Inner Products on Intervals in R^n

Authors

  • Daishi Kuroiwa Shimane University
  • Tomoya Mori

Keywords:

intervals in R^n, embedding to a vector space, inner products, interval linear programming problem, interval support vector machine

Abstract

In this paper, we defined an inner product on the collection of intervals in R^n within a vector space framework, demonstrating its consistency with the properties of standard inner products. We further established that the collection of intervals in R^n forms a Hilbert space under the proposed inner product. Additionally, we explored applications of this framework to interval linear programming problems and interval support vector machines, highlighting the practical relevance and usefulness of the theoretical results.

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Published

2024-12-20

How to Cite

Kuroiwa, D., & Mori, T. (2024). Inner Products on Intervals in R^n. Thai Journal of Mathematics, 22(3), 509–518. Retrieved from https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/1693

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