Fuzzy time series approaches are used when observations of time series contain uncertainty. Moreover, these approaches do not require the assumptions needed for traditional time series approaches. Generally, fuzzy time series methods consist of three stages, namely, fuzzification, determination of fuzzy relations, and defuzzification. Artificial intelligence algorithms are frequently used in these stages with genetic algorithms being the most popular of these algorithms owing to their rich operators and good performance. However, the mutation operator of a GA may cause some negative results in the solution set. Thus, we propose a modified genetic algorithm to find optimal interval lengths and control the effects of the mutation operator. The results of applying our new approach to real datasets show superior forecasting performance when compared with those obtained by other techniques.