## 2 Materials and Methods
### The lCrA Decision-Making Approach  
The classical lCrA combines two fundamental mathematical approaches--index matrices (IMs) and intuitionistic fuzzy sets (IFSs) [1]. The IMs approach represents an algebraic apparatus for data array processing with various dimensions, while the IFSs approach is a mathematical tool for uncertainty treatment. lCrA was developed to serve industry and scientific investigations to solve common problems, where it is necessary to work with datasets for multiple objects measured against different criteria. Let us consider the following initial IM\({}_{A}\):  
Figure 1: (**a**) Starting position; (**b**) position of maximal upper flexion with a wristband of 0.5 kg. Figure 2: A subject and raw EMG signals during TASK 5 performance of the FEP. \begin{tabular}{c|c c c c c c c}  & & Obj\({}_{1}\) & \(\ldots\) & Obj\({}_{k}\) & \(\ldots\) & Obj\({}_{n}\) & \(\ldots\) & Obj\({}_{n}\) \\ \hline Cr\({}_{1}\) & \(e_{Cr_{1},Obj_{1}}\) & \(\ldots\) & \(e_{Cr_{1},Obj_{k}}\) & \(\ldots\) & \(e_{Cr_{1},Obj_{1}}\) & \(\ldots\) & \(e_{Cr_{1},Obj_{n}}\) \\  & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) \\  & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) \\  & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) \\  & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) \\  & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) \\  & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) \\  & \(\mbox{Cr}_{m}\) & \(e_{Crm,Obj_{1}}\) & \(\ldots\) & \(e_{Crm,Obj}\) & \(\ldots\) & \(e_{Crm,Obj_{n}}\) \\ \end{tabular}   
where Cr\({}_{1}\), \(\ldots\), Cr\({}_{m}\) denote the IM criteria; Obj\({}_{1}\), \(\ldots\), Obj\({}_{n}\) represent the IM objects; and \(e_{Cr1,Obj_{1}}\ldots\)\(e_{Crm,Obj_{n}}\) are the IM elements. IM elements can be real numbers or other objects that are commensurate with relation \(R\) to the other e-objects, so that for each \(i\), \(j\), \(k\), \(R(e_{Crk,Obj_{i}}\), \(e_{Crk,Obj_{j}})\) is defined. Let \(\overline{R}\) be the dual relation of \(R\) in the sense that if \(R\) is satisfied, then \(\overline{R}\) is not satisfied, and vice versa is always true. Let \(N_{k,l}^{u}\) and \(N_{k,l}^{v}\) be the number of cases in which \(R(e_{Crk,Obj_{i}},e_{Crk,Obj})\) and \(R(e_{Crl,Obj_{i}},e_{Crl,Obj})\) and, respectively, \(R(e_{Crk,Obj_{i}},e_{Crk,Obj})\) and \(\overline{R}(e_{Crl,Obj_{i}},e_{Crl,Obj})\) are simultaneously satisfied. It is obvious that:  
\[N_{k,l}^{u}+N_{k,l}^{v}\ \leq\ \frac{n(n-1)}{2} \tag{1}\]  
For each \(k\), \(l\) such that \(1\leq k<l\leq m\) and for \(n\geq 2\), we define the following:  
\[\mu_{Crk,Crl}=2\frac{N_{k,l}^{u}}{n(n-1)},\ v_{Crk,Crl}=2\frac{N_{k,l}^{v}}{n( n-1)} \tag{2}\]  
The resulting ordered pair \(\mu_{Crk,Crl}\), \(v_{Crk,Crl}\) is an intuitionistic fuzzy pair (IFP). An IFP is an intuitionistic fuzzy evaluation of the relations established between two criteria \(Cr_{k}\) and \(Cr_{l}\). Thus, the index matrix \(A\), which gives the relationships between objects and the evaluating criteria, can be transformed into another index matrix \(A^{*}\) that contains the relations only between the criteria. \begin{tabular}{c|c c c c}  & & Cr\({}_{1}\) & \(\ldots\) & Cr\({}_{m}\) \\ \hline Cr\({}_{1}\) & \(\mu_{Cr1,Cr1}\), \(\mu_{Cr1,Cr1}\) & \(\ldots\) & \(\mu_{Cr1,Crm}\), \(\mu_{Cr1,Crm}\) \\  & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) \\ Cr\({}_{m}\) & \(\mu_{Crm,Cr1}\), \(\mu_{Crm,Cr1}\) & \(\ldots\) & \(\mu_{Crm,Crm}\), \(\mu_{Crm,Crm}\) \\ \end{tabular}   
IM\({}_{A^{*}}\) sets the degrees of correspondence and non-correspondence between the criteria \(\mbox{Cr}_{1}\), \(\ldots\), \(\mbox{Cr}_{m}\). Also, for each pair of criteria, the degree of uncertainty is taken into account. Correlation dependencies in ICrA are in the IFP form, with their values in the interval [0;1].