To deal with multicriteria decision making (MCDM) problems with interaction criteria, the Choquet integral (CI) is one of effective tools. This paper first proposes the reverse Choquet integral (RCI), which defines the importance of the ordered elements in an opposite principle to the CI. To show the principle of the RCI, we offer its concrete expression in view of the Möbius representation by which one can clearly see the difference and the relationship between the CI and the RCI. Then, we propose the “bi-direction Choquet integral” (BDCI), which is a convex combination of the CI and the RCI. To get the interactions of ordered coalitions comprehensively, this paper further proposes the generalized Shapley bi-direction Choquet integral (GSBDCI). Furthermore, the hybrid generalized Shapley bi-direction Choquet integral (HGSBDCI) is proposed, which defines the importance of ordered positions and the criteria with interactions simultaneously. With respect to these types of CIs, their exponent forms are also discussed. Finally, we use an application case to show the utilization of the proposed new CIs for MCDM. The proposed new Choquet integrals provide us a very useful way to deal with MCDM problems.

为了处理具有交互标准的多标准决策（MCDM）问题，Choquet积分（CI）是有效的工具之一。本文首先提出了反向Choquet积分（RCI），它以与CI相反的原理定义了有序元素的重要性。为了展示RCI的原理，我们鉴于Möbius表示法提供了具体的表达方式，使人们可以清楚地看到CI和RCI之间的区别和关系。然后，我们提出了“双向Choquet积分”（BDCI），它是CI和RCI的凸组合。为了全面了解有序联盟的相互作用，本文进一步提出了广义的Shapley双向Choquet积分（GSBDCI）。此外，提出了混合广义Shapley双向Choquet积分（HGSBDCI），它定义了有序职位的重要性以及同时进行互动的条件。关于这些类型的配置项，还讨论了它们的指数形式。最后，我们使用一个应用案例来说明为MCDM使用建议的新CI的情况。提出的新Choquet积分为我们提供了一种非常有用的方法来处理MCDM问题。