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A New Generalization of Fuzzy Soft Bi-ideals in Ordered Semigroups
Faiz Muhammad Khan, Violeta Leoreanu-Fotea, Ibrahim and Amanullah

A new emerging mathematical tool to handle uncertainty is still not a suitable mathematical tool to tackle complicated problems of advanced fields like structural engineering, decision making problems, coding theory, automata theory and economics involving imprecision and fuzzy parameters. The aim of the present paper is to construct a benchmark theory i.e., (∈, ∈ ∨𝑞𝑘)-fuzzy soft ideal theory in ordered semigroup 𝑆. More precisely, (∈, ∈ ∨𝑞𝑘)-fuzzy soft bi-ideals in an ordered semi- group S are introduced. Various classes such as regular and intraregular ordered semigroups are classified through fuzzy soft bi-ideals of type (∈, ∈ ∨𝑞𝑘). Ordinary and fuzzy soft bi-ideals of type (∈, ∈ ∨𝑞𝑘) are connected using level subsets of ⟨𝑓, 𝐴⟩. Finally, upper/lower parts of (∈, ∈ ∨𝑞𝑘)-fuzzy soft bi-ideals are developed and several results of ordered semigroups based on these newly developed fuzzy soft bi-ideals are presented.

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