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A very important issue in lattice theory is how to extend a given operator preserving its algebraic properties. For lattice-valued fuzzy operators framework, in 2008 Saminger-Platz presented a way to extend t-norms which was generalized by Palmeira et al. (2011) for t-norms, t-conorms, fuzzy negations and implications, considering the scenery provided by the (r,s)-sublattice.
In this paper we investigated how to extend QL-implications and which properties of it are preserved by the extension method via retractions (EMR).
As results, we proved that properties (LB), (RB), (CC1), (CC2), (CC3), (CC4), (L-NP), (EP) and (IP) are preserved by EMR.
However, the extension method via retractions fails in preserving the important properties (NP), (OP), (IBL), (CP), (P) and (LEM).
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- Some results on extension of lattice-valued QL-implications
Eduardo S. Palmeira
Benjamín R.C. Bedregal
José Anchieta G. dos Santos
- Springer London
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