Affiliations: [a] School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, P.R. China | [b] School of Mathematics and Statistics, Fuyang Normal University, Fuyang, Anhui, P.R. China | [c] Department of Mathematics, Yazd University, Yazd, Iran
Correspondence:
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Corresponding author. Jian Tang, School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, 730000, P.R. China. Tel./Fax: +86 0931 8912481; E-mail: [email protected].
Abstract: In this paper, we introduce the concept of hyperfilters of an ordered semihypergroup, and present some examples in this respect. Furthermore, we define and discuss the fuzzy hyperfilters of ordered semihypergroups. We also introduce the concept of completely prime fuzzy hyperideals of an ordered semihypergroup S, and establish the relation of fuzzy hyperfilters and completely prime fuzzy hyperideals of S . In particular, we prove that a fuzzy subset f of S is a fuzzy hyperfilter of S if and only if the complement f′ of f is a completely prime fuzzy hyperideal of S . As an application of the results of this paper, the corresponding results in ordinary semihypergroups can be also obtained by moderate modification.
Keywords: Ordered semihypergroup, ordered fuzzy point, hyperfilter, fuzzy hyperfilter, completely prime fuzzy hyperideal
