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Many applications deal with unconditional variance of the time series. Fuzzy time series allow an inexpensive computation to forecasting dynamic processes and uncertainties. In this paper we have extended the concept of nonstationary fuzzy sets to Fuzzy Time Series, termed Nonstationary Fuzzy Time Series (NSFTS). While some models require new data before adapting, the NSFTS is capable of adapting to heteroskedastic time series. In the experiments, NSFTS outperformed other known FTS methods with box-cox transformations available. Statistical tests in three different datasets indicate that the results achieved by the proposed model are either superior or non-inferior to other FTS models.