Ordinal Sum of Two Binary Operations Being a T-Norm on Bounded Lattice

The ordinal sum of t-norms on a bounded lattice has been used to construct other t-norms. However, an binary operations (not necessarily t-norms) defined the fixed subintervals may not be t-norm. Some necessary and sufficient conditions are presented in this article for ensuring that two is, fact, In particular, results here provide answer open problem put forward by Ertuğrul Yeşilyurt, ordinal sums triangular norms lattices , Inf. Sci., vol. 517, (2020) 198–216.