A novel grey possibility clustering method based on inverse perspective and its applications

The center-point mixed possibility functions (CMPFs), which are determined by the decision makers qualitatively, are the most important element to obtain the effective clustering results in a grey clustering model. However, different decision makers provide different CMPFs which may lead to inconsistent or contradictory clustering results. In response to this problem, this article proposes an inverse grey possibility clustering model which can determine the CMPFs based on the part of the given final results. This novel matrix-based method can derive all of the required CMPFs which satisfy the partially known clustering results. More specifically, four theorems are put forward to analyze the four different cases, which are single index single object (SISO), single index multiple objects (SIMO), multiple indices single object (MISO) and multiple indices multiple objects (MIMO), respectively, to derive the required CMPFs of a given clustering result using algebraic expressions. For the purpose of developing the matrix representations for the MISO and MIMO situations, a new unified expression of the CMPFs to replace their existing segmented function expression is proposed. Finally, in order to demonstrate how it can be used in practice, the proposed method is applied for evaluating the effects of the reduction of pollution and carbon emissions and determining aerospace equipment component suppliers with different types of data. Compared to the forward GPC models, the proposed IGPC model has higher accuracy.