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.
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