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18-10-2010, 05:18 PM
This article is presented by:Y.Y. Yao
Department of Computer Science, University of Regina
Regina, Saskatchewan, Canada
The basic ideas and principles of granular computing (GrC) have been studied explicitly or implicitly in many fields in isolation. With the recent renewed and fast growing interest, it is time to extract the commonality from a diversity of fields and to study systematically and formally the domain independent principles of granular computing in a unified model. A framework of granular computing can be established by applying its own principles. We examine such a framework from two perspectives, granular computing as structured thinking and structured problem solving. From the philosophical perspective or the conceptual level, granular computing focuses on structured thinking based on multiple levels of granularity. The implementation of such a philosophy in the application level deals with structured problem solving.
Human problem solving involves the perception, abstraction, representation and understanding of real world problems, as well as their solutions, at different levels of granularity [4, 6, 23, 28, 32-35]. The consideration of granularity is motivated by the practical needs for simplification, clarity, low cost, approximation, and tolerance of uncertainty . As an emerging field of study, granular computing attempts to formally investigate and model the family of granule-oriented problem solving methods and information processing paradigms [14, 23, 28]. Ever since the introduction of the term of “Granular computing (GrC)” by T.Y. Lin in 1997 [8, 32], we have witnessed a rapid development of and a fast growing interest in the topic [2, 5, 8-10, 13, 14, 16-20, 22-31, 33, 35, 37]. Many models and methods of granular computing have been proposed and studied. From the wide spectrum of current research, one can easily make several observations. There does not exist a general agreement about what is granular computing, nor there is a unified model . Many studies concentrate on concrete models in particular contexts, and hence only capture limited aspects of granular computing. Consequently, the potential applicability and usefulness of granular computing are not well perceived and appreciated. The studies of concrete models and methods are important for the development of a field in its early stage. It is equally important, if not more, to study a general theory that avoids constraints of a concrete model. The basic notions and principles of granular computing, though under different names, have in fact been appeared in many related fields, such as programming, artificial intelligence, divide and conquer, interval computing, quantization, data compression, chunking, cluster analysis, rough set theory, quotient space theory, belief functions, machine learning, databases, and many others [8, 23, 28, 32, 33]. However, granular computing has not been fully explored in its own right. It is time to extract the commonality from these diverse fields and to study systematically and formally the domain independent principles of granular computing in a unified and well-formulated framework. In this paper, we study high level and qualitative characteristics of a theory of granular computing. A general domain independent framework is presented, in which basic issues are examined.
Perspectives of Granular Computing
It may be difficult, if not impossible, to give a formal, precise and uncontroversial definition of granular computing. Nevertheless, one can still extract the fundamental elements from the human problem solving experiences and methods. There are basic principles, techniques and methodologies that are commonly used in most types of problem solving. Granular computing, therefore, focuses on problem solving based on the commonsense concepts of granule, granulated view, granularity, and hierarchy. They are interpreted as the abstraction, generalization, clustering, levels of abstraction, levels of detail, and so on in various domains. We view granular computing as a study of a general theory of problem solving based on different levels of granularity and detail .
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