## 1 Introduction
Interval analysis finds broad application when dealing with uncertain design parameters, extending to other problems related to the analysis of structural behavior under dynamic loads. In [29] by [PERSON] et al., it was applied to analyze the reliability of systems with viscoelastic dampers; in [30] by [PERSON] et al., it was applied to assess the reliability of systems with active vibration control; and in [31], [PERSON] and [PERSON] utilized it in the analysis of structural damage detection involving various types of uncertainties. Uncertainty consideration is also discussed in the context of optimization. In [32], [PERSON] et al. proposed a method for manipulator trajectory control, taking into account uncertainties. This method utilizes a non-probabilistic uncertainty quantification approach, ensuring precision and effectiveness in evaluating system response. On the other hand, in [33], [PERSON] et al. presented topology optimization for continuous structures, considering uncertainties and time-dependent reliability. It employs a parameterized level set method based on reliability criteria. Meanwhile, in [34], [PERSON] and [PERSON] introduced a hybrid optimization method for vibration controller design, considering mixed uncertainties. Uncertainties are treated as intervals and fuzzy models. As part of the analysis of systems with uncertain parameters, the issue of interval sensitivity is also considered, where the influence of individual uncertain input parameters on the range of obtained results is determined. In [35], [PERSON] and [PERSON] demonstrated a procedure for determining the sensitivity of frequency response function bounds. This article analyzes viscoelastically damped systems with uncertain design parameters. Methods for incorporating uncertainties in such systems, as described in the literature, can be divided into probabilistic methods, methods based on fuzzy theory, and methods where uncertainties are modeled as interval numbers. The first group includes works such as [36; 37] written by [PERSON] et al., which analyze dynamic characteristics for systems with uncertainties, and [3; 38] by [PERSON] et al. and [2] by [PERSON] et al., where the authors consider random design parameters in determining frequency response function. Fuzzy theory, on the other hand, is applied in works [39; 40] written by [PERSON] et al., where frames with viscoelastic dampers were analyzed. The third approach is described, among others, by [PERSON] and [PERSON] in [19], [PERSON] and [PERSON] in [20], [PERSON] in [21], and [PERSON] et al. in [29], which will be discussed later in this section. A detailed description of incorporating uncertainties in structures with viscoelastic elements can be found in the review paper [41] by [PERSON] et al. The choice of the appropriate approach depends on the description of uncertainty. In the case of viscoelastic materials, it is often difficult to determine the parameter distribution, making interval analysis a good solution as it requires knowledge of only the lower and upper bounds of parameter variability. In summary, based on the available information about the parameters and considering the nature of the problem under consideration, methods for addressing uncertainties can be summarized in the three following subpoints:  
* Probabilistic methods [1; 2; 3; 36; 37; 38], where parameters are modeled as random variables. Advantage: they allow for the consideration of a wide range of probability distributions; disadvantage: they require the consideration of a large number of examples. * Fuzzy theory methods [39; 40], where parameters are described using fuzzy sets. Advantage: they can be applied when probability distribution is lacking; disadvantages: operations are computationally expensive and results may be less precise than with probabilistic methods. * Methods based on interval analysis [4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 23; 24; 25; 26; 27; 28; 29; 30; 31; 35; 42; 43; 44], where parameters are modeled as intervals.