Abstract
In the present paper, we introduce the concept of
$\Delta^{f}-$lacunary statistical boundedness of order $\beta$\ with respect
to a modulus function $f$ for sequences of fuzzy numbers and give some
relations between $\Delta^{f}-$lacunary statistical boundedness of order
$\beta$\ and $\Delta^{f}-$statistical boundedness with respect to a modulus
function $f$ with the help of many examples and figures. Furthermore, we study
some properties like solidity, symmetricity, etc.