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Constructions of quasi-overlap functions and their generalized forms on bounded partially ordered sets.
- Source :
-
Fuzzy Sets & Systems . Oct2022, Vol. 446, p68-92. 25p. - Publication Year :
- 2022
-
Abstract
- 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 quasi-overlap functions from bounded lattices to bounded partially ordered sets and introduce the notions of 0 P -quasi-overlap functions, 1 P -quasi-overlap functions and 0 P , 1 P -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, 0 P -quasi-overlap functions, 1 P -quasi-overlap functions and 0 P , 1 P -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, 0 P -quasi-overlap functions, 1 P -quasi-overlap functions and 0 P , 1 P -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, 0 P -quasi-overlap functions, 1 P -quasi-overlap functions and 0 P , 1 P -quasi-overlap functions on P , such as, idempotent, Archimedean property and cancellation law. [ABSTRACT FROM AUTHOR]
- Subjects :
- *PARTIALLY ordered sets
*ARCHIMEDEAN property
*HOMOMORPHISMS
*SET functions
Subjects
Details
- Language :
- English
- ISSN :
- 01650114
- Volume :
- 446
- Database :
- Academic Search Index
- Journal :
- Fuzzy Sets & Systems
- Publication Type :
- Academic Journal
- Accession number :
- 158744421
- Full Text :
- https://doi.org/10.1016/j.fss.2021.03.004