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What is fuzzy theory?
Fuzzy theory refers to the theory that uses the basic concepts of fuzzy sets or continuous membership functions. It can be divided into five branches: fuzzy mathematics, fuzzy system, uncertainty and information, fuzzy decision, fuzzy logic and artificial intelligence. They are not completely independent, they are closely related. For example, fuzzy control will use the concepts in fuzzy mathematics and fuzzy logic. From the practical application point of view, the application of fuzzy theory mostly focuses on fuzzy systems, especially fuzzy control. There are also some fuzzy expert systems used for medical diagnosis and decision support. Because from the theoretical and practical point of view, fuzzy theory is still a new thing, and we expect that with the maturity of fuzzy field, there will be more reliable practical applications.

Concept is one of the basic forms of thinking, which reflects the essential characteristics of objective things. In the process of cognition, human beings abstract and summarize the same characteristics of things they feel, and form concepts. For example, abstract "white" from things such as white snow, white horse and white paper. A concept has its connotation and extension. Connotation refers to the sum of the essential attributes of things reflected by the concept, that is, the content of the concept. Extension refers to the scope of the object that the concept refers to. For example, the connotation of the concept of "human" refers to animals that can make tools and use them for labor, and the extension refers to all people at all times and in all countries.

The so-called fuzzy concept means that the extension of this concept is uncertain, or its extension is unclear and vague. For example, the concept of "young" is very clear to us, but its extension, that is, what age group people are young, is hard to say, because there is no clear boundary between "young" and "not young" and it is a vague concept.

There are several points to be noted: firstly, people are allowed to be subjective when understanding fuzziness, that is to say, everyone has different boundaries for vague things, and admitting a certain degree of subjectivity is a feature of understanding fuzziness. For example, if we ask 100 people to name the age range of "young people", we will get 100 different answers. Nevertheless, when we use the method of fuzzy statistics to analyze, the age distribution of young people has certain regularity;

Secondly, fuzziness is the opposite of accuracy, but it cannot be understood negatively that fuzziness represents backward productive forces. On the contrary, we often resort to vagueness when dealing with objective things. For example, in a crowded room, it is not difficult to find an "old tall man". The "old" and "high" mentioned here are vague concepts, but as long as we analyze and judge these vague concepts, we can quickly find this person in the crowd. If we ask for a computer query, then we must input specific data such as everyone's age and height into the computer, and then we can find such people from the crowd.

Finally, people's understanding of fuzziness is often confused with randomness, but they are essentially different. Randomness itself has a clear meaning, but due to insufficient conditions, there can be no definite causal relationship between conditions and events, so the occurrence of events shows an uncertainty. The fuzziness of things means that the concept of things we want to deal with is vague, that is, it is difficult to determine whether an object conforms to this concept, that is, the uncertainty brought by the fuzzy extension of the concept.