Using the belongs to relation (

) and quasi-coincidence with relation (q) between fuzzy points and fuzzy sets, the concept of (

,

)-fuzzy subalgebras where

and

areany two of {

, q,

,

} with

was already introduced, and related properties were investigated (see [3]). In this paper, we give a condition for an (

,

)-fuzzy subalgebra to be an (

,

)-fuzzy subalgebra. We provide characterizations of an (

,

)-fuzzy subalgebra. We show that a proper (

,

)-fuzzy subalgebra

of X with additional conditions can be expressed as the union of two proper non-equivalent (

,

)-fuzzy subalgebras of X. We also prove that if

is a proper (

,

)-fuzzy subalgebra of a CK/BCI-algebra X such that #(

< 0.5}

, then there exist two prope non-equivalent (

,

)-fuzzy subalgebras of X such that

can be expressed as the union of them.