In the era of Big Data, it is almost impossible to completely restrict access to primary non-aggregated statistical data. However, risk of violating privacy of individual respondents and groups of respondents by analyzing primary data has not been reduced. There is a need in developing subtler methods of data protection to come to grips with these challenges. In some cases, individual and group privacy can be easily violated, because the primary data contain attributes that uniquely identify individuals and groups thereof. Removing such attributes from the dataset is a crude solution and does not guarantee complete privacy. In the field of providing individual data anonymity, this problem has been widely recognized, and various methods have been proposed to solve it. In the current work, we demonstrate that it is possible to violate group anonymity as well, even if those attributes that uniquely identify the group are removed. As it turns out, it is possible to use third-party data to build a fuzzy model of a group. Typically, such a model comes in a form of a set of fuzzy rules, which can be used to determine membership grades of respondents in the group with a level of certainty sufficient to violate group anonymity. In the work, we introduce an evolutionary computing based method to build such a model. We also discuss a memetic approach to protecting the data from group anonymity violation in this case.