Measuring and aggregating ε-T-transitive fuzzy relations
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911637496135680 |
|---|---|
| author | Li, Dechao Yao, Yutao Duan, Jingyao |
| author_facet | Li, Dechao Yao, Yutao Duan, Jingyao |
| contents | The transitivity of fuzzy relations plays an important role in fuzzy set theory, artificial intelligence, clustering and decision-making. However, it is often difficult for fuzzy relations to satisfy the transitivity property in many practical applications. This has motivated researchers to investigate the degree to which a fuzzy relation is transitive. Therefore, this work first investigates two different measures of T-transitivity for fuzzy relations using some well-known fuzzy implications. And then, the relationship between two different degrees of transitivity is investigated. Further, the concept of an ε-T-transitive fuzzy relation is introduced, and the aggregation functions that preserve the ε-T-transitivity of fuzzy relations are characterized. Finally, the ε-T-transitive fuzzy relation is utilized to make inferences and cluster objects. Compared to finding the T-transitive closure, it is reasonable to cluster objects using the ε-T-transitive fuzzy relation under the permissible error. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00045 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Measuring and aggregating ε-T-transitive fuzzy relations Li, Dechao Yao, Yutao Duan, Jingyao General Mathematics The transitivity of fuzzy relations plays an important role in fuzzy set theory, artificial intelligence, clustering and decision-making. However, it is often difficult for fuzzy relations to satisfy the transitivity property in many practical applications. This has motivated researchers to investigate the degree to which a fuzzy relation is transitive. Therefore, this work first investigates two different measures of T-transitivity for fuzzy relations using some well-known fuzzy implications. And then, the relationship between two different degrees of transitivity is investigated. Further, the concept of an ε-T-transitive fuzzy relation is introduced, and the aggregation functions that preserve the ε-T-transitivity of fuzzy relations are characterized. Finally, the ε-T-transitive fuzzy relation is utilized to make inferences and cluster objects. Compared to finding the T-transitive closure, it is reasonable to cluster objects using the ε-T-transitive fuzzy relation under the permissible error. |
| title | Measuring and aggregating ε-T-transitive fuzzy relations |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2605.00045 |