Kybernetika 60 no. 5, 624-651, 2024

New constructions of uni-nullnorms on certain classes of bounded lattices by closure (interior) operators

Tao WuDOI: 10.14736/kyb-2024-5-0624

Abstract:

The primary aim of this article is to put forward new classes of uni-nullnorms on certain classes of bounded lattices via closure (interior) operators. Due to the new classes of uninorms combining both a t-norm $T$ and a t-conorm $S$ by various kinds of closure operators or interior operators, the relationships and properties among the same class of uninorms on $L$, we obtain new classes of uni-nullnorms on $L$ via closure (interior) operators. The constructions of uni-nullnorms on some certain classes of bounded lattices can provide another different perspective of t-norms and the dual of t-norms, uninorms and some other associative aggregation operations on bounded lattices. That is, the constructions seem to be the ordinal like sum constructions, but not limited to the ordinal like sum constructions.

Keywords:

bounded lattice, nullnorm, uni-nullnorm, closure operator, construction, ordinal like sum construction

Classification:

03B52, 06B20, 03E72

paper.pdf

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