In this article, we propose a novel center-based clustering algorithm based on bidirectional conical information granularity. The main purpose is to fully absorb the semantic information of the ordinal relationship between objects to improve the performance of central clustering in identifying interleaved and imbalanced data. The proposed algorithm includes two main stages: first, the stage of determining the cluster center and second, the division stage. In the stage of determining the cluster center, the first cluster center is determined by using the number of conical information granularity in the data, and the remaining cluster centers are determined by defining the statistical measure of 'fuzzy importance degree.' In the division stage, we divide the points to be clustered into stable and active areas. The former quickly and accurately identifies and assigns the objects belonging to a cluster by measuring the fuzzy similarity between the objects to be clustered and the cluster center, and the latter assigns the objects in the active area by using the information of the points already assigned. This method describes the position and sorting relationship of objects that are granulated through ordinal relationships more accurately in the global environment, thereby gaining a more comprehensive understanding of the structural characteristics of the data. This helps to improve the accuracy and stability of clustering algorithms in handling interleaved and imbalanced data. This article uses three clustering validity indicators to test the performance of our algorithm. We compare the results with those of six different types of popular clustering algorithms and new algorithms proposed in recent years. The experimental results show that the algorithm proposed in this article can identify clusters more accurately on the datasets with a complex and staggered distribution. It is significantly better than the clustering algorithm participating in the comparison and has good robustness on datasets with added noise. © 1993-2012 IEEE.