Using the belongs to relation (${in}$) and quasi-coincidence with relation (q) between fuzzy points and fuzzy sets, the concept of (${alpha}$, ${eta}$)-fuzzy subalgebras where ${alpha}$ and ${eta}$ areany two of {${in}$, q, ${in}{vee}q$, ${in}{wedge}q$} with ${alpha}{ eq}{in}{wedge}q$ was already introduced, and related properties were investigated (see [3]). In this paper, we give a condition for an (${in}$, ${in}{vee}q$)-fuzzy subalgebra to be an (${in}$, ${in}$)-fuzzy subalgebra. We provide characterizations of an (${in}$, ${in}{vee}q$)-fuzzy subalgebra. We show that a proper (${in}$, ${in}$)-fuzzy subalgebra $mathfrak{A}$ of X with additional conditions can be expressed as the union of two proper non-equivalent (${in}$, ${in}$)-fuzzy subalgebras of X. We also prove that if $mathfrak{A}$ is a proper (${in}$, ${in}{vee}q$)-fuzzy subalgebra of a CK/BCI-algebra X such that #($mathfrak{A}(x){mid}mathfrak{A}(x)$ < 0.5} ${geq}2$, then there exist two prope non-equivalent (${in}$, ${in}{vee}q$)-fuzzy subalgebras of X such that $mathfrak{A}$ can be expressed as the union of them.