# A Methodological Approach for the Smartification of a University Campus: The Smart ESI Use Case
## 3 A Methodology for the Smartification of Universities and Compuses
### Smartification Framework Description  
Let us start with the definition of a set of \(n\) smart universities (alternatives) \(\mathcal{U}=\{u_{1},u_{2},\ldots,u_{n}\}\) to be evaluated against a set of \(m\) dimensions \(\mathcal{D}=\{d_{1},d_{2},\ldots,d_{m}\}\). We denote as \(\mathcal{S}_{i,j}=\{s^{1}_{i,j},s^{2}_{i,j},\ldots,s^{p}_{i,j}\}\) to the \(p\) services provided for each university \(i\in[1,n]\) in each dimension \(j\in[1,m]\). For each dimension \(j\in[1,m]\), we may compute the set of core services \(\mathcal{S}_{j}^{*}\) as the intersection of the services corresponding to that dimension across the universities in \(\mathcal{U}\) as follows:  
\[\mathcal{S}_{j}^{*}=\bigcap_{i=1}^{n}S_{i,j} \tag{1}\]  
Note that \(p\) may differ across different \(\mathcal{S}_{i,j}\) but the size of \(\mathcal{S}_{j}^{*}\) is the same for all universities in a certain dimension since it corresponds to the common set of services. A service \(s_{i,j}^{k}\in\mathcal{S}_{i,j}\) defined for the university \(i\in[1,n]\) and the dimension \(j\in[1,m]\) has associated a set of \(q\) specific indicators \(\mathcal{Q}_{i,j}^{k}=\{q_{i,j_{1}}^{k},q_{i,j_{2}}^{k},\ldots,q_{i,j_{q}}^{k}\}\), where each indicator is defined by the tuple \(q_{i,j_{x}}^{k}=\langle Q_{i,j_{x}}^{k},\omega_{i,j_{x}}^{k}\rangle\), \(\forall x\in[1,q]\). The first value \(Q_{i,j_{x}}^{k}\) represents one and only one observed value of the indicator \(x\), which represents the contribution to the service \(k\) in the university \(i\) in dimension \(j\), with \(i\in[1,n],j\in[1,m],k\in[1,p]\). The second value of the tuple \(\omega_{i,j_{x}}^{k}\) is the weight, i.e., a score that represents the relative importance of the indicator \(x\) to the service \(k\), so that we can have preferred indicators over other indicators. Similarly, for a given service \(s_{i,j}^{k}\), the set of core indicators \(\mathcal{Q}_{j,k}^{*}\) is computed as the intersection of the indicators corresponding to the service \(s_{i,j}^{k}\in S_{j}^{*}\) across the universities in \(\mathcal{U}\) as follows:  
\[\mathcal{Q}_{j,k}^{*}=\bigcap_{i=1}^{n}\mathcal{Q}_{i,j}^{k}\quad\forall s_{i,j}^{k}\in S_{j}^{*} \tag{2}\]  
Now, let us define the smartness dimension \(\Omega\) aimed at evaluating specifically the ICT usage and smartness degree associated with a certain university across all its dimensions, to attempt answering the question _how smartness the university is_. Thus, \(\Omega\) is a transversal dimension to \(\mathcal{D}\), because the smart infrastructure is shared by the different dimensions accomplished within the university. The dimension \(\Omega\) of a university \(i\) is measured through a set of \(\lambda\) ICT/smartness indicators denoted by \(\mathcal{Q}_{i,\Omega}=\{q_{i,\Omega}^{1},q_{i,\Omega}^{2},\ldots,q_{i,\Omega }^{3}\}\). Such indicators may be used to measure horizontally any dimension, and thus they are defined similarly to the rest of indicators, i.e., \(q_{i,\Omega}^{y}=\langle Q_{i,\Omega}^{y},w_{\Omega}^{y}\rangle,\forall q_{i, \Omega}^{y}\in\mathcal{Q}_{i,\Omega}\), this means that, the smartness indicator \(q_{i,\Omega}^{y}\) takes one observed value for the university \(i\) with a score of \(w_{\Omega}^{y}\). Note that the weight of the smartness indicator is always the same for all universities. Theory of Smartification  
Based on the previous formulation, we define two decision matrices:  
\(\mathcal{M}_{1}\): Service matrix to account the contribution of each service \(k\) to the dimension \(j\) and university \(i\). To this end, we use the set of core services, i.e., the ones that are common for a specific dimension in all universities.