多层多维事元可拓集及其运算  

Multilayer multidimensional affair element extension set and its operations

作　　者：曹少中[1] 刘贺平[2] 涂序彦[2] 

机构地区：[1]北京印刷学院信息与机电工程学院,北京102600 [2]北京科技大学信息工程学院,北京100083

出　　处：《北京科技大学学报》2007年第6期641-646,共6页Journal of University of Science and Technology Beijing

基　　金：国家自然科学基金资助项目(No60374032;No60375038和No60375014)

摘　　要：为了建立复杂系统的事元可拓模型,针对现实世界中具有多层结构、每个子层次结构又具有多个特征的复杂系统中各子系统的相互作用问题,从可拓学原理出发,在n维事元可拓集概念的基础上,提出了多层多维事元可拓集及其正域、负域、拓界的概念.给出了多层多维事元可拓集的正可拓域、负可拓域、正稳定域、负稳定域的定义.研究了多层多维事元可拓集的交运算等,讨论了有关性质,并对性质进行了严格证明,得到了多层多维事元可拓集交的可拓域、稳定域的表达式.In reality, an object is often described as a complex system with multilayer structure, of which any sub-layer has many properties. According to the principle of extenics, in order to establish the extension model of affair element for a complex system, the concept of multilayer multidimensional affair element extension set and its positive field, negative field and extension boundary were presented based on the concept of n-dimensional affair element extension set. The definitions of positive extension field, negative extension field, positive stable field and negative stable field of a multilayer multidimensional affair element extension set were given. The properties and intersection operation of the set were discussed and proved strictly. The expressions of extension field and stable field for intersection operation of the set were gained.

关 键 词：多层多维事元可拓集 正域 负域 可拓域 稳定域 

分 类 号：O144[理学—数学] N94[理学—基础数学]