S P-Fuzzy Soft Ideals in Semigroups

Özet

In this paper, the definition of a new concept which is a member of the class ˜ (U, P) and which is referredto as UP-fuzzy soft subset of a soft set on the class (U, P) is introduced, where ˜ (U, P) denotes the fuzzy soft classand (U, P) denotes the soft class with the universal set U and the set of parameters P. We give the definitionsof the complement and α-level soft set of a UP-fuzzy soft subset of a soft set. It is demonstrated that UP-fuzzysoft subsets provide De Morgan rules for restricted union and restricted intersection. Furthermore, considering asemigroup S as an universal set, this paper presents some new algebraic notions which are called S P-fuzzy softsubsemigroup and S P-fuzzy soft left (right, bi-, quasi, interior) ideal of a soft semigroup. We examine some basicproperties such as restricted union, extended union, restricted intersection, extended intersection and product of thefamilies of S P-fuzzy soft subsemigroups and S P-fuzzy soft left (right, bi-, quasi, interior) ideals. It is obtainedthat the restricted intersection of the family of S P-fuzzy soft subsemigroups is a S P-fuzzy soft subsemigroup ofthe restricted intersection of the family of soft sets. Moreover it is indicated that an α-level soft set of a S P-fuzzysoft subset is a soft subsemigroup for all α ∈ [0, 1] if and only if the SP-fuzzy soft subset is a SP-fuzzy softsubsemigroup.