  In this paper, the origin of the generalized uncertainty principle (GUP) in
an $M$-dimensional theory with Lie-$N$-algebra is considered. This theory which
we name GLNA(Generalized Lie-$N$-Algebra)-theory can be reduced to $M$-theory
with $M=11$ and $N=3$. In this theory, at the beginning, two energies with
positive and negative signs are created from nothing and produce two types of
branes with opposite quantum numbers and different numbers of timing
dimensions. Coincidence with the birth of these branes, various derivatives of
bosonic fields emerge in the action of the system which produce the $r$ GUP for
bosons. These branes interact with each other, compact and various derivatives
of spinor fields appear in the action of the system which leads to the creation
of the GUP for fermions. The previous predicted entropy of branes in the GUP is
corrected as due to the emergence of higher orders of derivatives and different
number of timing dimensions.
