Geodesic
On the construction of t-norms (t-conorms) by using interior (closure) operator on bounded lattices
Kybernetika, Tome 58 (2022) no. 3, pp. 456-478
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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 Ertuğrul, Karaçal, Mesiar [15] and Çaylı [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.
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 Ertuğrul, Karaçal, Mesiar [15] and Çaylı [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.
DOI : 10.14736/kyb-2022-3-0456
Classification : 03B52, 03E72
Keywords: t-norm; t-conorm; ordinal sum; bounded lattice 
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Aşıcı, Emel. On the construction of t-norms (t-conorms) by using interior (closure) operator on bounded lattices. Kybernetika, Tome 58 (2022) no. 3, pp. 456-478. doi: 10.14736/kyb-2022-3-0456

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