• 科學研究
    報告題目:

    Constructions of quasi-overlap functions and their generalized forms on partially ordered sets

    報告人:

    喬軍勝 博士 (西北師范大學)

    報告時間:

    報告地點:

    騰訊會議 ID:666 851 513

    報告摘要:

    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 partially ordered sets. To be specific, firstly, we generalize the truth values set of quasi-overlap 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 setPby considering the weaker boundary conditions than the quasi-overlap functions onP. 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 partially ordered setPvia the so-called Galoiss-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 partially ordered setPto any other 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 onP, such as, idempotent, Archimedean property and cancellation law.

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