Omar, Barkat2019-06-182019-06-182019-05-04http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/14392Previously, ternary relations did not get enough attention from studies like binary relations, but recently there has been a noticeable turnout. Inspired by the importance of them, our thinking has led to the addition of a contribution to this framework. It means that the main aim of this work is to contribute to the addition of a new study in the field of ternary relations. More specifically, we aim to study the compatibility of a ternary relation with a binary fuzzy relation, similarly to the binary case. The study of above compatibility requires us to study effective tools to achieve this. In the present thesis, we focused on two of them. We aim to extend the interesting notions of traces and clone relations of a binary relation to the setting of ternary relations. The first study, allow us to characterize the compatibility in terms of traces, where we proved that this compatibility can be expressed in terms of inclusions of the binary fuzzy relation in the traces of the ternary relation . The second one, allow us to represent all the binary fuzzy tolerance relations that a crisp ternary relation is compatible with.enBinary relation; Ternary relation; Traces; Relational compositions; Clone relations; CompatibilityArticle