Let $K$ be a field and $R=K[x_1,\ldots, x_n]$ be the polynomial ring in $n$ variables over a field $K$. Let $Δ$ be a simplicial complex on $n$ vertices and $I=I_Δ$ be its Stanley-Reisner ideal. In this paper, we show that if $I$ is a matroidal ideal then the following conditions are equivalent: $(i)$ $Δ$ is sequentially Cohen-Macaulay; $(ii)$ $Δ$ is shellable; $(iii)$ $Δ$ is vertex decomposable. Also, if $I$ is a minimally generated by $u_1,\ldots,u_s$ such that $s\leq 3$ or ${\rm supp}(u_i)\cup {\rm supp}(u_j)=\{x_1,\ldots,x_n\}$ for all $i\neq j$, then $Δ$ is vertex decomposable. Furthermore, we prove that if $I$ is a monomial ideal of degree $2$ then $I$ is weakly polymatroidal if and only if $I$ has linear quotients if and only if $I$ is vertex splittable.