Generalized convex combination of implications on bounded lattices

Document Type : Research Paper


1 Department of Mathematics, Recep Tayyip Erdogan University, 53100 Rize, Turkey

2 Department of Mathematics, Karadeniz Technical University, Trabzon, 61080, Turkey


In this paper, the notions of the linear and g-convex combination for implications which extend the notion of convex combination of fuzzy implications on the unit interval to bounded lattices are introduced. A necessary and sufficient condition for the g-convex combination to be an implication is determined. Some basic properties of the g-convex combinations are discussed. Also, some sets which are defined by the linear (g-convex) combination of two implications on a bounded lattice are studied and the relationships between them are discussed. Moreover, the lattice theoretical structure of the mentioned sets is investigated.