the analytic expression of fuzzy measures.The results clarify the relation between the fuzzy measure and granular computing,open out the essence of fuzzy measures,and provide a simple way of constructing fuzzy measures.
出处
《中国科学：信息科学》
CSCD
2011年第7期820-832,共13页
Scientia Sinica(Informationis)
基金
国家自然科学基金(批准号:90820305,61073117)
国家基础研究发展计划(批准号:2007CB311003)资助项目
关键词
商空间
模糊集
模糊度
粗糙集
结构分析
quotient space
fuzzy set
fuzzy measure
rough set
structural analysis
