ON THE CONSTRUCTION OF T-NORMS (T-CONORMS) BY USING INTERIOR (CLOSURE) OPERATOR ON BOUNDED LATTICES

Abstract

Recently, the topic of construction methods for triangular norms (triangular conorms), uni-norms, nullnorms, etc. has been studied widely. In this paper, we propose construction methods for triangular norms (t-norms) and triangular conorms (t-conorms) on bounded lattices by us-ing interior and closure operators, respectively. Thus, we obtain some proposed methods given by Ertugrul, Kara,cal, Mesiar [15] and C,ayli [8] as results. Also, we give some illustrative ex-amples. Finally, we conclude 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.