Correlation measurement plays a key role in quantitative finance. Although numerous studies were established to design correlation measures, few were aware of the complexity of mixed market conditions. Mixed market conditions refer to situations where markets exhibit characteristics between fully stable and highly volatile conditions. Additionally, previous works fall short of processing big data and neglect the inherent uncertainty and flexibility of financial data. To address these challenges, a fuzzy correlation measurement framework for mixed market conditions is proposed. In this framework, the VIX is utilized to identify market conditions. A threshold-based approach classifies and quantifies markets into high- and low-volatility periods based on VIX. Besides, to process big data, the fuzzy theory is introduced and the \(\alpha\) -cut method is employed to incorporate investors’ optimism about the market and their risk preferences. By applying this framework, the weights of the correlation coefficients are adjusted flexibly and therefore, the correlations between financial variables are captured effectively. To validate the framework, an experiment is designed to analyze the correlation between the Shanghai Stock Price Index (SSI) and USD/CNY exchange rates using 2009-2010 and 2021 data, comparing its performance under high- and low-volatility market conditions. It is demonstrated that in high-volatility markets, the Root Mean Square Error (RMSE), representing the difference between predicted values and actual values, is reduced by 15%, and \(R^2\) , representing the fitness of the model (LightGBM) is improved by 12%. The result provides compelling evidence that the framework enhances the accuracy of correlation measurement in high-volatility markets. In low-volatility markets, the RMSE and \(R^2\) remain approximately similar to the methods that do not consider tail correlations, indicating that the framework maintains its robustness and stability.
