论线性空间中模糊数构建的模糊内积

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

Fuzzy Sets and Systems Pub Date : 2024-10-03 DOI:10.1016/j.fss.2024.109144

Jian-Zhong Xiao , Chen-Ying Wang

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引用次数: 0

摘要

本文提出了模糊内积空间的新定义。正如实数集可以嵌入到模糊数集中一样，脆内积空间可以看作是模糊内积空间的一个特例。举例说明了新定义是对脆内积空间的非难一般化。在某些限制条件下，模糊内积空间可以成为模糊规范空间。基于半内积端点族的一些基本性质，讨论了新空间的线性拓扑结构。此外，还考虑了两个向量之间的正交性，并给出了毕达哥拉斯定理的模糊版本。

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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On fuzzy inner products constructed by fuzzy numbers in linear spaces

In this paper a new definition for fuzzy inner product spaces is presented. Just as the set of real numbers can be embedded in a set of fuzzy numbers, a crisp inner product space can be considered as a special case of fuzzy inner product spaces. An example is given to demonstrate that, the new definition is a nontrivial generalization for the crisp inner product spaces. Under certain restrictions, a fuzzy inner product space can become a fuzzy normed space. Based on some elementary properties for the families of semi-inner products of endpoints, the linearly topological structure of new spaces is discussed. Moreover, the orthogonality between two vectors is considered and a fuzzy version of Pythagorean theorem is given.

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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.