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Uniqueness and Pareto-optimality of cross-efficiency scores are two main issues in the cross-efficiency evaluation. We address the Pareto-optimality issue in the cross-efficiency evaluation by presenting a natural notion of Pareto-optimality in the cross-efficiency evaluation, which is based on a new self-prioritizing principle and aligned with the concept of dominance. We then propose a multi-objective model whose Pareto-optimal solutions generate all the Pareto-optimal cross-efficiency score sets that fulfill the self-prioritizing principle. It is shown that there is a Pareto-optimal solution to the proposed multi-objective programming model which assigns a common set of weights to all decision-making units. We then propose a linear model to obtain such an optimal solution using the weighted sum technique, thereby we can determine an optimal weights profile to generate a set of Pareto-optimal cross-efficiency scores by solving only one linear model. We also demonstrate the possibility of better, compared to other cross-efficiency evaluation methods, resource allocation for RD project selection.