Accurate prediction of stock price movements has become an essential tool for investors, given the inherent chaos and uncertainty in the stock market. Traditional forecasting models often fall short in capturing the complex patterns hidden within stock data due to the market's unpredictable nature. To overcome these limitations, researchers have explored fuzzy sets, which involve representing observations as fuzzy sets or fuzzy numbers within a time series framework, referred to as fuzzy time series (FTS). This approach offers a promising direction for improving stock price forecasting techniques. This article introduces an innovative forecasting model called the Intuitionistic Fuzzy Time Series (IFTS) model, built on the principles of Intuitionistic Fuzzy Sets (IFS). The proposed model combines IFS with an adaptive hybrid genetic algorithm (HGA), resulting in a novel HGA-IFS forecasting method. In this approach, the HGA determines the optimal length, while the IFS component addresses indeterminacy in the fuzzy time series data (TSD). To demonstrate the effectiveness and practical value of the proposed forecasting method, it is applied to datasets containing the share prices of real data. The significant reduction in Mean Squared Error (MSE) and Average Forecasting Error (AFE) highlights the better performance of the HGA-IFS method over various existing methods.