In this article we have studied on lacunary I-convergent sequences of fuzzy real numbers. We verify and establish some algebraic properties such as linearity, symmetric, convergence free etc. and also established some other results.

For any lacunary sequence θ = (kr), the aim of the present work is to introduce strong θ-statistical limit and strong θ-statistical cluster points of sequences on probabilistic normed spaces (briefly PN-spaces). Some relations among the sets of ordinary limit points, strong θ-statistical limit and strong θ-statistical cluster points of sequences on PN-spaces are obtained.