SP-Fuzzy Soft Ideals in Semigroups

Authors : Canan AKIN, Ülkü KARAKAYA

Pages : 22-32

View : 39 | Download : 9

Publication Date : 2018-12-29

Article Type : Conference Paper

Abstract :In this paper, the definition of a new concept which is a member of the class $\tilde{insert ignore into journalissuearticles values(U,P);}$ and which is referred to as $UP$-fuzzy soft subset of a soft set on the class $insert ignore into journalissuearticles values(U,P);$ is introduced, where $\tilde{insert ignore into journalissuearticles values(U,P);}$  denotes the fuzzy soft class and $insert ignore into journalissuearticles values(U,P);$ denotes the soft class with the universal set $U$ and the set of parameters $P$. We give the definitions of the complement and $\alpha$-level soft set of a $UP$-fuzzy soft subset of a soft set. It is 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, this paper presents some new algebraic notions which are called $SP$-fuzzy soft subsemigroup and $SP$-fuzzy soft left insert ignore into journalissuearticles values(right, bi-, quasi, interior); ideal of a soft semigroup. We examine some basic properties such as restricted union, extended union, restricted intersection, extended intersection and product of the families of $SP$-fuzzy soft subsemigroups and $SP$-fuzzy soft left insert ignore into journalissuearticles values(right, bi-, quasi, interior); ideals. It is obtained that the restricted intersection of the family of $SP$-fuzzy soft subsemigroups is a $SP$-fuzzy soft subsemigroup of the restricted intersection of the family of soft sets. Moreover it is indicated that an $\alpha$-level soft set of a $SP$-fuzzy soft subset is a soft subsemigroup for all $\alpha \in [0,1]$ if and only if the SP-fuzzy soft subset is a SP-fuzzy soft subsemigroup.
Keywords : Fuzzy, soft set, UP fuzzy soft subset, SP fuzzy soft subsemigroup

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