## 4 The Proposed PIKC-CI Method
### Collaborative Innovation Knowledge Refinement Based on Knowledge-Social Trust Degree
#### 4.2.1. Credible Groups Construction  
In the process of innovation knowledge capturing, knowledge-social members give comments and evaluations on other members' knowledge activities and establish social trust relationships among them. Here, the participants' knowledge-social trust degree in a knowledge community is measured by two aspects: individual trust (\(KST_{ind}\)) and community trust (\(KST_{com}\)). **Definition 7. **\(KST_{ind}\) _is used to describe the trust level established on knowledge interaction between one user and another user. Suppose there are individuals \(d_{i}\) and \(d_{j}\) in the knowledge-social community, \(d_{i}\) and \(d_{j}\) had \(n_{1}\) times knowledge-social activities which has an interactive type of \(P_{h}\). Let \(jud_{d_{j}}(d_{i})\in[0,1]\) be an interactive evaluation of \(d_{j}\) toward \(d_{i}\) in a knowledge-social activity. Assuming that \(d_{j}\) has given \(m_{1}\) times negative comment on \(d_{i}\), the \(KST_{ind}\) of \(d_{j}\) toward \(d_{i}\) can be computed as:_  
\[KST_{ind}(d_{j},d_{i})=\frac{\sum\limits_{t=1}^{n_{1}}right(P_{h})\timesjud_{ d_{j}}(d_{i})}{n_{1}}\times\left(\frac{n_{1}-m_{1}}{n_{1}}\right)^{\frac{1}{n_{1} -n_{1}}} \tag{8}\]  
_where \(right(P_{h})\in[0,1]\) is weight coefficient of interactive type. This formula introduces the weight concept of knowledge interaction and considers the influence of malicious interaction on subjective trust, which makes the calculation more reliable._  
**Definition 8. **\(KST_{com}\) _indicates the overall trust and reliability of users in the knowledge-social community, given by all members of the community in which the individual resides. The \(KST_{com}\) calculation depends on the following two factors: (1) the common evaluation for someone's knowledge-social behavior from all members of knowledge community; (2) the number of knowledge communities in which this individual resides. Suppose thereis an individual \(d_{i}\in V\) in multiple knowledge communities \(V_{1},V_{2},\ldots,V_{e}\). Assuming that \(d_{i}\) has been evaluated by \(g\) members of knowledge communities \(V_{1},V_{2},\ldots,V_{e}\), we can obtain the \(KST_{com}\) of \(d_{i}\)._  
\[KST_{com}(d_{i})=1\Bigg{/}g\times\sum_{ \begin{array}{c}d_{j}\in V_{1}\cup V_{ 2}\cup\ldots\cup V_{e}\\ j\
eq i\end{array} }\Bigg{[}KST_{ind}(d_{j},d_{i})^{\frac{1}{|V_{d_{j}}|}}\times (KST_{com}(d_{j}))\Bigg{]}, \tag{9}\]  
_where \(V\) is the knowledge community set, and \(\Big{|}V_{d_{j}}\Big{|}\) is the number of knowledge communities \(V_{1},V_{2},\ldots,V_{e}\) in which the individual \(d_{j}\) resides. Considering the extensive influence of community participants, the number of communities is introduced as a factor in \(KST_{com}\) calculation. If a participant has identities in multiple knowledge communities, the influence from his evaluation will be more than the one from only one community. In the process of knowledge refinement, the credibility of knowledge refined by participants with multiple identities will certainly be higher than that refined by the user with single community identity._  
Suppose there are \(t\) members in a group \(G\), the degrees of group knowledge-social trust \(KST_{com}(d_{i})\), \(KST_{com}(d_{j})\) have not been determined. The specific procedures of credible groups construction based on \(KST\) are summarized as follows:  
**Step 1. ** Compute individual knowledge-social trust degree \(KST_{ind}(d_{j},d_{i})\) for \(t\) members of group \(G\) by using Formula (8). **Step 2. ** Initialize community knowledge-social trust degree for each group member \(i\), \(KST_{com}(d_{i})=k\in(0,1]\). **Step 3. ** Calculate temporary community knowledge-social trust degree \(\overline{KST_{com}(d_{i})}\) of each group member by applying Formula (9):  
\[\overline{KST_{com}(d_{i})}=1\Bigg{/}g\times\sum_{ \begin{array}{c}d_{j}\in V _{1}\cup V_{2}\cup\ldots\cup V_{e}\\ j\
eq i\end{array} }\Bigg{[}KST_{ind}(d_{j},d_{i})^{\frac{1}{|V_{d_{j}}|}} \times(KST_{com}(d_{j}))\Bigg{]} \tag{10}\]  
**Step 4.