Data analysis using system modeling

. Expert systems are increasingly being used to format safe operations. But the functions of expert systems can perform not only assistance in making decisions, but also analyze processes and help at various stages. These actions are possible when considering a system with fuzzy data. The work is devoted to solving the problem of fuzzy inference knowledge in intelligent systems based on the use of fuzzy logic. The scheme of construction of continuous logic, the computation of values of membership functions of linguistic variables of output knowledge. The proposed approach is based on the use of continuous logic, which allows for a more accurate representation of fuzzy data compared to traditional logic. The construction of the continuous logic scheme involves the use of fuzzy sets for both input and output variables, which are then used to compute the values of membership functions of linguistic variables of output knowledge. In this approach, the expert system is able to analyze processes and assist at various stages by making use of fuzzy inference knowledge. The fuzzy inference mechanism is based on the use of fuzzy logic, which allows for a more nuanced understanding of complex systems and processes. The expert system is able to analyze data from various sources and make informed recommendations based on the available information. Overall, the use of expert systems based on fuzzy logic is becoming increasingly popular in a variety of industries. By improving the accuracy of data analysis and decision-making, these systems can help to ensure safe and efficient operations.


Introduction
Data analysis using systems modeling is a technique that is used to study processes and systems in various industries such as science, engineering, economics, etc. It involves the development of models that display the behavior of the system, including its components, and their interaction.
Systems modeling is used to create an abstract model of a real system that can be used to analyze data and predict future trends. Such models can be mathematical, statistical, or a combination.
Systems modeling can also be used to determine the best strategy to control a system, find the optimal system configuration, or to predict unknown variables. In general, data analysis using systems modeling is a powerful tool that can be used to study complex systems and their interactions in real time.
Intelligent systems are widely implemented in various fields of science and technology. Various methods of knowledge derivation used in intelligent systems require the development of appropriate means of their implementation. In this work, using the example of the compositional rule of knowledge inference, implemented in fuzzy inference machines (FOM) of expert systems, the possibility of using continuous logic for the formation of knowledge inference functions is investigated.
Development of a design scheme for constructing continuous logic formulas that define membership functions of fuzzy sets of inferred knowledge. To develop a calculation scheme for constructing formulas of continuous logic to determine the membership functions of fuzzy sets of inferred knowledge, the following steps must be performed: 1. Determine the knowledge base and the values of the variables that will be used in the simulation.
2. Determine the membership functions for each of the variables. Membership functions can be of any shape, from linear to non-linear.
3. Define inference rules based on the knowledge base. Rules can be written in the form of "IF-THEN", where any of the variables can be used as a condition, and another variable can be used as an action.
4. Using the inference rules and membership functions, determine the membership function of the output knowledge.
5. Create a calculation scheme to evaluate the membership function of the derived knowledge. The calculation scheme may include equations, logical operations and other mathematical expressions. 6. Check the performance of the design scheme using various values of variables and the knowledge base.
The development of a computational scheme for constructing formulas of continuous logic to determine the membership functions of fuzzy sets of inferred knowledge is a complex process that requires accuracy and care in determining the values of variables and developing membership functions and inference rules.

Methods
The structure of the maximum convolution of knowledge inference using the rules of fuzzy deductive inference includes the following elements: 1) Fuzzy facts are information that is represented by fuzzy objects. They can be both numerical and unscrupulous values, for example, detected manifestations.
2) Fuzzy rules are the interaction of operators that require fuzzy actions and use to derive new applications.
3) Fuzzy retentions are the results of applying fuzzy rules to fuzzy facts, which can also be represented as fuzzy sets. 4) Maximal convolution is a fuzzy inference aggregation process that allows you to get one single conclusion based on all fuzzy rules and facts specified in the system.
5) The result is the final conclusion, which is a number or value, the quality of the guarantee in the validity of this conclusion.
This structure allows for complex fuzzy fences, on the presence of various rules and facts, while obtaining results depends on the quality of the approximation of fuzzy sets and rules.
1. The structure of the max -min convolution of knowledge inferences using the rules of fuzzy deductive inferences. Fuzzy sets A, B, A` and B` are used as knowledge in the derivation of fuzzy sets. And the inference of B` from A` according to the rule A → B is written as: When implementing deductive inference, first of all, the fuzzy relation R is defined as the convolution max -min:

