中文摘要：

为了能为粒计算的粒提供一种统一的表示形式,研究了粒的特征的基本含义、描述及其关系,分析了粒的对象、特征、关系及状态等四个基本要素,提出了基于数据层面的粒的四元组的形式化表示形式,即由对象集、特征集、关系集和约束集四元组组成。接着给出了几个特殊粒的表示形式,然后说明了该表示形式的统一性及其优点,并结合具体的例子进行了研究。该形式化表示形式具有重要的方法论意义,很好地解决了基于数据层面的粒的表示问题,有利于问题求解和粒计算理论的研究。

英文摘要：

In order to provide the granule unification representation of granular computing,the paper discusses the basic meaning,descriptions and the relations between the features of the granule,analyzes the four basic elements of the granule： The objects,the features,the relationships,and the states,presents four-tuples formal representation based on data levels,that is the object set,feature set,relationship sets and constraints set.Then the representation of several special granules are pre sented,and it shows the unity and advantage of the representation,gives a specific examples to study.The formal representation has important significance in methodology to solve well the granule representation based on data levels,and to be con- ductive to problem solving and granular computing theory studying.