Numerous studies have focused on preserving privacy when publishing data. Differential Privacy is a cutting-edge method for safeguarding privacy in a database. However, applying Differential Privacy to high-dimensional (HD) data presents challenges regarding the computational cost. A reasonable solution involves dimension reduction of the given database while maintaining the correlations. Our paper introduces Priv-Fuzzy, a straightforward and adaptable differentially private method that can publish private data by reducing their original dimension using Fuzzy logic. Using Fuzzy mapping, Priv-Fuzzy can: 1) reduce dimensions and create a new low-dimensional (LD) correlated database, 2) inject noise to each attribute to ensure differential privacy, and 3) subsequently publish a synthesized database. Priv-Fuzzy converts an HD dataset into an equivalent correlated LD, through fuzzy mapping. Experimenting with real-world data and comparing with PrivBayes and PrivGene, demonstrate that Priv-Fuzzy surpasses them regarding privacy preservation strength, simplicity, and utility improvement.