Hyperfilters and fuzzy hyperfilters of ordered semihypergroups

Abstract

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.

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