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The concept of almost interior  Γ -hyperideals ( A − I − Γ -hyperideals) in ordered  Γ -semihypergroups is a generalization of the concept of interior  Γ -hyperideals ( I − Γ -hyperideals). In this study, the connections between  I − Γ -hyperideals and  A − I − Γ -hyperideals in ordered  Γ -semihypergroups were presented. Also, we define the notion of  m , n - Γ -hyperfilters of ordered  Γ -semihypergroups and provide useful results on it. Moreover, we use the weak pseudoorders to construct quotient ordered  Γ -semihypergroups by using ordered regular equivalence relations. These concepts lead us to a new research direction in ordered  Γ -semihypergroups.

discrete dynamics in nature and society

A Study on<math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"><mi>A</mi><mo>−</mo><mi>I</mi><mo>−</mo><mi mathvariant="normal">Γ</mi></math>-Hyperideals and<math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"><mfenced open="(" close=")" separators="|"><mrow><mi>m</mi><mo>,</mo><mi>n</mi></mrow></mfenced><mo>−</mo><mi mathvariant="normal">Γ</mi></math>-Hyperfilters in Ordered<math xmlns="http://www.w3.org/1998/Math/MathML" id="M3"><mi mathvariant="normal">Γ</mi></math>-Semihypergroups

A Study onA−I−Γ-Hyperideals andm,n−Γ-Hyperfilters in OrderedΓ-Semihypergroups

A Study on $A - I - Γ$ -Hyperideals and $(m, n) - Γ$ -Hyperfilters in Ordered $Γ$ -Semihypergroups