## 4 Results  
After the conformity functions have been obtained, it is necessary to bring them to the global criterion via convolution. This operation can be performed using the \(t\)-norm, which is the real two-place function \(T:[0.1]\times[0.1]\rightarrow[0.1]\), and it satisfies the following conditions [19; 24; 25]:  
* Limitations: \[T(0.0)=0;T(s(*),1)=T(1,s(*))=s(*);\]
* Monotony: \[T(s_{1}(*),s_{2}(*))\leq T(s_{3}(*),s_{4}(*))\text{, if }s_{1}(*)\leq s_{3}(*),s_{2}(*)\leq s_{4}(*);\]
* Commutativity: \[T(s_{1}(*),s_{2}(*))=T(s_{2}(*),s_{1}(*));\]
* Associativity: \[T(s_{1}(*),T(s_{2}(*),s_{3}(*)))=T(T(s_{1}(*),s_{2}(*)),s_{3}(*)).\] (8)  
Figure 2: Reliability matching function. In the \(t\)-norm, the functions of \(s_{i}(*)\) are unary real functions \(s(*):\left[0.1\right]\rightarrow\left[0.1\right],\) and the correspondence functions \(s_{p}(p)\) and \(s_{g}\big{(}p_{g}\big{)}\) obtained above were found according to the particular criteria of \(p\) and \(p_{g}\). Therefore, the \(t\)-norm \(T\big{(}s_{p}(p),s_{g}\big{(}p_{g}\big{)}\big{)}\) determines the convolution of the correspondence functions \(s_{p}(p),s_{g}\big{(}p_{g}\big{)},\) and ultimately the convolution of the particular criteria of \(p\) and \(p_{\Gamma},\) since \(T\big{(}s_{p}(p),s_{g}\big{(}p_{g}\big{)}\big{)}=T\big{(}p,p_{g}\big{)}.\)  
We denote the function \(T\big{(}p,p_{g}\big{)}\) of two partial criteria through the previously used notation \(W_{np}\big{(}p,p_{g}\big{)},\) i.e., the set \(W_{np}\big{(}p,p_{g}\big{)}=T\big{(}p,p_{g}\big{)},\) and use the reduced efficiency function to distinguish it from the efficiency function \(W=p\cdot p_{g},\) given by relation (2). In the scientific and technical literature, various types of \(t\)-norms are given, whereby the simplest of them are the following [19; 24; 25]:  
* \(T\big{(}s_{p}(p),s_{g}\big{(}p_{g}\big{)}\big{)}=\min\big{[}s_{p},s_{g}\big{]};\)
* \(T\big{(}s_{p}(p),s_{g}\big{(}p_{g}\big{)}\big{)}=s_{p}\cdot s_{g}^{\prime};\)
* \(T\big{(}s_{p}(p),s_{g}\big{(}p_{g}\big{)}\big{)}=\max\big{[}0,s_{p}+s_{g}-1 \big{]}.\)  
In further studies, we will use the \(t\)-norm most appropriate to the problem under consideration in the following form:  
\[T\big{(}s_{p}(p),s_{g}\big{(}p_{g}\big{)}\big{)}=W_{np}\big{(}s_{p}(p),s_{g} \big{(}p_{g}\big{)}\big{)}=s_{p}(p)\cdot s_{g}\big{(}p_{g}\big{)}.\]  
Then, the expression for the reduced convolution criterion can be written as follows:  
\[W_{np}\big{(}s_{p}(p),s_{g}\big{(}p_{g}\big{)}\big{)}=\left\{ \begin{array}{ ll}\frac{\ln(1-p)}{\ln(1-W_{s})}\exp\{-\Big{\lvert}\frac{p_{g}-1}{\delta}\Big{\rvert} ^{n}\},&\text{if }p<W_{s},\\ \exp\{-\Big{\lvert}\frac{p_{g}-1}{\delta}\Big{\rvert}^{n}\},&\text{if }W_{s}\leq p\leq 1. \end{array} \right. \tag{9}\]  
Due to the associativity property for the \(t\)-norm in the case of \(n\) particular criterion \(p_{i},i=\overline{1,n},\) we find the following:  
\[W_{np}=\prod_{i=1}^{n}s_{i}(p_{\,i}). \tag{10}\]  
As follows from the comparison of dependencies (1) and (9), they have the same structure, but differ only in that dependence (1) folds the particular criterion, and dependence (9) collapses the particular correspondence functions. So, the criterion obtained via the convolution of the particular correspondence functions will be called a probabilistic criterion for correspondence (PCC criterion). We have obtained an analytical dependence for calculating the PCC criterion \(W_{np}\big{(}p,p_{g}\big{)},\) which differs significantly from the widely used Formula (1).