Normed Space of Fuzzy Intervals and Its Topological Structure

IF 1.9 3区数学 Q1 MATHEMATICS, APPLIED

Axioms Pub Date : 2023-10-22 DOI:10.3390/axioms12100996

Hsien-Chung Wu

引用次数: 0

Abstract

The space, Fcc(R), of all fuzzy intervals in R cannot form a vector space. However, the space Fcc(R) maintains a vector structure by treating the addition of fuzzy intervals as a vector addition and treating the scalar multiplication of fuzzy intervals as a scalar multiplication of vectors. The only difficulty in taking care of Fcc(R) is missing the additive inverse element. This means that each fuzzy interval that is subtracted from itself cannot be a zero element in Fcc(R). Although Fcc(R) cannot form a vector space, we still can endow a norm on the space Fcc(R) by following its vector structure. Under this setting, many different types of open sets can be proposed by using the different types of open balls. The purpose of this paper is to study the topologies generated by these different types of open sets.

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模糊区间的赋范空间及其拓扑结构

R中所有模糊区间的空间Fcc(R)不能构成一个向量空间。然而，空间Fcc(R)通过将模糊区间的加法处理为向量加法，将模糊区间的标量乘法处理为向量的标量乘法来保持向量结构。计算Fcc(R)的唯一困难是缺少加性逆元。这意味着从自身减去的每个模糊区间不可能是Fcc(R)中的零元素。虽然Fcc(R)不能形成一个向量空间，但我们仍然可以按照Fcc(R)空间的向量结构赋予它一个范数。在此设置下，通过使用不同类型的开球，可以提出许多不同类型的开球。本文的目的是研究这些不同类型的开集所产生的拓扑结构。

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

Axioms Mathematics-Algebra and Number Theory

自引率

10.00%

发文量

604

审稿时长

11 weeks

期刊介绍： Axiomatic theories in physics and in mathematics (for example, axiomatic theory of thermodynamics, and also either the axiomatic classical set theory or the axiomatic fuzzy set theory) Axiomatization, axiomatic methods, theorems, mathematical proofs Algebraic structures, field theory, group theory, topology, vector spaces Mathematical analysis Mathematical physics Mathematical logic, and non-classical logics, such as fuzzy logic, modal logic, non-monotonic logic. etc. Classical and fuzzy set theories Number theory Systems theory Classical measures, fuzzy measures, representation theory, and probability theory Graph theory Information theory Entropy Symmetry Differential equations and dynamical systems Relativity and quantum theories Mathematical chemistry Automata theory Mathematical problems of artificial intelligence Complex networks from a mathematical viewpoint Reasoning under uncertainty Interdisciplinary applications of mathematical theory.