Hierarchical similarity-based approximate reasoning with restricted equivalence function
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909006672429056 |
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| author | Li, Dechao Zhu, Yuhui |
| author_facet | Li, Dechao Zhu, Yuhui |
| contents | Given that the restricted equivalence functions (REFs) can serve to measure the similarity of two fuzzy sets, this motivates the integration of REFs with similarity-based approximate reasoning systems to enhance inference capabilities. Therefore, this work primarily constructs hierarchical similarity-based approximate reasoning (SBAR) using REFs. Specifically, we first characterize REFs with a given aggregation function, then discuss the approximation equality of SBAR method proposed by Raha et al. with REFs. Finally, we suggest two REF-based hierarchical Raha's SBAR methods which efficiently restrain the explosion of fuzzy rules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00048 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hierarchical similarity-based approximate reasoning with restricted equivalence function Li, Dechao Zhu, Yuhui General Mathematics Given that the restricted equivalence functions (REFs) can serve to measure the similarity of two fuzzy sets, this motivates the integration of REFs with similarity-based approximate reasoning systems to enhance inference capabilities. Therefore, this work primarily constructs hierarchical similarity-based approximate reasoning (SBAR) using REFs. Specifically, we first characterize REFs with a given aggregation function, then discuss the approximation equality of SBAR method proposed by Raha et al. with REFs. Finally, we suggest two REF-based hierarchical Raha's SBAR methods which efficiently restrain the explosion of fuzzy rules. |
| title | Hierarchical similarity-based approximate reasoning with restricted equivalence function |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2605.00048 |