In the field of information fusion and decision making, integral is very common and important for aggregating a large variety of information. The integral to be used is usually nonlinear due to the nonadditive measure determined by the real world. In this study, we put forward a new nonlinear integral, which is first expressed as an interval, containing the infimum and supremum of the integrand on the nonadditive measure. Furthermore, an attitudinal nonlinear integral is defined by introducing the subjective attitude of the decision maker based on the integral interval obtained. A multi-criteria decision-making (MCDM) method considering the interaction between attribute features is developed based on the proposed attitudinal nonlinear integral and a case study is provided to demonstrate the usefulness of the decision-making method. Inspired by the golden rule representation, we define the generalized golden rule representative value of the interval integral and use it to solve the problem in the case study to illustrate its usefulness.

在信息融合和决策领域，积分是非常普遍的，对于汇总各种信息非常重要。由于现实世界确定了非加性度量，因此要使用的积分通常是非线性的。在这项研究中，我们提出了一个新的非线性积分，该非线性积分首先被表示为一个区间，其中包含非加法测度上被积数的最小和最大。此外，基于所获得的积分区间，通过引入决策者的主观态度来定义态度非线性积分。基于提出的态度非线性积分，提出了一种考虑属性特征之间相互作用的多准则决策方法，并通过案例研究证明了该决策方法的有效性。