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Keywords:
nullnorm; extension method; bounded lattice; sublattice
nullnorm; extension method; bounded lattice; sublattice
Summary:
After nullnorms were defined on bounded lattices by Karaçal et al., construction methods for nullnorms on bounded lattices have been widely studied in which the existence of t-norms (t-conorms) on sublattices of the bounded lattice $L$ has generally been exploited. Extension methods of nullnorms are important as they also play a significant role for ordinal sum construction of nullnorms on bounded lattices. In this paper, we introduce extension construction methods for nullnorms on a bounded lattice $L$ by exploiting the existence of a nullnorm $V$ on a sublattice of $L$. Then, we demonstrate that our new construction methods are also different from the existing construction methods in the literature. Additionally, some illustrative examples are provided. Finally, we also give modified versions of our construction method by induction.
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