Granular computing I: the concept of granulation and its formal model
Granular computing I: the concept of granulation and its formal model
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DOI：
10.1504/ijgcrsis.2009.026723
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发表时间：
2009-06
期刊：
影响因子：
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通讯作者：
T. Lin
中科院分区：
文献类型：
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作者：
T. Lin
术语颗粒计算（GRC）是由Lin和Zadeh（Zadeh（源自Zadeh的粒状数学）在1996年秋季创造的。从那时起，就提出了九个GRC模型。在GRC2008主题演讲中，提出基于类别理论的模型（第8个GRC模型）为“（最终）GRC模型”；但是，该公告没有及时纳入诉讼程序。因此，本文是第一个印刷的演示文稿。本文以三种方式解释了肉芽的概念：它是通过经典示例定义的。 2）非正式的Zadeh，3）正式通过基于类别的GRC模型。它概述了如何通过将抽象类别指定为“九个模型”： 1）设置/类型I模糊集； 2）函数/广义函数，例如随机变量（可测量函数），测量/概率； 3）计算机的图灵机/集群； 4）定性模糊集。定性模糊集的概念是新的，而且很新颖。我们已经通过邻里系统解释了这一点。
The term granular computing (GrC) was coined by Lin and Zadeh (derived from Zadeh's granular mathematics) in Fall, 1996. Since then, nine GrC models have been proposed. In GrC2008 keynote, the category theory based model (8th GrC model) was proposed to be 'the (final) GrC model'; however, the announcement was not in time to be included in the proceedings. So this paper is the first printed presentation. This paper explains the concept of granulation in three ways: it is defined 1) inductively by classical example; 2) informally by Zadeh, 3) formally by the category-based GrC model. It outlines how this model can be specified into nine models by specifying the abstract category to the category of; 1) sets/type I fuzzy sets; 2) functions/generalised functions such as, random variables (measurable functions), measures/probabilities; 3) Turing machines/clusters of computers; 4) qualitative fuzzy sets. The concept of qualitative fuzzy sets is new and quite novel; we have explained it via neighbourhood systems.