(s, t-fuzzy Subalgebras and R-fuzzy SubalgebraofBCK-algebras

Two new kinds of definiting offuzzy subalgebras of BCK-algebras are proposed in this paper. First, by the use ofthe relations between fuzzy points and fuzzy subsets, the definition of a(s, t-fuzzysubalgebras of BCK-algebras is introduced. The acceptable non-trivial conceptsobtained in this manner are the(∈,∈∨q)-fuzzy subalgebras, and(∈ ^-,∈ ^-∨q^-)-fuzzysubalgebras. Furthermore, their relations and properties are discussed. Second, howto deal with the homomorphic image and inverse image of(s, t-fuzzy subalgebrasare studied, and the relations between a(s, t-fuzzy subalgebra in BCK-algebrasand a(s, t-fuzzy subalgebra in the product algebra of BCK-algebras are given.Finally, by the use of the implicative operators of fuzzy logic, the concepts of R-fuzzy subalgebras and R _λ-fuzzy subalgebras of BCK-algebras are proposed and theirproperties are discussed, some relations among the(s,t-fuzzy subalgebras, R-fuzzysubalgebras and R _λ-fuzzy subalgebras are studied.