A novel clustering approach based on grey possibility functions for multidimensional systems

Abstract

In order to determine all the required algebraic relationships among the parameters of the grey possibility functions with the given final clustering results, a matrix-based approach for the bidirectional perspective of the grey clustering model based on the grey possibility functions is developed in this work. The definition of the bidirectional problem in a grey clustering model is defined. The matrix representations for the symmetric and asymmetric grey possibility functions and grey clustering coefficients are derived. Two key theorems, one corollary, and two matrix relations are put forward for calculating the parameters in the novel model. Four matrix-based inequalities are proposed to obtain all the available grey possibility functions under the four different situations. The more general grey clustering model with asymmetric grey possibility functions is derived. To explain how it can be utilized in practice, this novel approach is applied to determine the group of the Pacific Rim countries with the partial known results in the Fukushima nuclear wastewater discharge.