Matrix representations and interdependency on L-fuzzy covering-based approximation operators

In this paper, we study the matrix representations and interdependency of three pairs of L-fuzzy covering-based approximation operators. Matrices play an important role in machine learning and data mining, such as the Laplacian matrix of a graph in clustering analysis and matrix linear transformation in feature selection based on principle component analysis. Therefore, the matrix representations of the three pairs of L-fuzzy covering-based approximation operators are important problems which should be solved. Moreover, we give some necessary and sufficient conditions under which two L-fuzzy coverings to generate the same L-fuzzy covering-based approximation operators.