The conventional K‐Means clustering algorithm is widely used for grouping similar data points by initially selecting random centroids. However, the accuracy of clustering results is significantly influenced by the initial centroid selection. Despite different approaches, including various K‐Means versions, suboptimal outcomes persist due to inadequate initial centroid choices and reliance on common normalization techniques like min‐max normalization. In this study, we propose an improved algorithm that selects initial centroids more effectively by utilizing a novel formula to differentiate between instance attributes, creating a single weight for differentiation. We introduce a preprocessing phase for dataset normalization without forcing values into a specific range, yielding significantly improved results compared to unnormalized datasets and those normalized using min‐max techniques. For our experiments, we used five real datasets and five simulated datasets. The proposed algorithm is evaluated using various metrics and an external benchmark measure, such as the Adjusted Rand Index (ARI), and compared with the traditional K‐Means algorithm and 11 other modified K‐Means algorithms. Experimental evaluations on these datasets demonstrate the superiority of our proposed methodologies, achieving an impressive average accuracy rate of up to 95.47% and an average ARI score of 0.95. Additionally, the number of iterations required is reduced compared to the conventional K‐Means algorithm. By introducing innovative techniques, this research provides significant contributions to the field of data clustering, particularly in addressing modern data‐driven clustering challenges.

The problem of ordered clustering in the context of decision‐making with multiple criteria has garnered significant interest from researchers in the field of management science and operational research. In real‐world scenarios, the datasets often exhibit imprecision or uncertainty, which can lead to suboptimal ordered‐clustering outcomes. However, the intuitionistic fuzzy c‐means (IFCM) clustering algorithm enhances the accuracy and effectiveness of decision‐making processes by effectively handling uncertain dataset information for clustering. Therefore, we propose a new clustering algorithm, called the generalized ordered intuitionistic fuzzy c‐means (G‐OIFCM), based on PROMETHEE and the IFCM clustering algorithm. Different from the classical IFCM clustering algorithm, we use positive flow (φ+(si) ∈ [0, 1]) and negative flow (φ−(si) ∈ [0, 1]) of PROMETHEE to generate ordered clusters within the intuitionistic environment. We define a new objective function based on the positive and negative flow of the PROMETHEE and IFCM clustering algorithm, whose properties are mathematically justified in terms of convergence and optimization. The performance of the proposed algorithm is evaluated using two different real‐world datasets to assess both the ordered clustering and the quality of partitioning. To demonstrate the effectiveness of G‐OIFCM, a comparison is conducted with three other algorithms: fuzzy c‐means (FCM), ordered fuzzy c‐means (OFCM), and an adaptive generalized intuitionistic fuzzy c‐means (G‐IFCM). The results demonstrate the effectiveness of G‐OIFCM in enhancing optimal ordered clustering and utility when dealing with uncertainty in datasets.