Attribute reduction in inconsistent grey decision systems based on variable precision grey multigranulation rough set model

This paper mainly deals with attribute reduction of inconsistent grey decision systems (IGDSs) based on the variable precision grey multigranulation rough set (VP-GMGRS). Firstly, we present two transformation models to transform IGDS into consistent decision confidence system. One is the consistent decision system transformation model, based on which, an IGDS can be transformed into a VP-GMGRS approximate distribution consistent decision system. The other is the decision confidence system transformation model, which can be degenerated to a classical group decision system. Meanwhile, we educe related judgement theorems of approximation distribution consistent set in IGDS. Following that, a theoretical attribute reduction approach is presented by employing discernibility attribute sets and function based on VP-GMGRS approximate distributions. In addition, algorithms and illustrative examples with IGDS are employed and assisted to understand and explain the mechanism of attribute reduction theoretical approaches. Finally, comparison experiments are organized to verify the validity and feasibility of the proposed reduction method.