摘要
给出函数单向S-粗集(function one direction singular rough sets)、函数单向S-粗集对偶(dual of function one direction singular rough sets)、函数双向S-粗集(function two direction singular rough sets)与函数粗集(function roughsets)。它们都是把函数概念引入到S-粗集中,改进S-粗集得到的。函数粗集是把函数概念引入到Z.Pawlak粗集中,改进Z.Pawlak粗集得到的。函数单向S-粗集、函数单向S-粗集对偶、函数双向S-粗集是函数S-粗集的三类形式。给出函数S-粗集与S-粗集的关系;给出函数粗集与Z.Pawlak粗集的关系;给出函数S-粗集与函数粗集的关系。利用这些结果,给出函数的区间离散与有限元素集的生成、函数离散-元素集合生成原理;给出函数S-粗集生成的信息规律、函数等价类动态特性-属性补充与删除原理;给出数据拆分-合成原理、信息规律动态拆分-合成的属性特征;给出信息规律动态拆分-合成不变性原理;利用这些概念与结果,给出信息规律拆分-合成与信息图像嵌入-分离的应用,给出嵌入信息图像的分离-辨识。函数S-粗集、函数粗集是粗集理论与应用研究中的一个新的研究方向。
Function one direction singular rough,dual of function one direction singular rough sets and function two direction singular rough sets were given.They are three types of forms about function S-rough sets.They came from improved S-rough sets by introducing function concept to S-rough sets.Function rough sets came from improved Z.Pawlak rough sets by introducing function concept to Z.Pawlak rough sets.This paper gave the relation between function S-rough sets and function S-rough sets,the relation between function S-rough sets and Z.Pawlak rough sets,the relation between function S-rough sets and function rough sets.Using these results,this paper presented the generation of the interval discretization for function and finite element set,the principle of function discretization and element generation,the information law which was generated by function S-rough sets,the principle of the dynamic properties for function equivalence class and supplementary and deletion for properties,the separation-composition principle for data,the attri-bute characteristics of the dynamic separation-composition for information law,the invariance principle of the dynamic separation-composition for information law and so on.Using these concepts and results,the application of the separation-composition for information law,the application of embedment-separation for information images and the separation-identification of embedded information images were given.In short,function S-rough sets and S-rough sets are a new research direction in rough sets.
出处
《计算机科学》
CSCD
北大核心
2010年第10期1-10,共10页
Computer Science
基金
山东省自然科学基金项目(Y2007H02)资助
关键词
函数S-粗集
函数粗集
关系定理
信息规律生成
拆分-合成原理
信息图像嵌入
应用
Function S-rough sets
Function rough sets
Relation theorem
Information law generation
Separation-Composition principle
Information image embedment
Application
