Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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GENERAL TYPES OF(∈,∈∨qk)-FUZZY SUBSEMIGROUPS IN SEMIGROUPS

  • Kang, Jeong Gi (Department of Mathematics EducationGyeongsang National University)
  • Received : 2016.06.30
  • Accepted : 2016.12.01
  • Published : 2016.12.25
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Abstract

More general form of an (${\in},{\in}{\vee}q_k$)-fuzzy subsemigroup is considered. The notions of (${\in},q^{\delta}_k$)-fuzzy subsemigroup, ($q^{\delta}_0,{\in}{\vee}q^{\delta}_k$)-fuzzy subsemigroup and (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy subsemigroup are introduced, and related properties are investigated. Characterizations of an (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy subsemigroup are considered. Conditions for an (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy subsemigroup to be a fuzzy subsemigroup are provided. Relations between ($q^{\delta}_0,{\in}{\vee}q^{\delta}_k$)-fuzzy subsemigroup, (${\in},q^{\delta}_k$)-fuzzy subsemigroup and (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy subsemigroup are discussed.

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