SP-fuzzy soft subsemigroups and ideals

In this thesis, a definition of UP-fuzzy soft subset of a soft set on the class (U,P) is introduced as a new concept which is a member of the class ((U,P)) ̃, where ((U,P)) ̃ denotes the fuzzy soft class and (U,P) denotes the soft class with the universal set U and the set of parameters P. We give some basic definitions such as complement and α-level soft set of a UP-fuzzy soft subset of a soft set. It is also demonstrated that UP-fuzzy soft subsets provide De Morgan rules for restricted union and restricted intersection. Furthermore, considering a semigroup S as an universal set, in this thesis, we present some new algebraic notions which are called SP-fuzzy soft subsemigroup and SP-fuzzy soft left (right, bi-, quasi, interior) ideal of a soft semigroup. We examine some basic properties such as restricted intersection, extended intersection and product of the families of SP-fuzzy soft subsemigroups and SP-fuzzy soft left (right, bi-, quasi, interior) ideals. Moreover it is indicated that an α-level soft set of a SP-fuzzy soft subset of a soft set is a soft subsemigroup for all α∈[0,1] if and only if the SP-fuzzy soft subset is a SP-fuzzy soft subsemigroup of related soft set.