Extension of discrete t-norms and t-conorms to discrete fuzzy numbers

The aim of this paper is to extend a monotone operation defined on a discrete setting to a closed binary operation on the partially ordered set A1 of discrete fuzzy numbers whose support is a subset of natural numbers. Moreover, we study several properties like the monotonicity, commutativity, associativity or the boundary condition when the extended operation is a discrete t-norm or a discrete t-conorm defined on a finite chain L={0,1,…,n}⊂N. Also, we study the Frank's equation for t-norms and t-conorms defined on a special subset of A1. Finally, we propose an application to obtain consensus opinion based on discrete fuzzy weighted normed operators.