In this paper, we consider the problem of aggregating a collection of transitive fuzzy binary relations in such a way that the aggregation process preserves transitivity. Specifically, we focus our efforts on the characterization of those functions that aggregate a collection of fuzzy binary relations which are transitive with respect to a collection of t-norms preserving the transitivity. We characterize them in terms of triangular triplets. Further, the relationship between triangular triplets, the monotonicity of the aggregation function and an appropriate dominance notion is explicitly stated. Special attention is paid to a few classes of transitive fuzzy binary relations that are relevant in the literature. Concretely, we describe, in terms of triangular triplets, those functions that aggregate a collection of fuzzy pre-orders, fuzzy partial orders, relaxed indistinguishability relations, indistinguishability relations and equalities. A surprising relationship between functions that aggregate transitive fuzzy relations into a $T_M$-transitive fuzzy relation and those that aggregate relaxed indistinguishability relations is shown. A few consequences of the new results are also provided for those cases in which all the t-norms of the given collection are the same. Some celebrated results are retrieved as a particular case from the exposed theory.

在本文中，我们考虑以聚合过程保持传递性的方式聚合传递模糊二元关系集合的问题。具体来说，我们将我们的努力集中在那些聚合模糊二元关系集合的函数的表征上，这些函数对于保持传递性的 t 范数集合是传递的。我们用三角形三元组来描述它们。此外，明确说明了三角形三元组、聚合函数的单调性和适当的优势概念之间的关系。特别注意文献中相关的几类传递模糊二元关系。具体来说，我们用三角形三元组来描述那些聚合一组模糊预购的函数，模糊偏序、松弛的不可区分关系、不可区分关系和等式。将传递模糊关系聚合成一个函数之间的惊人关系${吨}_{米}$- 传递模糊关系和那些聚合松弛的不可区分关系的关系。对于给定集合的所有 t 范数相同的情况，还提供了新结果的一些结果。一些著名的结果是从公开的理论中检索出来的一个特例。