Towards the definition of spatial granules

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2024-06-03 DOI:10.1016/j.fss.2024.109027

Liquan Zhao, Yiyu Yao

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引用次数: 0

Abstract

Three basic issues of granular computing are construction or definition of granules, measures of granules, and computation or reasoning with granules. This paper reviews the main theories of granular computing and introduces the definition of spatial granules. A granule is composed of one or more atomic granules. The rationality of this definition is explained from the four aspects: simplicity, applicability, measurability and visualization. A one-to-one correspondence is established between the granules and the points in the unit hypercube, and the coarsening and refining of the granules are the descending and ascending dimensions of the points, respectively. The weak fuzzy tolerance relation and weak fuzzy equivalence relation are defined so as to study on all fuzzy binary relations. The notion of layer granularity/fineness is introduced and each granule can be easily denoted by two numbers, which can be used to pre-process macro knowledge space and greatly improve the search speed. This paper also discusses the main properties of granules including the necessary and sufficient conditions of coarse-fine relation and the main principles of granular space.

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空间颗粒的定义

粒度计算的三个基本问题是粒度的构造或定义、粒度的度量以及使用粒度进行计算或推理。本文回顾了颗粒计算的主要理论，并介绍了空间颗粒的定义。颗粒由一个或多个原子颗粒组成。本文从简洁性、适用性、可测量性和可视化四个方面阐述了这一定义的合理性。颗粒与单位超立方体中的点之间建立一一对应关系，颗粒的粗化和细化分别是点的降维和升维。定义了弱模糊容差关系和弱模糊等价关系，以研究所有模糊二元关系。本文引入了层粒度/细度的概念，每个粒度可以很容易地用两个数字来表示，这可以用来预处理宏知识空间，大大提高搜索速度。本文还讨论了颗粒的主要性质，包括粗细关系的必要条件和充分条件以及颗粒空间的主要原理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Fuzzy Sets and Systems 数学-计算机：理论方法

CiteScore

6.50

自引率

17.90%

发文量

321

审稿时长

6.1 months

期刊介绍： Since its launching in 1978, the journal Fuzzy Sets and Systems has been devoted to the international advancement of the theory and application of fuzzy sets and systems. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including (and not restricted to) aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. Fuzzy sets are also the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling: fuzzy rule-based systems. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies. In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Furthermore, fuzzy sets have strong logical underpinnings in the tradition of many-valued logics.