Recently, Paiva et al. introduced the concept of quasi-overlap functions on bounded lattices and investigated some vital properties of them. In this paper, we continue consider this research topic and focus on the constructions of quasi-overlap functions along with their generalized forms on bounded partially ordered sets. To be specific, firstly, we generalize the truth values set of quasioverlap functions from bounded lattices to bounded partially ordered sets and introduce the notions of 0P -quasi-overlap functions, 1P -quasi-overlap functions and 0P , 1P -quasi-overlap functions on any bounded partially ordered set P by considering the weaker boundary conditions than the quasi-overlap functions on P. Secondly, we give the constructions of quasi-overlap functions, 0P quasi-overlap functions, 1P -quasi-overlap functions and 0P , 1P -quasi-overlap functions on any bounded partially ordered set P via the so-called Galois s-connections and 0,1-homomorphisms, 1-homomorphisms, 0-homomorphisms and ord-homomorphisms, respectively. In particular, we prove that those constructions contain the methods of extending the known quasi-overlap functions, 0P -quasi-overlap functions, 1P -quasi-overlap functions and 0P , 1P -quasi-overlap functions from any bounded partially ordered set P to any other bounded partially ordered sets. Finally, we show that those extensions maintain some basic properties of the known quasi-overlap functions, 0P -quasi-overlap functions, 1P -quasi-overlap functions and 0P , 1P -quasi-overlap functions on P, such as, idempotent, Archimedean property and cancellation law.(c) 2021 Elsevier B.V. All rights reserved.
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