粒集及其描述

Granular Set and its Description

本文在已有的有关粒计算研究成果的基础上,提出了粒集的概念,并利用统一集的形式对粒集进行了描述,即是(U,D,B,J),其中U是论域,D是描述域,B是由D到U的映射,J是约束。由此出发,分析统一集与粒集的异同,给出与粒集相关的一些概念,描述了用粒集形式来表达其他各种各样的集合,诸如经典集合、模糊集合、可拓集合、V ague集合、粗糙集合等。粒集理论为粒计算提供很好的理论基础,从而使粒计算确立自己独立的研究领域。

This paper based on the existing relevant granular computing research results puts forward the concept of granular set.And it expresses granular set in the form of all set,that is quaternary group——(U,D,B,J),in which U is the universe of the problem discussed,D describes all of the elements in U,B is the map from D to U,and J restricts B.From this modal,we analyze the similarity and dissimilarity of granular set and all set,provide some concepts with relation to granular set,present some expressions of granular set,such as crisp set,fuzzy set,extension set,vague set,rough set,etc.The theory of granular set offers very good theoretical foundation for granular computing so that it establishes its own independent research field.