The paper develops an important method related to using algebraic inequalities for uncertainty and risk reduction and enhancing systems performance. The method consists of creating relevant meaning for the variables and different parts of the inequalities and linking them with real physical systems or processes. The paper shows that inequalities based on multivariable sub-additive functions can be interpreted meaningfully and the generated new knowledge used for optimising systems and processes in diverse areas of science and technology. In this respect, an interpretation of the Bergström inequality, which is based on a sub-additive function, has been used to increase the accumulated strain energy in components loaded in tension and bending. The paper also presents an interpretation of the Chebyshev’s sum inequality that can be used to avoid the risk of overestimation of returns from investments and an interpretation of a new algebraic inequality that can be used to construct the most reliable series-parallel system. The meaningful interpretation of other algebraic inequalities yielded a highly counter-intuitive result related to assigning devices of different types to missions composed of identical tasks. In the case where the probabilities of a successful accomplishment of a task, characterising the devices, are unknown, the best strategy for a successful accomplishment of the mission consists of selecting randomly an arrangement including devices of the same type. This strategy is always correct, irrespective of existing uknown interdependencies among the probabilities of successful accomplishment of the tasks characterising the devices.

本文开发了一种与使用代数不等式来降低不确定性和风险以及提高系统性能相关的重要方法。该方法包括为变量和不等式的不同部分创建相关含义，并将它们与真实的物理系统或过程联系起来。该论文表明，可以对基于多变量次可加函数的不等式进行有意义的解释，并且生成的新知识可用于优化不同科学和技术领域的系统和流程。在这方面，基于次可加函数的 Bergström 不等式的解释已被用于增加承受拉伸和弯曲载荷的组件中的累积应变能。本文还介绍了可用于避免高估投资回报风险的切比雪夫总和不等式的解释，以及可用于构建最可靠的串并联系统的新代数不等式的解释。对其他代数不等式的有意义的解释产生了与将不同类型的设备分配给由相同任务组成的任务相关的高度反直觉的结果。在成功完成任务的概率（表征设备）未知的情况下，成功完成任务的最佳策略包括随机选择包括相同类型设备的布置。这个策略永远是正确的，