A Survey on Weak Pseudoorders in Ordered Hyperstructures
DOI:
https://doi.org/10.61360/BoniGHSS242016861002Keywords:
ordered superring, weak pseudoorder, regular relationAbstract
As a generalization of pseudoorders, the weak pseudoorder in ordered (semi)hyperrings was defined by Qiang et al., and some results were studied. In order to further study, we apply weak pseudoorders for an ordered superring R and show relations with pseudoorders of R. Moreover, we present some illustrative examples and regular equivalence relation σ on ordered superring R, such that R/σ is an ordered superring. Furthermore, we show that if η is a weak pseudoorder on an ordered superring R, F is the set of all weak pseudoorders on R/η* and E = {ζ | ζ is a weak pseudoorder on R such that η ⊆ ζ},then card(E) = card(F).
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