基于分形理论的病态结构问题研究

A STUDY ON ILL STRUCTURED PROBLEMS BASED ON FRACTAL THEORY

基于问题导向的观点，按照综合集成思路研究病态结构问题（ＩＳＰ）的“病态”机理，作为决策支持理论的基础．分析概括出ＩＳＰ的３大内禀特性：多粒度、不封闭、自增殖．运用分形理论给出结构函数和结构指数的概念定义，用以刻画决策对象的结构复杂性．首次揭示了结构冗余现象并给予了严格论证，进而给出结构冗余指数作为结构冗余性度量．基于结构冗余指数，对决策对象进行了分类，并对ＩＳＰ进行了形式化定义．剖析了ＩＳＰ的结构实质，其结果表明ＩＳＰ的分形结构是其结构复杂性之源．

According to the problem oriented view,this paper makes a study on the illness mechanism of ill structured problems(ISP) inspired by meta synthetic approach,which can lay a foundation for theories of decision support.The three intrinsic characteristics of ISP,viz.,multiple granularity,unclosed and self increasing,are outlined.The concepts of structure function and structure index are given by utilizing fractal theory so as to portray the structural complexity of decision objects.The phenomenon of structure redundancy is brought to light for the first time and some statements are made in detail.The structure redundancy index is given to measure its redundant degree.Based on the structure redundancy index,a taxonomy of decision objects as well as a formal definition of ISP is given.The structure substance of ISP is analysed which shows that the fractal structure of ISP is the source of its structural complexity.Some discussion on the related problems is also made in the paper.