Abstract
We continue the study of (isotone) Galois connections, also called adjunctions, in the framework of fuzzy preordered structures, which generalize fuzzy preposets by considering underlying fuzzy equivalence relations. Specifically, we present necessary and sufficient conditions so that, given a mapping $f:\mathbb {A}\rightarrow B$ from a fuzzy preordered structure $\mathbb {A}=\langle A,\approx _A,\rho _A\rangle$ into a fuzzy structure $\langle B,\approx _{B}\rangle$ , it is possible to construct a fuzzy relation $\rho _B$ that induces a suitable fuzzy preorder structure on $B$ and such that there exists a mapping $g:B\rightarrow \mathbb {A}$ such that the pair $(f,g)$ constitutes an Galois connection.
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