摘要
通过综合经典集合、模糊集合、可拓集合、Vague集合、粗糙集合、集对分析、FHW (模糊灰色物元空间 )、FEEC (模糊可拓经济控制 )等多种理论 ,提出了统一集概念 ,并详细讨论统一集的各种运算以及相关性质。从分析集合理论和人类思维形式之间的关系入手 ,把统一集理论初步应用到模式识别、聚类分析、逻辑推理、机器学习、智能决策等多种人工智能领域 ,指出了集合论及其运算系统与逻辑推理系统的等价关系。统一集能对现有的理论进行总结、统一 ,还为开辟崭新的集合论。
This paper presents a brand new set theory, All Set theory, which is the united set form of the current set theories including crisp set, fuzzy set, extension set, vague set, rough set, set pair analysis, FHW(fuzzy gray matter-element),FEEC(fuzzy extension economic control) and so on. The operation of the all set is also discussed in detail. A kind of style of the human being's intelligence can be described by a kind of set form, thus all set is the united form. An all set is comprised of four parts, that is ( A,B,F,J). A is the universe of the problem discussed. One of the elements in A can be described by an element of B. F is the map from A to B . And J restricts F . From this model, the concept of subjection that is the basic conception of human's intelligence can be simulated. Hence the wide application of all set theory in the field of artificial intelligence including pattern recognition, clustering, logic, machine learning, intelligent decision, etc., can be developed. Especially the relation among all set, logic and human intelligence style is illustrated in the paper. The theory of all set can not only unify and summarize the current theories but also provide the primary method for establishing new set theory and new logic. [
出处
《中国工程科学》
2002年第3期40-47,共8页
Strategic Study of CAE
基金
"八六三"高科技发展计划资助项目 (863 -3 0 6ZD0 6-0 3 -6)