R=
Zade L.A. [1] defined output B` as follows: Formalized derived knowledge can be used to construct a computational scheme for constructing continuous logic functions. Such a calculation scheme can be used to calculate values that correspond to the membership functions of the linguistic variables of the output knowledge.
To do this, it is necessary to convert the formalized output knowledge into mathematical expressions that describe the corresponding membership functions. Then you can use these expressions to build a calculation scheme that takes the values of input variables as input and calculates the corresponding values of the membership functions.
For example, if at the output of the formalized inferred knowledge we get a fuzzy set A, which describes the probability that an object belongs to a certain class, then we can construct a membership function for this class using a mathematical expression that describes the properties of the fuzzy set A.
Thus, the use of formalized inferred knowledge and calculation schemes built on the basis of this knowledge makes it possible to implement fuzzy logical inference and perform calculations that can be used in various tasks, including artificial intelligence and control systems.
The presented formalized deduced knowledge allows us to construct a design scheme for constructing functions of continuous logic, the calculated values of which correspond to the membership functions of linguistic variables of deduced knowledge.
2. Calculation scheme for constructing functions of continuous logic. The calculation scheme for constructing functions of the continuous logic of knowledge inference includes the following steps: 1. Definition of input and output variables of the system. These can be physical quantities such as temperature, speed, pressure, etc.
2. Definition of each input and output variable of a fuzzy set. A fuzzy set is defined using a membership function that evaluates the degree to which each value of a variable belongs to each set. As a result of performing all the steps, a system is obtained that is able to make decisions based on the input data and the rule base. This system can be used for process control, decision making, robot control, etc. Using formula (1), we will present a scheme according to which it is possible to write down functions of continuous logic that define the inferred knowledge (Fig. 1).

Results
According to the calculation scheme, we write the expressions of the functions of continuous logic associated with the inferred knowledge.
b`1 = b1 a1 a`1 ˅ b1 a2 a`2 ˅ b1 a3 a`3 ˅ … ˅ b1 am a`m b`2 = b2 a1 a`1 ˅ b2 a2 a`2 ˅ b2 a3 a`3 ˅ … ˅ b2 am a`m b`3 = b3 a1 a`1 ˅ b3 a2 a`2 ˅ b3 a3 a`3 ˅ … ˅ b3 am a`m ... . .. ... b`m = bm a1 a`1 ˅ bm a2 a`2 ˅ bm a3 a`3 ˅ … ˅ bm am a`m Calculation of the values of the functions gives the values of the membership functions of the linguistic variable of the derived knowledge: The computation process can be carried out according to the continuous logic selection table [2]. The selection table for calculating the value of the function b`1, of the form b`1 = b1 a1 a`1 ˅ b1 a2 a`2 ˅ b1 a3 a`3 is presented in Table 1. For example, let us set the specific values of the function variables ordered in ascending order. The first variant of ordering the variables gives the value of the function equal to a3. The second option is the value a`3.

Conclusions
In order to obtain continuous logic functions for linguistic variables A and B, it is necessary to describe each of them by a fuzzy set that expresses the degree of their belonging to a certain linguistic category.
Similarly, the fuzzy rule A → B can be represented by a function that determines the relationship between linguistic variables A and B, that is, the degree of confidence that if A belongs to one linguistic category, then B must belong to another category.
Further, using the calculation scheme of fuzzy logic, it is possible to calculate the values of the membership functions of linguistic variables of fuzzy knowledge derivatives. To do this, you need to know the values of the linguistic variable A` and apply the function that corresponds to the given fuzzy rule A → B.
For example, if linguistic variable A has two categories "low" and "high", and variable B has three categories "little", "medium" and "many", then the fuzzy rule function A → B can be represented as a table, in where each cell contains the value of the relationship function between categories A and B.
Then, if the value of the linguistic variable A` is equal to 0.4, then for each category of variable B, its membership function can be calculated using the selection table and the value of A`. In this case, the value of the functions for the three categories of variable B will be: -"little": 0.2 -"medium": 0.6 -"many": 0.2 Thus, having obtained membership functions for derivatives of fuzzy knowledge, one can further use them to solve problems and make decisions in fuzzy systems.
The results obtained allow using the known linguistic variables A and B, the rule A → B, the given values A` according to the calculation scheme to write down the functions of continuous logic and using the selection table to calculate the values of the membership functions of the linguistic variables of the derived fuzzy knowledge.