Subalgebras of BCK/BCI-algebras based on (α, β)-type fuzzy sets

The notion of (alpha,delta)-characteristic fuzzy sets is introduced. Given a subalgebra F of a BCK/BCI-algebra X, conditions for the (epsilon,delta)-characteristic fuzzy set in X to be an (epsilon, epsilon V q)-fuzzy subalgebra, an (is an element of, q)-fuzzy subalgebra, an (E, GA q)-fuzzy subalgebra, a (q, q)-fuzzy subalgebra, a (q, is an element of)-fuzzy subalgebra, a (q, is an element of V q)-fuzzy subalgebra and a (q, GA q)-fuzzy subalgebra are provided. Using the notions of (a, /3)-fuzzy subalgebra 4'5), conditions for the F to be a subalgebra of X are investigated where (a, p) is one of (is an element of, is an element of V q), (is an element of, is an element of Lambda q), (is an element of, q), (q, is an element of V q), (q, is an element of Lambda q), (q, is an element of) and (q, q).