What is the mathematical description of an expert system?

Question

Mathematics

I myself have never dealt with expert systems, but it became necessary to find out what the mathematical description of an expert system is. From the huge amount of information that I found on this topic, I could not understand what such a description of it should be like. mathematically describes mainly individual processes of systems tailored to a specific area of ​​activity, and the answer should be in a more generalized form.

Answer 1

quote from the lecture
Fuzzy inference rules form a rule base. It is important that in a fuzzy expert system, unlike the traditional one, all the rules work simultaneously, but the degree of their influence on the output can be different.
The principle of calculating the superposition of many influences on the final result underlies fuzzy expert systems.
The process of processing fuzzy inference rules in an expert system consists of 4 stages;
1. calculation of the degree of truth of the left parts of the rules (between "if" and "then") - determining the degree of belonging of the input values ​​to the fuzzy subsets indicated in the left part of the inference rules;
2. modification of the fuzzy subsets indicated on the right side of the inference rules (after "then"), in accordance with the truth values ​​obtained at the first stage;
3. union (superposition) of modified subsets;
4. scalarization of the result of superposition - the transition from fuzzy subsets to scalar values.
in short, the description of the expert system will mathematically be like a neuron, only the functions differ, the wrong choice of functions at each stage leads to bugs such as