## 2 Background and Related Work
### Example of Proposed Approach in CNICS Problem  
Herein, we introduce the procedure of the proposed approach in Algorithm 1. Furthermore, we present an example to describe our proposed approach more clearly. Table 2 shows a user-item rating information table about rating scores obtained from four users and seven items; \(i_{it1}\) and \(i_{it2}\) denote the target items and have no ratings from users. The rating value is from 1 to 5, and a higher value indicates that the user likes the given item more. Table 3 shows the item attribute information table about seven items, and three attributes \(at_{1},\ at_{2}\), and \(at_{3}\) are considered, where a value of 1 indicates that the item has that attribute and a value of 0 means it does not have that attribute. Note that items can be in several attributes simultaneously. Herein, we suppose user \(u_{4}\) is the target user, therefore, we need to predict rating scores of \(i_{it1}\) and \(i_{it2}\) for user \(u_{4}\). **Step 1:** Construct interrelated attributes. Based on three item attributes \(\{at_{1},\ at_{2},\ at_{3}\}\) shown in Table 3, we extract the relation between each pair of attributes using Equations (8)-(10). Table 4 is the interrelated attribute information table. **Step 2:** Similarity computation. Based on the information of new interrelated attributes, we employ Equation (14) to compute similarity between each pair of items. Herein, we use the similarity computation of \(i_{1}\) and \(i_{3}\) as an example. From Table 3, according to discussions in Section 3.4, we obtain that the following. * Both \(i_{1}\) and \(i_{3}\) have \(n_{1}=1\) attribute \(at_{1}\). * There is no attribute that \(i_{1}\) has but \(i_{3}\) does not have, so \(n_{2}=0\). * \(i_{3}\) has \(n_{3}=1\) attribute \(at_{3}\) but \(i_{1}\) does not have that. * Both \(i_{1}\) and \(i_{3}\) do not have \(n_{4}=1\) attribute \(at_{2}\). ```
0: User-item matrix \(RM\), item-attribute matrix \(AM\), and a target user \(u_{tu}\). 0: Recommended items for the target user \(u_{tu}\). 0:\(AT\): The set of items' attributes. 0:\(AT_{int}\): The set of interrelated attributes. 0:\(N_{ti}(L)\): Neighborhood of the target item \(i_{it}\). 0:\(L\): Number of items in the neighborhood \(N_{ti}(L)\) of the target item \(i_{it}\). 0:\(N\): Number of items recommended to the target user \(u_{tu}\). 0:\(I_{tu}^{c}\): The set of items that the target user \(u_{tu}\) has not rated. 0:\(P_{tu,ti}\): Rating prediction of target item \(i_{it}\) for the target user \(u_{tu}\). 1:\(AT_{int}=\varnothing\)
2:For each pair of attributes \(\left\{a_{i},a_{j}\right\}\subseteq AT(i<j)\) do
3: Obtain the three interrelated attributes: \(AT_{int}AT_{int}\cup\left\{a_{i},Ra_{j}\right\}\)\(\left|R\in\left\{<_{k},=_{oi},>_{m0}\right\}\right|\)
4:Endfor
5:For each interrelated attribute \(a_{i}Ra_{j}\in AT_{int}\) do
6:For each item \(i_{x}\in I\) do
7:Set the attribute value \(\rho\left(x,a_{i}Ra_{j}\right)\) of \(i_{x}\) by Equations (8)-(10)
8:Endfor
9:Endfor
10:For each pair of items \(\left\{i_{in},i_{t}\right\}\subseteq I\)do
11: Compute the similarity between \(i_{m}\) and \(i_{n}\) according to interrelated attributes
12:Endfor
13:For each target item \(i_{it}\in I_{tu}^{c}\)do
14: Find the \(L\) most similar items of target item \(i_{it}\) to comprise neighborhood \(N_{ti}(L)\)
15: Predict rating score \(P_{tu,ti}\) of target item \(i_{it}\) from the items in \(N_{ti}(L)\)
16:Endfor
17: Recommend the top \(N\) target items having the highest predicted rating scores to the target user \(u_{tu}\)
```  
**Algorithm 1** Proposed approachAccording to Equations (12) and (13), we can obtain the number of interrelated attributes of \(i_{1}\) and \(i_{3}\), respectively. \[ \begin{split} num\Big{(}i_{1};l,m_{i_{1}}\Big{)}&=C_{n_{ 1}+n_{2}}^{2}+n_{1}n_{4}+(n_{1}n_{3}+n_{2}n_{3}+n_{2}n_{4})=2;\\ num\Big{(}i_{3};l,m_{i_{3}}\Big{)}&=C_{n_{1}+n_{3}}^{2}+n _{1}n_{4}+(n_{1}n_{2}+n_{2}n_{3}+n_{3}n_{4})=3;\end{split}