## 2 Materials and Methods  
The following steps can be identified in solving the problem of creditworthiness assessment based on fuzzy modeling. Let us assume that the borrower has a certain set of characteristics (indicators) that are subject to evaluation when making a decision on lending, represented as: \(X=\big{\{}x_{i}|i=\overline{1,N}\big{\}}\), where \(X\) is the set of borrower indicators, \(x_{i}\) is the i-th characteristic of the borrower, and \(N\) is the number of characteristics of the borrower. The characteristics are assessed based on a set of criteria, \(C=\big{\{}c_{j}|j=\overline{1,M}\big{\}}\), where \(C\) is the set of criteria for assessing the borrower, \(c_{j}\) is the j-th criterion for assessing the borrower, and \(M\) is the number of criteria for assessing the feasibility of granting a loan to the borrower. Next, a set of possible outcomes (alternatives) is determined, \(A=\big{\{}a_{t}|t=\overline{1,T}\big{\}}\), where \(A\) is the set of alternatives, \(T\) is the number of alternatives, and \(a_{t}\) is the classification level. The following values are used: \(a_{1}\)--low (L), \(a_{2}\)--below average (LM), \(a_{3}\)--average (M), \(a_{4}\)--above average (HM), and \(a_{5}\)--high (H). The next step is to build a set of rules for fuzzy inference in the form \"If..., then... \" \(\to P=\big{\{}p_{l}|l=\overline{1,L}\big{\}}\), where \(P\) is the set of rules for fuzzy inference and \(L\) is the number of rules. Then, the left part of the rules is collapsed according to the schemes that will be described in more detail below. The choice of one or another alternative is also a fuzzy measure that determines characteristics of the loan such as the maximum loan amount, interest rate, or loan period. The determination of a set of indicators and logical rules in the result is the choice of a lending scheme, \(S=\big{\{}s_{k}|k=\overline{1,K}\big{\}}\), where \(S\) is a set of credit schemes, \(s_{k}\) is a specific credit scheme, and \(K\) is the number of credit schemes. Next, consider the indicators for assessing the creditworthiness of a small or medium-sized business. The initial indicators are displayed on the interval [0, 1]. This set of parameters is represented as a set of linguistic variables. In general, the issue of how exactly to display this requires serious research. More useful information is contained in the literature [16; 17]. In the general case, we assume that any parameter takes values on a certain interval of real numbers [18]. The simplest case is when each parameter is associated with one linguistic one, which can be called the \"degree of favorableness of the indicator\". In explicit form, it is necessary to specify the mapping of the interval of real numbers that this parameter can take to the interval [0, 1]. This process is called the process of standardizing indicators. Taking the composition of the \"degree of auspiciousness\" with the functions presented below, we accordingly obtain new linguistic variables: \"the value of the parameter is low\" (L); \"average parameter value\" (M); \"high parameter value\" (H). Note that these kinds of linguistic variables are often used in technical systems. An even greater number of gradations are also often considered: below average, above average, close to zero, etc. Each linguistic variable has its own membership function. One of the possible ways to define the membership functions was proposed in [19]. It examines the management of a technical system, namely, a steam boiler. In principle, in our case, the situation is very similar. In the result, the choice of the type of membership functions, both of the alternatives themselves and of the evaluated criteria, is determined based on expert preferences. It is obvious that the expert's uncertainty in the assessment grows with an increase in the deviation of the value of the estimated parameter from the optimal value. Moreover, in most cases, this uncertainty does not grow linearly.