An Overall Framework of Modeling, Clustering, and Evaluation for Trapezoidal Information Granules

In existing granular clustering algorithms, the design of coverage and specificity does not fully capture the inherent structural characteristics of granular data together with the optimization issue, and the current weight setting for the granular data is not sufficient. To address these problems, in this study, the trapezoidal information granule, which is rarely studied before, is concentrated, and we come up with a novel granular clustering algorithm called the weighted possibilistic fuzzy c-means algorithm for trapezoidal granularity (WPFCM-T). First, under the acknowledged principle of justifiable granularity, novel functions of coverage and specificity are designed for trapezoidal information granules, considering the internal characteristics of such granules. The idea of particle swarm optimization (PSO) is exploited to upgrade the established granular data, and then the trapezoidal information granule construction (TIGC) method is proposed to realize granular modeling. Second, an exponential weight is constructed with regard to coverage and specificity, while a novel distance via
$\alpha$
-cuts is given. The possibilistic fuzzy c-means structure is introduced into granular clustering, in which the new weight and distance are integrated, resulting in the proposed WPFCM-T algorithm. Third, the RC is studied to evaluate granular clustering, and hence an overall framework including granular modeling, clustering, and evaluation is constructed. Finally, through experiments completed on artificial datasets, UCI datasets, large datasets, high-dimensional datasets, and noisy datasets, WPFCM-T has superior granular data reconstruction ability by contrast with other granular clustering algorithms, indicating that the granular clustering performance of WPFCM-T is better than the others.