## 3 Methodology
### Development Fuzzy Model
It is shown in the following how the dependability \(D\) is determined based on indicators of maintainability \(M\), reliability \(R\), and logistical support \(F\), while the maintenance convenience \(M\) is obtained similarly based on partial indicators \(t\), \(e\), \(u\), \(d\), \(m\), and \(s\). The idea of this work is to obtain a more accurate assessment of the dependability of CCS systems at the open pit Gacko. This assessment was identified as the best possible among the worst expected ratings of the partial availability indicators (\(R\), \(M\), and \(F\)). Let the partial indicators \(R\), \(M\), and \(F\) be shown in the form of the following triangular fuzzy numbers  
\[\mu_{R}\left(\mu_{R}^{1},\mu_{R}^{2},\mu_{R}^{3},\mu_{R}^{4},\mu_{R}^{5}\right),\ \mu_{M}\left(\mu_{M}^{1},\mu_{M}^{2},\mu_{M}^{3},\mu_{M}^{4},\mu_{M}^{5}\right),\ \mu_{F}\left(\mu_{F}^{1},\mu_{F}^{2},\mu_{F}^{3},\mu_{F}^{4},\mu_{F}^{5}\right). \tag{2}\]  
In the next step, the max-min composition is performed on them. If the mentioned partial indicators \(R\), \(M\), and \(F\) are observed, it is possible to make \(C=5^{3}=125\) combinations of corresponding membership functions, which will be further denoted with  
\[\mu^{ijk}\left(\mu_{R}^{i},\mu_{M}^{j},\ \mu_{F}^{k}\right),\qquad i,j,k\in\{1,2, 3,4,5\} \tag{3}\]  
Each of these combinations represents one possible assessment of the dependability and the following two values can be associated with it  
\[\Omega_{ijk}=\frac{[i+j+k]}{3} \tag{4}\]  
and  
\[m^{ijk}=\min\Bigl{\{}\mu_{R}^{i},\mu_{M}^{j},\mu_{F}^{k}\Bigr{\}} \tag{5}\]  
\(\Omega_{ijk}\) takes values from the set \(\{1,\,2,\,3,\,4,\,5\}\), and each of the mentioned values can be associated with the number \(\mu^{l}\), which represents the maximum value of \(m^{ijk}\) of all those combinations for which \(\Omega_{ijk}\) is equal to \(l\), za \(l\in\{1,\,2,\,3,\,4,\,5\}\), that is  
\[\mu^{l}=\min\Bigl{\{}m^{ijk}:\Omega_{ijk}=l\Bigr{\}}. \tag{6}\]  
In this way, a rating for the dependability of \(D\) is obtained  
\[\mu=\left(\mu^{1},\mu^{2},\mu^{3},\mu^{4},\mu^{5}\right) \tag{7}\]  
Using the best-fit method, see [11], to transform the obtained ratings into belonging to the fuzzy set, determined by (2), the distance is used that is defined by  
\[d_{i}=d(\mu,\mu_{i})=\sqrt{\sum_{j=1}^{5}\bigl{(}\mu^{j}-\mu_{i,j}\bigr{)}^{2 }},\qquad\mu_{i}=(\mu_{i,1},\mu_{i,2},\mu_{i,3},\mu_{i,4},\mu_{i,5}), \tag{8}\]  
For \(\mu_{i}\in\Bigl{\{}\mu_{poor},\mu_{adeq},\,\mu_{aver},\mu_{good},\mu_{exc} \Bigr{\}}\). Small values \(d_{i}\) indicate proximity to the linguistic variable \(\mu_{i}\). Accordingly, let \(d_{min}\) be the minimum value of the obtained distances \(d_{1},d_{2},\ d_{3},\ d_{4},\ d_{5}\), and then the reciprocal value of the relative distances can be associated to each of them that is determined by:  
Figure 5:0  
If for some \(i\) the distance value \(d_{i}\) is equal to \(0\), then the corresponding value of the reciprocal value of relative distance is \(\alpha_{i}=1\), while the other values of the reciprocal relative distances are equal to 0. The normalized values of the therefore obtained reciprocal values of the relative distances are determined by:  
Figure 5:1  
and present belonging to the appropriate rating:  
Figure 5:2  
In the end, the appropriate linguistic rating is obtained as follows:  
Figure 5:3  
In a similar way, a rating for maintainability \(M\) is obtained from the linguistic variables \(t,e,u,d,m,\) and \(s\), which are later used to determine the dependability \(D\). Initially, experts were provided with a questionnaire to gather their opinions on various indicators. These responses were then subjected to statistical analysis, a crucial step before moving on to the fuzzification process. The fuzzy proposal marks the initial application of artificial intelligence (AI) by assigning each indicator a corresponding fuzzy number.