Pavlodar, 2021

**3.2.2 Fuzzification**

Fuzzification refers to not only a separate stage of fuzzy inference, but also the actual process or procedure for finding the values of membership functions of fuzzy sets based on ordinary source data. Fuzzification is also called the introduction of fuzziness [19].

As can be seen from the code in Figure 3.1, the variable income was divided into 3 parts, and each of them was assigned a linguistic label, such as low, medium and high.

**3.2.3 Means of fuzzy output**

The most important two types of fuzzy inference method are Mamdani and Sugeno fuzzy inference methods. The model under consideration is based on the Mamdani derivation method.

The process of fuzzy inference in the Mamdani style is carried out in four steps: fuzzification of input variables; assessment of the rules; aggregation of rule outputs; defazzification. The role of the fuzzy inference mechanism is in accordance with the fuzzy rules contained in the rule base, with the entered values for these indicators, which are stored in the database to determine which rules should be applied and control the reasoning process [61].

Various forms can be used to form membership functions, such as «Gaussian», «trapezoidal», «Bell curve», etc.

The triangular membership function was used to create the model due to its simple formula and computational efficiency [52].

**3.2.4 Fuzzy Production Rule Base**

The rule base is intended for the formal presentation of empirical knowledge or expert knowledge in a particular problem area. Creating a fuzzy rule base If-Then is necessary in order to determine how the variable affects the result.

The following are some of the rules that were used to determine the assessment of the financial condition of the candidate.

If (Salary is low) and (Job status is maintenance staff) and (Work experience is small), then (Financial condition is low).

If (Salary is average) and (Job status is specialist) and (Work experience is average), then (Financial condition is average).

a) Г-function; b) S-function; c) L-function; d) A-function; e) Gaussian function; f) П-function

Figure 3.2 – Types of membership functions

If (Salary is high) and (Job status is director) and (Work experience is large), then (Financial condition is high).

It is known that the information that comes from a person is often less accurate when as information from various measuring devices is more accurate.

Thanks to the fuzzy set, new possibilities have appeared, such as: the possibility of creating artificial intelligence similar to human intelligence; creation of computers programmed using natural language; application of information of any degree of granularity in the problems of modeling, control, optimization and diagnostics.

The main element of the fuzzy model is the rule base, since it contains information about the structure of the model.

The rule base contains the basic information about the simulated system or the main component of the «intelligence» of the fuzzy controller, and therefore the ability to correctly form it is a very important condition. This skill allows you to prevent errors that, given the importance of the rule base for a fuzzy model, usually belong to the category of «rough». When compiling the rule base, the expert’s experience matters, since the correctness of the result depends on the correctness of the preparation of the legal basis. When compiling the rule base, certain combinations are used, and the combination of data can be quite large, but this does not mean that the more rules, the more accurate the result will be.

**3.2.5 Defuzzification**

Defuzzification is a procedure or process of finding the usual value for each of the output linguistic variables of the set W = (w_{1}, w_{2}, ... w_{s}). The purpose of defuzzification is to obtain the usual quantitative value of each of the output variables using the results of the accumulation of all output linguistic variables [19]. In this work, the center of gravity method is used as a defuzzification strategy.

In this example, the centroid method was used for defazzification, since this method is usually better compared to other methods in terms of consistency of results [63–64].

Defuzzification of a fuzzy set means the operation of finding a clear value that would represent this set in the most «rational» way. Naturally, there may be various criteria for evaluating the «rationality» of the value of a given parameter to represent a fuzzy set.

The number of such criteria can be judged by the number of existing defuzzification methods, the most famous of which are: the average maximum method, the first maximum method, the last maximum method, the center of gravity method, the center of the sum method, the height method.

For example, the average maximum method has the following advantages: it is easy to calculate, which allows the use of cheaper microprocessors in control systems. However, this method has disadvantages. The disadvantage is that only the fuzzy set Bj with the highest degree of activation influences the result of defuzzification – sets that are activated to a lesser extent have no effect on the result.

An important indicator in the application of the above methods is the sensitivity of the defuzzification method and the resulting sensitivity of the fuzzy model. This sensitivity can be defined as the existence of a response of the output parameter of the model to changes in the degrees of activation of fuzzy sets corresponding to the conclusions of the rule base.