<p>In the context of hesitant fuzzy sets (HFSs), scholars have proposed multiple definitions for correlation coefficients to capture correlations among fuzzy variables. However, there are still some limitations in the existing correlation coefficients. When HFSs exhibit a perfect linear relationship, meaning that there is a fixed increment, multiplicative relationship, or both corresponding to the membership degrees they contain, most of the existing correlation coefficients return a value of 1. This does not provide sufficient information to describe the scale of correlation between objects, which can be regarded as a disadvantage from the decision-making viewpoint. Furthermore, some correlation coefficients rely exclusively on the average value of hesitant fuzzy elements, leading to considerable information loss. Even within probabilistic hesitant fuzzy environments, the existing correlation coefficients exhibit similar shortcomings. To overcome these limitations, the innovative concept of proximity is introduced to quantify differences between HFSs. Then, we propose modified correlation coefficients for HFSs using the proximity and derive their related properties in depth. Additionally, we extend this theory to probabilistic hesitant fuzzy sets and apply the correlation coefficients in medical diagnosis. Comparative analysis and simulation experiments confirm their effectiveness and applicability.</p>