Granular structure evaluation and selection based on justifiable granularity principle

Abstract

Granular structures are fundamental components of human granulation intelligence and different views or scales of granulation result in different granular structures. Therefore, the evaluation and selection of optimal granular structures can lay the foundation for problem-solving. Information granules are basic components of granular structures. The principle of justifiable granularity presents a coherent method for designing information granules. Therefore, this study performs granular structure evaluation and selection based on the justifiable granularity principle. First, it proposes a new evaluation criterion for granular structures that considers the coverage and specificity of all information granules in a granular structure. Thereafter, coverage and specificity are evaluated based on a core sample of the information granule. Subsequently, a detailed formulation is provided to compute the significance of the granular structure according to the proposed evaluation criterion. Finally, a general framework for granular structure selection is presented, and a detailed algorithm for selecting the optimal granular structure with the aid of the justifiable granularity principle is provided. The proposed method is employed to determine the optimal attribute and select the optimal neighborhood size for neighborhood classifiers. Experiments and analyses have demonstrated the necessity, reasonableness, and effectiveness of the proposed method.