## 2 Materials and Methods
### ICrA Analysis  
InterCriteria analysis combines index matrices (IMs) and intuitionistic fuzzy sets (IFS) for establishing the dependencies (positive or negative consonance) along with the dissonances between the considered criteria [1]. For the initial ICrA application, it is necessary to prepare data sets of multiple objects measured against different criteria, presented in the form of an index matrix (IM) as follows:  
\[ \begin{array}{c|cccc}&Obj_{1}&\ldots&Obj_{k}&\ldots&Obj_{n}\\ \hline Cr_{1}&e_{Cr1,Obj1}&\ldots&e_{Cr1,Obj2}&\ldots&e_{Cr1,Objn}\\ \ldots&\ldots&\ldots&\ldots&\ldots&\ldots\\ Cr_{i}&e_{Cri,Obj1}&\ldots&e_{Cri,Obj2}&\ldots&e_{Cri,Objn}\\ \ldots&\ldots&\ldots&\ldots&\ldots&\ldots\\ Cr_{m}&e_{Crm,Obj1}&\ldots&e_{Crm,Obj}&\ldots&e_{Crm,Objn}\\ \end{array} \]  
In the initial IM \(Cr_{1}\)\(\ldots\)\(Cr_{m}\) denotes criteria; \(Obj_{1}\)\(\ldots\)\(Obj_{n}\) represents objects; and \(e_{Cr1,Obj1}\)\(\ldots\)\(e_{Crm,Objn}\) are elements, respectively. IM elements are commensurated by relation \(R\), so that for each \(i\), \(j\), \(k\) is defined \(R(e_{Crk}\), \(Obj_{ij}\), \(e_{Crk}\), \(Obj_{ij})\). Let \(N_{k,l}^{u}\) and \(N_{k,l}^{v}\) be the numbers of cases in which \(R(e_{Crk}\), \(Obj_{i}\), \(e_{Crk}\), \(Obj_{ij})\) and \(R(e_{Crl}\), \(Obj_{ij})\) and, respectively, \(R(e_{Crk}\), \(Obj_{ij}\), \(e_{Crk}\), \(Obj_{ij})\) and \(\overline{R}(e_{Crl}\), \(Obj_{ij}\), \(e_{Crl}\), \(Obj_{ij})\) are simultaneously satisfied. \(\overline{R}\) is the dual relation of \(R\), so if \(R\) is satisfied, \(\overline{R}\) is not satisfied, and vice versa. Then, we obtain the following:  
\[N_{k,l}^{u}+N_{k,l}^{v}\ \leq\ \frac{n(n-1)}{2} \tag{1}\]  
From Equation (1), we obtain two numbers for each \(k\), \(l\), (\(1\leq k<l\leq m\)) and for \(n\geq 2\) as follows:  
\[\mu_{Crk,Crl}=2\frac{N_{k,l}^{u}}{n(n-1)},\ v_{Crk,Crl}=2\frac{N_{k,l}^{v}}{n( n-1)} \tag{2}\]  
where \(\mu_{Crk,Crl}\), \(v_{Crk,Crl}\) is an intuitionistic fuzzy pair (IFP) that presents intuitionistically fuzzy evaluations of the relations established between \(Cr_{k}\) and \(Cr_{l}\). Thus, the final IM, which contains the relationships between the criteria, is obtained in the following form:  
\[ \begin{array}{c|ccccc}&Cr_{1}&\ldots&Cr_{i}&\ldots&Cr_{m}\\ \hline Cr_{1}&\langle 1,0\rangle&\ldots&\mu_{Crl,Crl},v_{Crl,Cri}&\ldots& \mu_{Cr1,Crm},v_{Crl,Crm}\\ \ldots&\ldots&\ldots&\ldots&\ldots&\ldots\\ Cr_{i}&\mu_{Cri,Crl},v_{Cri,Cr1}&\ldots&\langle 1,0\rangle&\ldots&\mu_{Cri,Crm},v_{Crm} \\ \ldots&\ldots&\ldots&\ldots&\ldots&\ldots\\ Cr_{m}&\mu_{Crm,Crl},v_{Crm,Cr1}&\ldots&\mu_{Crm,Cri},v_{Crm,Cri}&\ldots& \langle 1,0\rangle\\ \end{array} \]  
The final IM sets the degrees of correspondence and non-correspondence between the criteria \(Cr_{1}\), \(\ldots\), \(Cr_{m}\). Also, the degree of uncertainty is calculated. ICrA correlation dependencies have intuitionistic fuzzy pairs form with values between 0 and 1. The algorithm determines the degrees of correlation between the criteria, known as positive or negative consonance and dissonance, depending on the threshold values \(\alpha\) and \(\beta\) (\(0\leq\alpha\leq 1\), \(0\leq\beta\leq 1\), and \(\alpha+\beta\leq 1\)) for \(\mu\) and \(\
u\). The two criteria \(Cr_{R}\) and \(Cr_{l}\) are in positive consonance (PC) when \(\mu_{Crk,Crl}>\alpha\) and \(v_{Crk,Crl}<\beta\), or the \(\mu\) value is in the interval (0.75, 1.00]. Negative consonance (NC) is detected when \(\mu_{Crk,Crl}<\beta\) and \(v_{Crk,Crl}>\alpha\), or the \(\mu\) value is in the interval [0.00, 0.25]. Dissonance appears in the other cases, when the \(\mu\) value is in the interval (0.25, 0.75]. According to [38; 39], the threshold values are \(\alpha=0.75\) and \(\beta=0.25\). In greater detail, according to [1; 38], PC can be considered as strong (\(\mu\in(0.95,1.00]\)), only positive (\(\mu\in(0.85,0.95]\)), and weak (\(\mu\in(0.75,0.85]\)). The same is valid for NC and dissonance.