摘要
该文着力于研究粒计算的基本理论.粒计算作为一种粒数数系被研究,在这种数系中研究粒运算的基本定律、粒与粒之间的不可区分关系;研究这种粒数系中描述型的形式语言等.采用的方法是基于非标准分析中的超实数理论研究实值粒运算应遵循的规则,也研究了伴随二元关系的信息粒的合成、加粗、加细、并和交运算等;在分析前人工作的基础上、基于超实数理论进一步为粒计算研究定义了一种新的不可区分关系,得到了几个相关性质,并且证明了相关结果.随后定义了描述这种粒数数系的描述型形式语言——一种带不可区分关系词的二阶粒逻辑;粒常量、粒变量、粒函数项的相关运算定律也被定义了.最后,以示例演示了这种粒逻辑适应于描述粒数学定理、粒公式化简等.
In the article,we focus on studying fundamental theory of granular computing.Granular computing is studied as a granular number systems.Operation laws of granulations,the indiscernibility relation of granulations in the granular number systems are also studied.The formal language for describing the granular number systems needs also to be studied.We study the operation rules of real granulations to adopt the theory of hyperreal numbers in nonstandard analysis.The operations of compound,coarsening and refining,union and intersection of information granularity with binary relations are also studied in the article.We define further a new indiscernibility relation by hyperreal theory and get several related properties based on current relative researches.And related results are proved.Subsequently,the formal language for describing granular computing—agranular language with indiscernibility relation is defined.It is called a second order granular logic in the article.The related operations of granular constants,granular variables and granular function items used in the second-order granular logic are handled necessarily in the article.Finally,the significance of describing granular mathematical theorems defined in the granular number systems is illustrated with real examples.
出处
《计算机学报》
EI
CSCD
北大核心
2015年第8期1618-1627,共10页
Chinese Journal of Computers
基金
国家自然科学基金(61070139)
江西省自然科学基金(20114BAB201039)
江西省教育厅科技计划项目(GJJ14134)资助
关键词
粗糙集
模糊集
粒计算
二阶粒逻辑
粒数学
超实数
非标准分析
Rough sets
fuzzy sets
granular computing
second-order granular logic
granular mathematics
hyperreal number
nonstandard analysis
