Accurate mathematics and stochastic mathematics based on classical set theory have made remarkable achievements in describing the internal laws of various objective phenomena in nature. However, like random phenomena, there are a lot of fuzzy phenomena in nature and people's daily life, such as cloudy days, cloudy days, light rain, heavy rain, poverty, food and clothing and so on.
Because the classical set theory can only limit its expressive force to those phenomena and concepts with clear extension, it requires that the subordinate relationship of elements to the set must be clear and not ambiguous, so people are used to trying to avoid those concepts with unclear extension that can not be reflected by the classical set.
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Fuzzy mathematics was originally applied to fuzzy control, fuzzy identification, fuzzy cluster analysis, fuzzy decision-making, fuzzy evaluation, system theory, information retrieval, medicine, biology and so on. There are concrete research results in meteorology, structural mechanics, control and psychology. But the most important application field of fuzzy mathematics is computer intelligence, which many people think is closely related to the development of a new generation of computers.
Developed countries in the world are actively researching and trial-producing intelligent fuzzy computers. 1986, Dr. Liede Yamagata of Japan successfully trial-produced the fuzzy inference machine for the first time, and its inference speed was100000 times per second. 1988, under the guidance of Professor Wang Peizhuang, several Chinese doctors also successfully developed a fuzzy inference machine-a prototype of discrete components, and its inference speed is150,000 times per second.