Constructing t-norms and t-conorms by using interior and closure operators on bounded lattices

Document Type : Research Paper

Author

Department of Software Engineering, Faculty of Technology, Karadeniz Technical University, 61830 Trabzon, Turkey

Abstract

In this paper, we propose construction methods for triangular norms (t-norms) and triangular conorms (t-conorms) on bounded lattices by using interior and closure operators, respectively. Thus, we obtain some proposed methods by Ertu\u{g}rul, Kara\c{c}al, Mesiar \cite{Ertugrul} and \c{C}ayl{\i} \cite{Gul} 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. This paper has further constructed the t-norms and t-conorms on bounded lattices from a mathematical viewpoint.

Keywords