k-Medoids Clustering algorithm is one of the most commonly used clustering methods. However, it does not consider the weight of each feature, and the selection of center points is random, which may affect the clustering results. Granularity computing analyzes knowledge from various perspectives, considering the level of detail and completeness of that knowledge. This approach helps identify which features have the most significant impact on clustering outcomes, allowing for a focus on key features and the selection of more effective initial clustering centers. Based on this, we propose an Effective Intelligent k-Medoids Clustering Scheme Based on Granularity Rough Entropy (IKCS). Specifically, the granularity roughness entropy is first defined based on indistinguishable relationships and roughness, and feature weights are determined based on the roughness entropy. In addition, feature weight coefficients are introduced to explain the similarity function between samples, and they are integrated into k-Medoids. In the similarity calculation of clustering algorithms, the samples are subjected to coarse-grained clustering based on the above similarity function to obtain a set of coarse clusters. Subsequently, the algorithm uses the maximum minimum distance method to select initial cluster centers from the coarse clustering set. Experimental results on both artificial and well-known UCI datasets effectively demonstrate the superiority of the proposed IKCS. On artificial datasets with complex cluster distributions, IKCS achieves an Adjusted Rand Index (ARI) of 0.7582, outperforming the second-best algorithm (fast k-Medoids) by 8.1%. Meanwhile, running on 12 UCI datasets with high dimensionality, IKCS achieves an average accuracy that is 13.89% higher than the PAM algorithm and 7.19% higher than the FKM (fast k-Medoids) algorithm. Moreover, it shows strong performance in other key metrics, consistently achieving a lower clustering Sum of Squared Errors (SSE) and a higher average ARI compared to the baseline methods.