(Mohamed Boudiaf University of M’sila, Faculty of Mathematics and Computer Science, Mathematics Department, 2024-06-11) Layadi, Halima; Debih, Kenza; Yettou, Mourad: Supervisor
In this memory, we first have recalled the necessary basic concepts and properties of binary
relations on a set and partially ordered sets. Then, we have provided general properties and
information on lattices. Also, we have presented binary operations and their properties on
bounded lattices. More precisely, we have given some spacial classes of binary operations as
aggregation operations, triangular norms and conorms. Moreover, we have expanded their
concept to uni-norms and null-norms. After that we have presented how they lead to the new
mathematical concepts of uni-nullnorms and null-uninorms. Finally, we supported this
memory by mentioning some applications of binary operations in various fields.