Measuring and aggregating {\epsilon}-T-transitive fuzzy relations

Dechao Li; Yutao Yao; Jingyao Duan

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arXiv · 2605.00045

Measuring and aggregating {\epsilon}-T-transitive fuzzy relations

Dechao Li·Yutao Yao·Jingyao Duan

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Abstract

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 {\epsilon}-T-transitive fuzzy relation is introduced, and the aggregation functions that preserve the {\epsilon}-T-transitivity of fuzzy relations are characterized. Finally, the {\epsilon}-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 {\epsilon}-T-transitive fuzzy relation under the permissible error.

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Dechao Li, Yutao Yao, Jingyao Duan. 2026-04-29. Measuring and aggregating {\epsilon}-T-transitive fuzzy relations. https://arxiv.org/abs/2605.00045

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