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1)  two-variables function one direction S-rough sets
二元函数单向S-粗集
1.
The mathematical structure and characteristics of two-variables function one direction S-rough sets are given in the paper.
给出了二元函数单向S-粗集的数学结构和特性。
2)  structure of two-variables function one direction S-rough sets
二元函数单向S-粗集的结构
3)  function one direction S-rough sets
函数单向S-粗集
1.
Function one direction S-rough sets(function one direction singular rough sets) was defined by the R-function equivalent class [u],which has dynamic characteristic,and the function one direction S-rough sets has law(function) characteristic.
函数单向S-粗集(Function one direction singular rough sets)是用具有动态特性的R-函数等价类[u]定义的,函数单向S-粗集具有规律(函数)特征。
2.
Based on the functions generated from the upper approximation and the lower approximation in function one direction S-rough sets,the concept and characteristics of rough area and double rough integrals were given.
以函数单向S-粗集的上、下近似生成的函数为基础,提出了粗区域的概念,进而提出基于函数单向S-粗集的二重粗积分的概念,研究其性质得出了二重粗积分是普通二重积分、一元粗积分的推广。
3.
Using function one direction S-rough sets(function one direction singular rough sets),this paper presents the concepts of fp-state,the distance of state,and the system state being randomly disturbed by fp-law.
利用函数单向S-粗集,提出了fp-状态、状态距离、系统状态被fp-规律随机入侵的概念。
4)  function one-direction S-rough sets
函数单向S-粗集
1.
An F-model generated by function one-direction S-rough sets;
函数单向S-粗集生成的F-模型
2.
It was proved that a function one-direction SPF-rough set was the generalization of function one-direction SPF-rough sets,and the function one-direction S-rough sets was a special case of function one-direction SPF-rough sets according to t.
证明了在概率的意义下,函数单向SPF-粗集是函数S-粗集,函数单向S-粗集的推广;函数S-粗集,函数单向S-粗集是函数单向SPF-粗集的特例。
5)  dual of function one direction S-rough sets
函数单向S-粗集对偶
1.
■-model generated by dual of function one direction S-rough sets
函数单向S-粗集对偶生成的■-模型
2.
Using dual of function one direction S-rough sets(Dual of function one direction singular rough sets),this paper presents the concepts of p-state,the distance of state,and the system state being randomly disturbed by p-law.
函数单向S-粗集对偶是函数S-粗集(function singular rough sets)的基本形式之一。
3.
Based on functions generated from the upper approximation and the lower approximation in dual of function one direction S-rough sets,the definition of rough area,and the definition of double rough integrals was given and there dynamic characteristics were pointed out.
以函数单向S-粗集对偶的上、下近似生成的函数为基础,提出了粗区域的定义,二重粗积分的定义及其动态特征,通过动态特征给出了扩张度和扩张率的概念,并且通过计算扩张度和扩张率来度量系统受干扰的程度。
6)  dual of founction one direction singular rough sets
单向函数S-粗集对偶
补充资料:宋庆元二年周必大刻本《欧阳文忠公集》
      南宋庆元二年(1196)周必大刻于吉州(今江西吉安)。半叶10行,行16字,白口,左右双边,版心上记字数,下记刻工名。共153卷,又附录5卷。避讳谨严,宋讳缺笔至慎字。附录后有周必大跋,称欧集自汴京、江浙、闽、蜀皆有讹谬,而庐陵所刊又甚,此本重加编校,自绍熙辛亥(二年,1191),迄庆元丙辰(二年,1196),凡经六载,参与编校者如曾三异、罗泌、孙谦益皆吉州名儒。此本出,遂成欧集最后定本,其他州郡刻本皆散佚不传。明代所刻欧集诸本,皆出于此本。此本刻成稍后,江西地区又据此本翻版重刻,与此本行款版式全同,刻工亦皆江西良工,世多误认为周必大刻本。
  
  清末,内阁大库旧藏群籍散出,欧集宋刻残卷不下六、七种,周必大本与翻周必大本杂见。此本全者今存一部,周必大刻存一百三十四卷,另二十四卷配明抄本。原藏傅增湘处,有乾学、徐健庵二印,初印精好,纸墨莹润。传世欧集当以此本为最,今藏北京图书馆。
  

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