Asymptotically lacunary statistical equivalence set sequences of order $(\alpha,\beta)$}

In this paper we define asymptotically lacunary statistical equivalence set sequences of order $(\alpha,\beta)$ and studied some properties of this concept. We also make an effort to define strongly asymptotically lacunary $p$-equivalence and strongly Cesaro asymptotically $p$-equivalence of order $(\alpha,\beta)$ and examine some topological properties.