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Some further results about t-norms and t-conorms on some special classes of bounded lattices

In the last years, the constructions of triangular norms (t-norms) and triangular conorms (t-conorms) on bounded lattices are an active research area. In this paper, we propose construction methods for t-norms and t-conorms on appropriate bounded lattices by using interior and closure operators, respectively. By using these methods, we obtain some proposed methods given by Ertuğrul, Karaçal, and Mesiar [2015. “Modified Ordinal Sums of Triangular Norms and Triangular Conorms on Bounded Lattices.” International Journal of Intelligent Systems 30: 807–817] and Çaylı [2018. “On a New Class of T-Norms and T-Conorms on Bounded Lattices.” Fuzzy Sets and Systems 332: 129–143] as results. Also, we give some illustrative examples. Finally, we show that the introduced construction methods can not be generalized by induction to a modified ordinal sum for t-norms and t-conorms on bounded lattices, in general.