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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.14900 |
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| _version_ | 1866915455587844096 |
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| author | Laiate, Beatriz Sussner, Peter |
| author_facet | Laiate, Beatriz Sussner, Peter |
| contents | This paper investigates the solutions of a family of certain linear fuzzy arithmetic equations that involve fuzzy numbers belonging to certain finite-dimensional vector spaces of $\mathbb{R}_{\mathcal{F}}$, called $\mathcal{S}\left(\mathcal{A}\right)$-linearly correlated fuzzy numbers. Here, $\mathcal{A}$ stands for a strongly linearly independent (SLI) set of fuzzy numbers. The arithmetic operations in the aforementioned linear equations are the sum in the vector space $\mathcal{S}(\mathcal{A})$ and the so-called $ψ$-cross product that turns $\mathcal{S}(\mathcal{A})$ into a commutative ring. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_14900 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear Equations in the Ring of $\mathcal{S}(\mathcal{A})$-Linearly Correlated Fuzzy Numbers Laiate, Beatriz Sussner, Peter Rings and Algebras This paper investigates the solutions of a family of certain linear fuzzy arithmetic equations that involve fuzzy numbers belonging to certain finite-dimensional vector spaces of $\mathbb{R}_{\mathcal{F}}$, called $\mathcal{S}\left(\mathcal{A}\right)$-linearly correlated fuzzy numbers. Here, $\mathcal{A}$ stands for a strongly linearly independent (SLI) set of fuzzy numbers. The arithmetic operations in the aforementioned linear equations are the sum in the vector space $\mathcal{S}(\mathcal{A})$ and the so-called $ψ$-cross product that turns $\mathcal{S}(\mathcal{A})$ into a commutative ring. |
| title | Linear Equations in the Ring of $\mathcal{S}(\mathcal{A})$-Linearly Correlated Fuzzy Numbers |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2508.14900 |