Soft rough fuzzy sets ( $\mathcal{S}RFSs$) represent a powerful paradigm that integrates soft computing, rough set theory, and fuzzy logic. This research aimed to comprehensively investigate the various dimensions of $\mathcal{S}RFSs$ within the domain of approximation structures. The study encompassed a wide spectrum of concepts, ranging from covering approximation structures and soft rough coverings to soft neighborhoods, fuzzy covering approximation operators, and soft fuzzy covering approximation operators. We introduced three models of $\mathcal{S}RFSs$ based on covering via the core of soft neighborhood. We discussed and analyzed our models' characteristics and properties. The relations between our models for soft fuzzy covering sets and Zhan's model for soft rough fuzzy covering were presented.