Measuring and aggregating {\epsilon}-T-transitive fuzzy relations
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.
Cite
@article{arxiv.2605.00045,
title = {Measuring and aggregating {\epsilon}-T-transitive fuzzy relations},
author = {Dechao Li and Yutao Yao and Jingyao Duan},
journal= {arXiv preprint arXiv:2605.00045},
year = {2026}
}