In decision-making systems, how to address uncertainty plays an important role for the improvement of system performance in uncertainty reasoning. Dempster-Shafer evidence (DSE) theory is an effective method to address uncertainty in decision-making problems by means of basic belief assignments (BBAs) and Dempster's combination rule. In the DSE theory, divergence measure between BBAs, which is beneficial for conflict information management in decision making, remains an open issue. In this paper, several generalized evidential divergences (EDs) are proposed and studied to measure the difference and discrepancy between BBAs in DSE theory, which have more universal applicability in decision theory. On this basis, a uniform <inline-formula><tex-math notation="LaTeX">\mathcal {BJS}</tex-math> <mml:math><mml:mi mathvariant="script">BJS</mml:mi></mml:math><inline-graphic xlink:href="xiao-ieq1-3177896.gif"/> </inline-formula> divergence-based decision-making algorithm is devised to improve the decision level. Furthermore, the extensions of weighted <inline-formula><tex-math notation="LaTeX">\mathcal {BJS}</tex-math> <mml:math><mml:mi mathvariant="script">BJS</mml:mi></mml:math><inline-graphic xlink:href="xiao-ieq2-3177896.gif"/> </inline-formula> to decision-making algorithms are discussed by considering not only subjective weights but also objective weights. Notably, this is the first work to propose the weighted <inline-formula><tex-math notation="LaTeX">\mathcal {BJS}</tex-math> <mml:math><mml:mi mathvariant="script">BJS</mml:mi></mml:math><inline-graphic xlink:href="xiao-ieq3-3177896.gif"/> </inline-formula> divergence in DSE theory providing a promising way to analyze decision-making problems from different perspectives. Besides, experiments demonstrate the effectiveness and superiority of the proposed methods. Finally, the proposed <inline-formula><tex-math notation="LaTeX">\mathcal {BJS}</tex-math> <mml:math><mml:mi mathvariant="script">BJS</mml:mi></mml:math><inline-graphic xlink:href="xiao-ieq4-3177896.gif"/> </inline-formula>-based decision-making algorithm is applied to pattern classification. The results validate that the proposed decision-making algorithm is beneficial for diverse real-world datasets and outperforms several well-known related works and demonstrates higher classification accuracy as well as robustness.