The most relevant property that a quality indicator (QI) is expected to have is Pareto compliance, which means that every time an approximation set strictly dominates another in a Pareto sense, the indicator must reflect this. The hypervolume indicator and its variants are the only unary QIs known to be Pareto-compliant but there are many commonly used weakly Pareto-compliant indicators such as R2, IGD++$+$⁠, and ε+ε+$ε+$⁠. Currently, an open research area is related to finding new Pareto-compliant indicators whose preferences are different from those of the hypervolume indicator. In this article, we propose a theoretical basis to combine existing weakly Pareto-compliant indicators with at least one being Pareto-compliant, such that the resulting combined indicator is Pareto-compliant as well. Most importantly, we show that the combination of Pareto-compliant QIs with weakly Pareto-compliant indicators leads to indicators that inherit properties of the weakly compliant indicators in terms of optimal point distributions. The consequences of these new combined indicators are threefold: (1) to increase the variety of available Pareto-compliant QIs by correcting weakly Pareto-compliant indicators, (2) to introduce a general framework for the combination of QIs, and (3) to generate new selection mechanisms for multiobjective evolutionary algorithms where it is possible to achieve/adjust desired distributions on the Pareto front.

质量指标 (QI) 最相关的属性是帕累托顺应性，这意味着每当一个近似集在帕累托意义上严格支配另一个时，指标必须反映这一点。超容量指标及其变体是唯一已知符合帕累托的一元 QI，但有许多常用的弱帕累托指标，例如 R2、IGD++$+$⁠ , 和ε +ε+$ε+$⁠. 目前，一个开放的研究领域与寻找新的帕累托兼容指标有关，这些指标的偏好与超容量指标的偏好不同。在本文中，我们提出了一个理论基础，将现有的弱 Pareto 兼容指标与至少一个 Pareto 兼容指标结合起来，从而得到的组合指标也符合 Pareto。最重要的是，我们表明，帕累托兼容 QI 与弱帕累托兼容指标的组合导致指标在最佳点分布方面继承了弱兼容指标的属性。这些新的组合指标的后果是三重的：（1）通过纠正弱帕累托兼容指标来增加可用的帕累托兼容 QIs 的种类，（2）引入 QIs 组合的一般框架，