A Benchmark Generalization of Fuzzy Soft Ideals in Ordered Semigroups

In real life, variability and inaccuracy are always presentand must be calculated by either possibilistic, probabilistic, polymorphic or other uncertainty approach. This benchmark study is about to construct new types of fuzzy soft ideals i.e., (∈, ∈ ∨q_k)-FSR(L)Is of ordered semigroup(OSG). Based on this inception, fuzzy soft level subsets are defined which link ordinary ideals with (∈, ∈ ∨q_k)-fuzzy soft left(right) ideals. Some binary operations like ◦_λ, intersection ∩_λ and union of fuzzy soft sets ∪_λ are given and various fundamental results of ideal theory are developed through these types of fuzzy soft ideals.