## 2 Literature Review
### Nonadditive Measure  
Mathematically, a measure is a function that assigns a number to a subset of a set. This number can be compared with the size, volume, probability, etc. The characteristic of classical measures is additivity. For example, the probability of several mutually exclusive events is the sum of the probability of each event. However, in certain cases, the additive measure does not satisfy this requirement. For example, the work efficiency of two people is not simply the sum of their work efficiency. Similarly, in CBR, interactions may exist between attributes, indicating that attributes are not always independent of each other. Therefore, the combined weight of two interactive attributes is not always the sum of the weights of the two attributes.  
In response to the above violation of additivity, [PERSON] (1954) [31] and [PERSON] (1974) [32] proposed nonadditive measures, namely fuzzy measures, which were, respectively, the Choquet and [PERSON] integrals. These two nonadditive measures have a wide range of applications, particularly in MCDM situations [33]. The MCDM with fuzzy measures can not only fully consider the relative weight of the decision criteria, but also flexibly describe the interaction between criteria [34]. However, with an increase in parameters, the complexity of the nonadditive measure increases exponentially, which is one of the defects of the fuzzy measure. For example, when the cardinality of set \(X\) is \(n\), the values of \(n\) parameters must be determined for additive measures; for a nonadditive measure, we must compute the values of all subsets of \(X\) with \(2^{n}\) parameters. To address the complexity of the model, many other nonadditive measures have been proposed, such as \(\lambda\)-addition fuzzy measures [35], in which only \(n-1\) parameters are required. However, \(\lambda\)-addition fuzzy measures also have some disadvantages. For nonadditive measures, there are three types of interactions: independent, redundant, and complementary. In the \(\lambda\)-addition fuzzy measure model, only one interaction exists [36].  
[PERSON] (1997) [37] proposed an additive discrete fuzzy measure of order \(k\). The definition of the \(k\)-order additive measure is based on the pseudo-Boolean function [38], which is an approximate representation of the \(k\)-order nonadditive measure. In addition, the Mobius transformation is used to describe \(k\)-order additive measures [39]. The \(k\)-order additive measures can not only deal with the complexity of nonadditive measures, but also represent three different types of interactions using Shapley indices as the development of the Shapley value [40]. Many scholars have improved and developed \(k\)-order additive measures and applied them in various fields. For example, [PERSON] et al. (2022) developed a \(k\)-order additive measure for a nondiscrete case [41]. The 2-order additive measure can solve the contradiction between complexity and precision in a wide range of applications [42]. [PERSON] et al. (2021) proposed a 2-order additive fuzzy measure based on intuitionistic fuzzy sets to quantitatively evaluate the interactions between attributes [43]. [PERSON] et al. (2016) proposed a simulation credibility group evaluation method using 2-order additive fuzzy measure to train a traction-drive simulation system [44]. The 2-order additive measure is only concerned with the importance of each attribute and the interaction between two attributes, which is a perfect compromise between the performance and computational complexity of the nonadditive measure, and has been widely used in MADM methods [45].