Abstract
In this study, several products of fuzzy transformation semigroups are generalized to the case where their truth structure is a complete lattice. We show that the direct product of two such fuzzy transformation semigroups is again a fuzzy transformation semigroup if and only if the lattice is distributive. In addition, after extending the cascade product, we introduce a novel way of building a fuzzy transformation semigroup starting from a unique automaton. The particular case of the lattice comprising all the closed subintervals contained in [0,1] is analyzed.
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