## 2 Uncertainty Generators and Their Influence on Solving ILSs  
In the system determined by the equation \([a]x=[b]\), the uncertainty of the coefficient \(a\in[\underline{a},\overline{a}]\) adversely affects the quality of control and the possibility of \"hits\" in the tolerance corridor \([\underline{b},\overline{b}]\). It should be added here that the uncertainty \([\underline{b},\overline{b}]\) determining the control tolerance is not a control disturbance (difficulty), but facilitates the control objective. If, with one tolerance \([\underline{b},\overline{b}]\), it is not possible to find a tolerance solution, then maybe it will be found after increasing the tolerance. However, in practice, such an enlargement is often not possible due to precision requirements. As shown by the authors of [6; 7], as well as other publications, with just one disturbance uncertainty generator (DUG), it is quite often impossible to implement TC due to obtaining empty sets of solutions. Note, however, that in the 2V-ILS system there are as many as 4 DUGs and only 2 tolerance uncertainties (TUs) \([\underline{b}_{1},\overline{b}_{1}]\), \([\underline{b}_{2},\overline{b}_{2}]\), (20).  
\[[\underline{a}_{11},\overline{a}_{11}]x_{1}+[\underline{a}_{12}, \overline{a}_{12}]x_{2} =[\underline{b}_{1},\overline{b}_{1}] \tag{20}\] \[[\underline{a}_{21},\overline{a}_{21}]x_{1}+[\underline{a}_{22}, \overline{a}_{22}]x_{2} =[\underline{b}_{2},\overline{b}_{2}]\]  
It is understandable that in a 2V-ILS system, it will be much more difficult to implement TC. Let us now consider the uncertain quadratic system (21).  
\[[\underline{a}_{2},\overline{a}_{2}]x^{2}+[\underline{a}_{1},\overline{a}_{1 }]x+[\underline{a}_{0},\overline{a}_{0}]=[\underline{b},\overline{b}] \tag{21}\]  
In this system, there is only one TC \([\underline{b},\overline{b}]\) per 3 DUGs. This is a worse situation than in the system (20). Additionally, complex solutions may appear in the quadratic system, which will make it even more difficult to obtain TC. If we want to implement TC in the 3V-ILS system, the number of DUGs is then 9 and the number of TUs is 3. It can be seen that in \(n\)V-ILS systems the number of DUGs grows much faster (\(n^{2}\)) than the number of TUs, which is \(n\). Therefore, in more complex systems, the implementation of TC becomes practically impossible. An example here is the task of hitting a plane with a missile fired from an anti-aircraft gun. The following DUGs appear here: uncertainty in measuring the \(x,y,z\) position, uncertainty in measuring the vertical and horizontal angle of the plane's movement direction, uncertainty in measuring the plane's speed, uncertainty of the initial velocity of the fired projectile, error in setting the horizontal and vertical angle of the common barrel, uncertainty of wind speed and direction, and other. Is it possible to guarantee a hit in the silhouette of the plane with such a number of DUGs? This is a rather unrealistic task. Therefore, the authors believe that the realistic goal of TC is not to look for the value of the control (decision) variable, which guarantees reliable implementation of TC, but to look for its value that will give the maximum probability of TC implementation--and if possible, full probability, i.e., certainty. In the next section, we will briefly introduce the multidimensional interval arithmetic (MIA) that will be used to realize realistic TC.