BOUREMEL, Hassane2018-03-152018-03-152017-06-01http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/3643The main aim of this work is to analyze the properties of the clone relation and clonal set of a binary relation on the theoretical side in order to solve the general problem of characterizing the L-fuzzy equivalence relations defined on resituated lattice a given relation is compatible with (ِ the application side). Also, we aim to provide a representation of all L-fuzzy equivalence relations compatible with a given order relation. In this thesis, we have extended the notion of clone relation of a strict order relation introduced by De Baets et al. to an arbitrary binary relation. Throughout this work, the basic properties of this clone relation have been analysed. We have also proposed a partition of the clone relation in terms of three different types of pairs of clones. One type of pairs of clones leads to an antitransitive relation, while both the two other types of pairs of clones lead to a transitive relation. This partition of the clone relation has not only been an important tool in the proofs of this work, but it also helps to gain a deeper understanding of the structure of the clone relation and it will be a key element in future work especially in the study of the compatibility of fuzzy relations. . The clone relation of the three different types of disjoint union has been characterized. In this work, we have tackled and solved the general problem of characterizing the L-equivalence relations a given relation is compatible with. To that end, we have expanded our knowledge on the clone relation of a relation by studying two important subrelations of the partition of this clone relation, informally described as reflexive related clones and irreflexive unrelated clones. Also, we have studied the compatibility of a L-equivalence relations relation with an order relation, and we have provided a representation of all fuzzy equivalence relations compatible with a given order relation. Finally, general conclusions and future research are drawn.enCrisp relation, order (strict) relation, Clone relation, Clonal set, Disjoint union, Complete lattice, residuated lattice, T-norm, L-fuzzy equivalence relation, L-fuzzy tolerance relation, Closure operation, Compatibility.Thesis