On a new class of t-norms and t-conorms on bounded lattices

The ordinal sum of triangular norms on unit interval has been used to construct other triangular norms. But, in general, ordinal sum construction of triangular norms and triangular conorms may not work on an arbitrary bounded lattice. In this study, we focus on ordinal sums of triangular norms and triangular conorms on an arbitrary bounded lattice. Moreover, we show a complete generalization of our ordinal sums of triangular norms and triangular conorms on an arbitrary bounded lattice. And some illustrative examples are added for clarity. (C) 2017 Elsevier B.V. All rights reserved.