From 65438 to 0965, Professor L.A.Zadeh of the University of California, USA, in his famous paper "Fuzzy Sets", put forward the fuzzy set theory which used the concept of "membership function" to quantitatively describe the fuzziness of things for the first time, which laid the foundation of fuzzy mathematics.

Laozi, a great philosopher and thinker in ancient China, said: "Accuracy is vague; Vague and accurate. "Fuzzy mathematics is not fuzzy mathematics, but uses mathematical methods to describe fuzzy phenomena in the objective world and reveal their essence and laws. Fuzzy mathematics builds a bridge between classical mathematics and the real world full of fuzziness.

1974, the British scholar E.H.Mamdani successfully applied the fuzzy set theory to the control of boilers and steam engines for the first time, which initiated the application of fuzzy control in practical engineering in the field of automatic control.

In just over 30 years, fuzzy mathematics has made great progress and achieved amazing and fruitful results in theory and application. The application fields of fuzzy mathematics have involved many aspects, such as automatic control, image and text recognition, artificial intelligence, geology, earthquake, medical diagnosis, meteorological analysis, aviation, aerospace, train, automobile and ship driving, traffic management, decision evaluation, enterprise management and social economy.

The application of fuzzy mathematics in automation technology is a very active and fruitful field. Austrom, a famous authority on automatic control, once pointed out that fuzzy logic control, neural network control and expert control are three typical analytical intelligent control methods.

In the early 1990s, fuzzy household appliances became popular in Japan, which brought huge commercial profits to Japanese enterprises, and also promoted countries such as Europe and America, further promoting the development of fuzzy technology. 1985, the world's first fuzzy logic chip appeared in Bell Laboratories, which is another milestone in the practical application of fuzzy technology. Many famous companies such as Japan, America and Germany are actively engaged in this research and have developed many commercial fuzzy logic chips. 1986, Japan established the hardware system of fuzzy controller (special device for fuzzy control). From the late 1980s to the mid-1990s, fuzzy approximate reasoning, fuzzy adaptive control, fuzzy neural network and fuzzy adaptive reasoning system were put forward successively. It injects new vitality into the application of fuzzy technology and opens up a very attractive bright future.

China's research in the field of fuzzy theory is at the advanced level in the world, and has published dozens of books on fuzzy theory. The application of engineering technology is weak, and the design method of continuous monitoring system and fuzzy comprehensive control method which are convenient for engineering application are put forward. In the late 1990s, fuzzy home appliance control began to appear.

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