Considering the high volume, wide variety, and rapid speed of data generation, investigating feature selection methods for big data presents various applications and advantages. By removing irrelevant and redundant features, feature selection reduces data dimensions, thereby facilitating optimal decision-making within decision systems. One of the key tools for feature selection in hybrid information systems is fuzzy rough set theory. However, this theory faces two significant challenges: First, obtaining fuzzy equivalence relations through intersection operations in high-dimensional spaces can be both time-consuming and memory-intensive. Additionally, this method may produce noisy data, complicating the feature selection process. The purpose and innovation of this paper are to address these issues. We proposed a new feature selection model that calculates the combined distance between objects and subsequently used this information to derive the fuzzy equivalence relation. Rather than directly solving the feature selection problem, this approach reformulates it into an optimization problem that can be tackled using appropriate meta-heuristic algorithms. We have named this new approach FSbuHD. The FSbuHD model operates in two modes - normal and optimistic - based on the selection of one of the two introduced fuzzy equivalence relations. The model is then tested on standard datasets from the UCI repository and compared with other algorithms. The results of this research demonstrate that FSbuHD is one of the most efficient and effective methods for feature selection when compared to previous methods and algorithms.