【作者】 张强；

【导师】 刘晓东；

【作者基本信息】 大连海事大学 ， 应用数学， 2005， 硕士

【摘要】 AFS理论是刘晓东教授于1995年首先提出的。AFS(Axiomatic Fuzzy Sets)即公理模糊集,将L.A.Zadeh于1965年提出的模糊子集思想数学公理化。它使数据库中大量的、复杂的、混乱的信息,数学规范化,并将人类依据原始数据所形成的概念及其逻辑运算的部分机理抽象化。AFS结构正是蕴涵在复杂数据库和弱偏好关系中的数学模式的抽象。在AFS理论中,隶属函数及其逻辑运算是由原始数据和AFS结构上的AFS代数确定的。从而使得在计算机上,可应用AFS理论直接处理复杂数据系统,这种处理能力远远超出人脑。 模糊认知图(Fuzzy cognitive map,FMC)~[1](1986)为知识表示和推理提供了非常灵活和有力的架构。特别是最近10年,模糊认知图已经被用来表示知识和人工智能。数据挖掘作为一个新兴的多学科交叉应用领域,从多个科学汲取营养,正在各行各业的决策支持活动中扮演着越来越重要的角色。如何有效利用丰富的数据海洋宝藏以达到为人类服务的目的,业已成为广大信息技术工作者所关注的焦点之一。 本文系统概要地从五个方面介绍了AFS理论中的AFS代数,AFS结构,AFS模糊逻辑系统,AFS方法的基本思想及其工程意义及其在模糊聚类分析等方面的应用。此外,本文详细的对近年来模糊认知图,数据挖掘以及AFS理论的发展和应用进行了综述,分析了现有的关于模糊认知图的研究的局限和尚待研究的问题,进而指出可以应用AFS理论来研究模糊认知图并应用于数据挖掘,同时建立一套严密、系统、统一的模糊认知图建立和分析方法,从而降低模糊认知图设计的难度和复杂程度,提高其分析水平,改变实际系统的模糊认知图由于包含大量的节点和复杂的连接关系很难进行分析和处理的现状。本文还讨论了研究基于AFS理论的模糊认知图的意义,需要解决的主要问题以及应用前景。更多还原

【Abstract】 AFS (Axiomatic Fuzzy Sets) theory was proposed by Professor Liu Xiaodong in 1995. It can be applied to study the law of human thinking and is easily operated by computers. It is a mathematical abstract of the mechanisms of decompose and compose of human conceptions. And it preferably opened out both the essential mechanism that human describe complex fuzzy conceptions depending on experiences and intuitions and the essential mechanism that human choosing the corresponded membership functions. AFS theory applies topological molecular lattices to human conceptions. In the framework of AFS theory, operations are more objective, rigor and unity.Fuzzy cognitive map (FCM) offers a far more flexible and powerful framework for representing human knowledge and for reasoning. In FCM, it is able to represent all types of concepts and express the arcs (edges) connecting these concepts in terms of symbols or numeric values. As a new crossed field of multiple applied subjects, data mining absorbed nutrition from many subjects and played a more and more important role in variety activities of designs-making. How to make use of the rich data to serve human being effectively has already become one of the focuses of all the information fields.This paper introduces the AFS theory systemic from five aspects: AFS algebra, AFS structure, AFS fuzzy logic system, the basic ideas and the engineering meaning also presents a brief review of the developments and applications about Fuzzy Cognitive Maps, data mining and AFS theory. It also analyses the problems existing in the Fuzzy Cognitive Maps and points out there is advantage using AFS theory to study Fuzzy Cognitive Maps. A set of rigorous, systemic and unitize analytic and design method about Fuzzy Cognitive maps have been studied. This paper also discusses the significance, the main problems the foreground about the study of Fuzzy Cognitive Maps based on AFS theory and its application on data mining.更多还原