Binary Operations On Bounded lattices - Layadi, Halima; Debih, Kenza; Yettou, Mourad: Supervisor (Mohamed Boudiaf University of M’sila, Faculty of Mathematics and Computer Science, Mathematics Department, 2024)
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.
Keywords: Bounded lattice; binary operations; aggregation; t-norms; t-conorms; uni-norms; null-norms; uni-nullnorms; null-uninorms