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A Study of (α, β)-fuzzy Hyperfilters of Ordered Semihypergroups

Fuzzy set theory is a powerful mathematical tools for dealing with uncertainty and provides a general mathematical framework for dealing with uncertainty. In this paper, we introduce, as a generalization of ordinary fuzzy hyperfilters, the concept of an (α, β)-fuzzy hyperfilter of ordered semihypergroups 𝑆, where α, β ∈ {∈, 𝑞,∈ ∨𝑞,∈ ∧𝑞} with α ≠∈ ∧𝑞. Moreover we discuss some fundamental aspects of (∈,∈ ∨𝑞)-fuzzy hyperfilters. The concept of (,q)-fuzzy hyperfilters is also introduced and some related properties are investigated. The relationships among ordinary fuzzy hyperfilters (∈,∈ ∨q)-fuzzy hyperfilters and (,q)-fuzzy hyperfilters are discussed. Finally we define the notion of fuzzy hyperfilters with thresholds (𝑟, 𝑠) and some related properties are investigated.

Keywords: Ordered semihypergroup, left (right) hyperfilter, (∈,∈ ∨q)-fuzzy left (right) hyperfilter, (α, β)-fuzzy hyperfilter

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