(2102-6510) Constructing t-norms and t-conorms by using interior and closure operators on bounded lattices, respectively

Document Type : Research Paper

Author

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

10.22111/ijfs.2021.6321

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
Ertugrul, Karacal, Mesiar [15] and Cayli [8] 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