【作者】 陈万里；

【导师】 程家兴；

【作者基本信息】 安徽大学 ， 计算机应用， 2005， 博士

【摘要】 在不同的抽象层次上观察、理解、表示现实世界问题连同其解,并进行分析、综合、推理,是人类问题求解过程的一个明显特征,也是人类问题求解能力的强有力的表现。从一定意义上来说,这就是人类问题求解过程中智能之所在。针对人类问题求解的这种能力和特征,人工智能研究者对其进行了深入的研究,并建立了各种形式化的模型。作为一种正在兴起的人工智能研究领域,粒计算的目的就是建立一种体现人类问题求解特征的一般模型,其基本思想是在不同的粒度层次上进行问题求解。粒是粒计算的最基本的原语,它是一簇点(对象、物体)由于难以区别,或相似、或接近、或某种功能而结合在一起所构成的。从狭义上看,粒计算可以理解为在不同粒度层次上以粒作为运算对象进行计算和推理。从广义上看,作为一种术语,粒计算可以理解为在问题求解过程中使用粒的理论、方法论、技术和工具的统称。粒、由某个粒化准则所得到的粒层、所有粒层构成的层次结构是组成粒计算模型的三个基本组成;粒化、关于粒的计算和推理是粒计算的两个基本问题,而这两者都可以从语义和算法两个方面来进行研究。 本文主要在集合论背景下从理论上研究了两种分明粒计算模型,即基于问题求解的商空间理论和基于粗糙集理论的粒计算模型。具体内容如下: 1、分别从论域的结构和粒化准则这两个角度推广了商空间理论。 从粒计算的角度来看,问题求解的商空间理论用拓扑来描述论域的结构、用等价关系来完成粒化,借助于自然映射实现在不同粒度层次上的转换。Cech意义下的闭包运算是比拓扑更一般的描述论域的结构的数学语言,本文从论域结构的角度对问题求解的商空间理论进行推广,用闭包运算代替拓扑来描述结构而依然用等价关系来完成粒化,结果表明商空间理论的结论可以推广到这种更一般的情形。等价关系的传递性公理在很多实际应用中很难满足,因此可能会限制商空间理论的可应用领域。本文又讨论了在相容关系,即满足自反性、对称性的二元关系,条件下的商空间理论。在这种情形下,拓扑描述结构,相容关系完成粒化而集值映射充当自然映射的角色,本文的研究表明在这种情形下商空间理论的大部分结论依然成立。这两种推广在一定程度上从理论上丰富了问题求解的商空间理论的内容,并进一步扩大了其可应用的范围。更多还原

【Abstract】 Perception, understanding and representation, as well as analysis, synthesis and reasoning, of real world problem together with its solution at different levels of granularity, is an obvious feature in the process of human problem solving, and it also embodies the outstanding ability of human problem solving. In a sense, it is precisely the intelligence in the process of human problem solving. Considering such ability of human, researchers of artificial intelligence have made some further investigation and presented many formal models. As an emerging research sub-field of artificial intelligence, granular computing, whose philosophy is to implement the problem solving at different levels of granularity, aims to establish much more general model reflecting the process of human problem solving. Granule, a clump of points (objects) drawn together by indistinguishability, similarity, proximity or functionality, is the primitive notion of granular computing. In a narrow sense, granular computing can be understood as the computing and reasoning with granules at different levels of granularity. In a broader sense, granular computing is a unified notion of theories, methodologies, techniques and tools that utilize granules in the process of problem solving. Three basic components of a granular computing model are granule, granular level derived by a given granulation criteria and hierarchy composed of all granular levels. Granulation and computing or reasoning with granules, either of them can be studied from both the semantic and algorithmic perspectives, are two related issues of granular computing.The thesis mainly studies two crisp models of granular computing in the framework of set theory, namely, quotient space theory of problem solving and rough set theory. More specifically, the research includes:1、 Quotient space theory of problem solving is generalized from two directions, namely the structure of the universe of discourse and granulation criteria. In the light of granular computing, quotient space theory of problem solving exploits topology to describe the structure of the universe of discourse, and utilizes equivalence relation to implement granulation, and relies on the natural mapping to realize the translations among different levels of granularity. Closure operation in the sense of Cech is more general mathematical language that can be used to describe the structure of the universe of discourse. When generalizing quotient space theory of problem sohing. the thesis exploits closure operation of Cech sense to describe structure. It turns out thatconclusions of classical quotient space theory keep being true in such a general framework. The axiom of transitivity is a tough condition for many applications, which may confine the applicable fields of quotient space theory of problem solving, so a weakened version of quotient space theory with topology describing the structure, compatibility relation that is reflexive and symmetric binary relation implementing granulation, set-valued function playing the role of natural mapping, are presented. The discussion implies that there are corresponding conclusions of classical quotient space theory. To some degree, these two generalizations enrich the intension of quotient space theory of problem solving, and extend its applicable fields.2 > The thesis presents the topological interpretation of the upper and lower approximate operators of generalized rough set model based on reflexive binary relation, as well as the order-theoretic interpretation of the upper and lower approximate operators of generalized rough set model based on covering. Classical rough set theory lays its foundation on the indiscemibility relation, which is represented as equivalence relation in mathematics, between objects. Generalized rough set models based on binary relation and covering respectively are two important studies. The thesis proves that the upper approximate operator of generalized based rough set models based on binary relation is precisely quasi-discrete closure operation, in the sense of Cech. derived by the given binary relation. Dually, the lower approximate operator is preciseh- the quasi-discrete interior operation. Then the topological understandings of generalized approximate rough operators are proposed. As far as covering based rough approximate operators are concerned, it is proved, by constructing Galois connection between the power set of object set and the power set of the covering, that the upper approximate operator is preciseh’ the closure operator, which satisfies special axioms, in the sense of order theory. Also, the dual result about the lower approximate operator is given. The studies of the thesis provide, to some extent, the foundations for the further application of generalized rough set theory.3-, A generalized multi-valued information system and its corresponding formal language, a -decision logic language, are proposed. Simply, information system, also called information table, is a 2-dimension table used as the carrier of information, which includes the finite set of objects, die finite set of attribute (name), the finite domain for each attribute and the information function for each attribute that maps objects to the domain of this attribute. It is the information function that distinguishes different ft-pe information systems. Based on the analysis of single-valuedinformation system, multi-valued one, relational attribute one and fuzzified single-valued one, a fuzzified multi-valued information system, which generalizes all of the mentioned ones, is presented in which the information function for each attribute maps a object to a fuzzy set of corresponding domain. Consequently, a -decision logic language that generalizes decision logic language of single information system is proposed. By the selection of parameter a one can describes, analyzes and solves of problem at different level of granularity.Undoubtedly, considering the philosophy of granular computing, the thesis discusses the problem of granular computing at rather coarse granularity. Namely, the granular computing is studied at a very abstract level. Therefore, how to combine discussed theories and methods of granular computing with concrete problems is an important issue of further research.更多还原