In this paper, we have characterized big data fuzzy sets and shown that topological data points form singleton fuzzy sets which are closed. Besides, fuzzy sets of topological data points are compact and have at least one closed point. We have also shown that the fuzzy set of all condensation points of a fuzzy Hausdorff space is infinite and the cardinality of a topological data fuzzy set is also infinite and arbitrarily distributed in fuzzy Hausdorff spaces.