Abstract

In the present paper, we introduce the notion of (Φ, Ψ)-neutrosophic subsemigroups of a semigroup where Φ, Ψ ∈ {∈, q, ∈ ∨ q}, and related properties are investigated. We consider characterizations of an (∈, ∈)-neutrosophic subsemigroup and an (∈, ∈ ∨ q)-neutrosophic subsemigroup. Conditions for the neutrosophic ∈-subsets, neutrosophic q-subsets and neutrosophic ∈ ∨ q-subsets to be subsemigroups are discussed. Finally, we discuss conditions for a neutrosophic set to be a (q, ∈ ∨ q)-neutrosophic subsemigroup.