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Bases and dimension of interval vector space
Computational and Applied Mathematics ( IF 2.998 ) Pub Date : 2021-01-05 , DOI: 10.1007/s40314-020-01386-2
Min Zhu , Dechao Li

Linear independence of interval vectors is one of the most important issue in analyzing the controllability or observability of systems under uncertainty. From the viewpoint of quasilinear space, this paper aims to determine the linear independence of interval vectors by the conjunctive and disjunctive views of sets, respectively. We first show the concept of linear independence of interval vectors as conjunctive sets. And then, the dimension of \(\langle {\mathbb {I}}{\mathbb {R}}^n, +,\cdot \rangle \) is investigated. Second, viewed the interval as a disjunctive set, we introduce the weak, strong, tolerable, and controllable linear independence of interval vectors, respectively. The method and algorithms are developed to check the weak, strong, tolerable, and controllable linear independence of a set of interval vectors. Moreover, the linear independence of fuzzy number vectors is studied, too. Finally, four numerical examples are provided to illustrate and substantiate our theoretical developments and established algorithms.



中文翻译:

间隔向量空间的底和维

间隔向量的线性独立性是分析不确定性下系统的可控制性或可观察性的最重要问题之一。从拟线性空间的观点出发,本文旨在分别通过集合的合取和析取视图确定区间向量的线性独立性。我们首先展示区间向量的线性独立性作为连接集的概念。然后,\(\ langle {\ mathbb {I}} {\ mathbb {R}} ^ n,+,\ cdot \ rangle \)的维度被调查。其次,将间隔视为分离集,我们分别介绍了间隔向量的弱,强,可容忍和可控制的线性独立性。开发了该方法和算法以检查一组间隔向量的弱,强,可容忍和可控制的线性独立性。此外,还研究了模糊数向量的线性独立性。最后,提供了四个数值示例来说明和证实我们的理论发展和已建立的算法。

更新日期:2021-01-05
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