Using the \emph{belongs to} relation ($\in$) and
\emph{quasi-coincidence with} relation (q) 
between fuzzy points and fuzzy sets, the concept of
$(\alpha, \beta)$-fuzzy ideals where $\alpha, \, \beta$ 
are any two of
$\{\in, {\rm q}, \in \!\vee \, {\rm q}, \in \!\wedge \, {\rm q}\}$ 
with $\alpha \ne \, \in \!\wedge \, {\rm q}$ 
is introduced, and related properties are discussed. 
Relations between 
$(\in\! \vee \, {\rm q}, \in\! \vee \, {\rm q})$-fuzzy ideals and 
$(\in, \in\! \vee \, {\rm q})$-fuzzyideals 
are investigated, 
and conditions for an $(\in, \in\! \vee \,   {\rm q})$-fuzzy ideal 
to be an $(\in, \in)$-fuzzy ideal are provided. 
Characterizations of $(\in, \in\! \vee \, {\rm q})$-fuzzy ideals 
are given, and conditions for a fuzzy set 
to be a $({\rm q}, \in\! \vee \, {\rm q})$-fuzzy ideal are provided.