Kybernetika 58 no. 3, 456-478, 2022

On the construction of t-norms (t-conorms) by using interior (closure) operator on bounded lattices

Emel AşıcıDOI: 10.14736/kyb-2022-3-0456

Abstract:

Recently, the topic of construction methods for triangular norms (triangular conorms), uninorms, 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 using interior and closure operators, respectively. Thus, we obtain some proposed methods given by Ertu\u{g}rul, Kara\c{c}al, Mesiar [15] and \c{C}ayl{\i} [8] as results. Also, we give some illustrative examples. 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.

Keywords:

t-norm, ordinal sum, t-conorm, bounded lattice

Classification:

03E72, 03B52

paper.pdf

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