In general, the task of extending functions is not simple. It is necessary, in most cases, to impose some properties to the function and their domain. As, in particular, t-subnorms (t-subconorms) are functions, it is pertinent to question under what conditions a t-subnorm (t-subconorm) can be extended from a sublattice M to a lattice L. We present an answer to this question considering a more relaxed definition of sublattices, defined using retractions where the sublattice is not necessarily a subset. In addition, we prove some results related to these extensions with relevant concepts, such as De Morgan triples and automorphisms.
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