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Study On The Model Of Granular Computing

Posted on:2008-12-29Degree:DoctorType:Dissertation
Country:ChinaCandidate:L Q ZhaoFull Text:PDF
GTID:1118360215496374Subject:Computer application technology
Abstract/Summary:PDF Full Text Request
The idea of granular computing (GrC) emerged in the late 1970's. It imitates the manner of human thinking, just as Zhang and Zhang said: A well known feature of human intelligence is that human can not only observe and analyze a problem at different grain-sizes but also translate from one granule world to the others with no difficulty. As a new tool dealing with incomplete, uncertain, imprecise and inconsistent knowledge, GrC is a big umbrella which covers all the research of the theories, methodologies, technologies, and tools about granules. It is an important base of artificial intelligence and now becomes a hot research topic domestically and abroad which includes quotient space theory, rough set theory and fuzzy set theory. The thesis covers the following aspects.1. The background, status and main theories of GrC are introduced. The relations and differences among quotient space theory, rough set theory and fuzzy set theory are discussed in detail, thus explaining the research background and significance of the thesis.2. We research into the basics of GrC, including the description and measurement of granules. We present the micro and macro hierarchical figure and the general definition of granules. Then we introduce the dynamic model of granular space on the basis of quotient space theory, rough set theory and fuzzy set theory and discuss its main properties. We place emphasis on the measurement of granules and define the granularity, fineness, granularity entropy, conditional granularity, conditional fineness and conditional granularity entropy under a normal equivalence relation. Then we analyze these definitions and get their basic properties. Besides, we also discuss the measurement of infinite set and put forward a general idea concerning the definition of granules.3. The main characteristics of fuzzy relation matrix are introduced. By the relation matrix we present the general definitions of (conditional) granularity. (conditional) fineness, and (conditional) granularity entropy tinder any relation. We also define closeness and difference between two granules and discuss their properties. In this way, the quotient space theory, rough set theory and fuzzy set theory are unified.4. The basic operations such as quotient intersection, quotient union, quotient not, quotient subtraction and so on are defined and analyzed.. The knowledge space of granules is researched. We can obtain its corresponding macro and micro knowledge space according to macro and micro characteristic of knowledge. We introduce the definition of knowledge base, picture the knowledge space by the base, and thus visually get a knowledge space algorithm of feature reduction in rough set theory (the optimal feature reduction algorithm).5. Constructing methods of granular space are introduced: constructing methods of quotient granular including feature partition, structure partition, constraint partition and so on; constructing methods of quotient structure when the domain is a topological or semi-order structure; constructing method of quotient feature when the domain has or has no structure. Then the main operations and principle of granular space are discussed.6. The knowledge space with structure is discussed. We not only think about the quotient intersection and quotient union of granules, but also the quotient intersection and quotient union of structures. When we research on the knowledge base, we should think about both the base of granules and that of structures. In general when there is only one kind of structure, a problem is simplified as a knowledge space with no structure; when there are several kinds of structures, the corresponding knowledge space is much more complicated. Then taking the topological structure as an example we research on the knowledge space with structure, which is produced by granular base and topological base.7. We investigate the applications of granular computing focusing on structure. We carry out granularity analysis of time sequence based on space, and get the following result: when a system is a Markov chain and is observed in a coarser-grain space, we can get a corresponding HMM; on the contrary, for any HMM, there must be a corresponding Markov chain M and a relevant granularity T, that is, HMM is the observation of M based on T.8. We discuss the application of constructing learning method in AVE local model partition and study granular problems based on structure including constructing of structure relation matrix, granular partition based on structure, constructing of relation matrix of quotient structure, carrying out granular partition by constructing learning methods, and so on.
Keywords/Search Tags:Granular Computing, Quotient Space Theory, Rough Set Theory, Fuzzy Set Theory, Granularity Space, Knowledge Space, HMM
PDF Full Text Request
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