类别中的结构拓扑

IF 1.9 4区数学 Q1 MATHEMATICS

Iranian Journal of Fuzzy Systems Pub Date : 2021-12-01 DOI:10.22111/IJFS.2021.6332

S. Hosseini, R. Amini

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引用次数: 0

摘要

不同的作者定义和研究了几种模糊拓扑。在本文中，我们统一了文献中存在的五种最常见的模糊拓扑，以及标准拓扑。这是通过在范畴对象上引入结构拓扑的概念来实现的，并证明集合上的拓扑以及模糊集合上的模糊拓扑和模糊子集上的模糊拓扑都是结构拓扑。本文还引入了结构连续性的概念，并证明了在上述所有情况下，文献中定义的模糊连续性和标准连续性都是结构的。

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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Structural topology in a category

Several fuzzy topologies are defined and studied by different authors. In this article, we unify five of the most common fuzzy topologies existing in the literature, as well as the standard topology. This is done by introducing the notion of structural topology on objects in a category and proving that topologies on a set as well as fuzzy topologies on fuzzy sets and fuzzy topologies on fuzzy subsets are all structural topologies. We also introduce the notion of structural continuity and we show that the fuzzy continuity defined in the literature in all the above mentioned cases, as well as the standard continuity are structural.

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来源期刊

Iranian Journal of Fuzzy Systems 数学-数学

CiteScore

3.50

自引率

16.70%

发文量

期刊介绍： The two-monthly Iranian Journal of Fuzzy Systems (IJFS) aims to provide an international forum for refereed original research works in the theory and applications of fuzzy sets and systems in the areas of foundations, pure mathematics, artificial intelligence, control, robotics, data analysis, data mining, decision making, finance and management, information systems, operations research, pattern recognition and image processing, soft computing and uncertainty modeling. Manuscripts submitted to the IJFS must be original unpublished work and should not be in consideration for publication elsewhere.