Because Deng’s grey relational degree is inconspicuous, Deng’s relational degree with an exponential function is first presented. Then, we demonstrate that improved Deng’s relational degree is more conspicuous than the original model. Then, we construct a multiple-attribute decision-making model, based on improved Deng’s relational degree with multiple stages, and a method for determining the weight of the index is also developed. Finally, the core competence of private enterprises in Henan province is analyzed, illustrating the validity and feasibility of the improved model.
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