Some results of weighted quasi-arithmetic mean of continuous triangular norms

The weighted quasi-arithmetic mean of continuous triangular norms is investigated. Some results on convex combination of continuous triangular norms in Ouyang and Fang [Y. Ouyang, J.X. Fang, Some observations about the convex combination of continuous triangular norms, Nonlinear Anal. – TMA 68 (2008) 3382–3387] are generalized. Several open problems are posed.