A Generalization of Semidetached Subalgebras in <i>BCK</i>/<i>BCI</i>-algebras

Abstract

Generalization of the paper [Y. B. Jun and S. Z. Song, Semidetached subalgebras in BCK/BCI-algebras, to appear in Bulletin of the Korean Mathematical Society] is discussed. Several conditions for a semidetached structure in BCK/BCI-algebras to be a semidetached subalgebra are provided. The concepts of ((is an element of) over bar, (is an element of) over bar boolean OR (q(kappa)) over bar -fuzzy subalgebra, kappa-left q(kappa),is an element of boolean OR q(kappa))-fuzzy subalgebra and ((is an element of) over bar boolean OR (q(kappa)) over bar, (is an element of) over bar boolean OR (q(kappa)) over bar)-fuzzy subalgebra are introduced, and relative relations and properties are discussed.