A dynamic framework for updating neighborhood multigranulation approximations with the variation of objects

Accelerating Update of Variable Precision Multigranulation Approximations While Adding Granular Structures

In multigranulation environments, variable precision multigranulation rough set (VPMGRS) is a useful framework that has a tolerance for errors. Approximations are basic concepts for knowledge acquisition and attribute reductions. Accelerating update of approximations can enhance the efficiency of acquiring decision rules by utilizing previously saved information. In this study, we focus on exploiting update mechanisms of approximations in VPMGRS with the addition of granular structures. By analyzing the basic changing trends of approximations in VPMGRS, we develop accelerating update mechanisms for acquiring approximations. In addition, an incremental algorithm to update variable precision multigranulation approximations is proposed when adding multiple granular structures. Finally, extensive comparisons elaborate the efficiency of the incremental algorithm.

Compromised multi-granulation rough sets based on an attribute-extension chain

The multi-granulation rough sets serve as important hierarchical models for intelligent systems. However, their mainstream optimistic and pessimistic models are respectively too loose and strict, and this defect becomes especially serious in hierarchical processing on an attribute-expansion sequence. Aiming at the attribute-addition chain, compromised multi-granulation rough set models are proposed to systematically complement and balance the optimistic and pessimistic models. According to the knowledge refinement and measure order induced by the attribute-enlargement sequence, the basic measurement positioning and corresponding pointer labeling based on equilibrium statistics are used, and thus we construct four types of compromised models at three levels of knowledge, approximation, and accuracy. At the knowledge level, the median positioning of ordered granulations derives Compromised-Model 1; at the approximation level, the average positioning of approximation cardinalities is performed, and thus the separation and integration of dual approximations respectively generate Compromised-Models 2 and 3; at the accuracy level, the average positioning of applied accuracies yields Compromised-Model 4. Compromised-Models 1–4 adopt distinctive cognitive levels and statistical perspectives to improve and perfect the multi-granulation rough sets, and their properties and effectiveness are finally verified by information systems and data experiments.