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CLASSIFICATIONS OF (α, β)-FUZZY SUBALGEBRAS OF BCK/BCI-ALGEBRAS

Jun, Young Bae;Ahn, Sun Shin;Lee, Kyoung Ja

  • Received : 2014.07.15
  • Accepted : 2014.08.20
  • Published : 2014.09.25

Abstract

Classications of (${\alpha},{\beta}$)-fuzzy subalgebras of BCK/BCI-algebras are discussed. Relations between (${\in},{\in}{\vee}q$)-fuzzy subalgebras and ($q,{\in}{\vee}q$)-fuzzy subalgebras are established. Given special sets, so called t-q-set and t-${\in}{\vee}q$-set, conditions for the t-q-set and t-${\in}{\vee}q$-set to be subalgebras are considered. The notions of $({\in},q)^{max}$-fuzzy subalgebra, $(q,{\in})^{max}$-fuzzy subalgebra and $(q,{\in}{\vee}q)^{max}$-fuzzy subalgebra are introduced. Conditions for a fuzzy set to be an $({\in},q)^{max}$-fuzzy subalgebra, a $(q,{\in})^{max}$-fuzzy subalgebra and a $(q,{\in}{\vee}q)^{max}$-fuzzy subalgebra are considered.

Keywords

(fuzzy) subalgebra;(${\alpha},{\beta}$)-fuzzy subalgebra;$({\alpha},{\beta})^{max}$-fuzzy subalgebra;t-q-set;t-${\in}{\vee}q$-set;$({\in},q)^{max}$-fuzzy subalgebra;$(q,{\in})^{max}$-fuzzy sub-algebra;$(q,{\in}{\vee}q)^{max}$-fuzzy subalgebra

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