One seed is definitely not called a heap, nor two, let alone three ... On the other hand, everyone agrees that 100 million seeds must be called a heap. So, where is the appropriate boundary? Can it be said that 123585 seeds are not called heaps, but 123586 seeds constitute the same heaps? There are no absolute boundaries between tall and short, beautiful and ugly, clean and polluted, mineral and non-mineral, and even between man and ape, vertebrate and invertebrate, living and non-living concepts.

This is fuzzy phenomenon, which refers to the state that it is difficult to distinguish objective things with clear boundaries. It comes from people's identification and classification of objective things, and is reflected in the concept. Concepts with different extensions are called different concepts and reflect different phenomena. The concept of extensional fuzziness is called fuzzy concept, which reflects fuzzy phenomenon.

The discussion of fuzziness can be traced back to a long time ago. Russell, the great philosopher of the 20th century, in a paper entitled Fuzziness in 1923, specifically discussed what we call "fuzziness" today, and clearly pointed out: "It is a big mistake to think that fuzzy knowledge must be unreliable." Although Russell is famous, this article published in the Journal of Southern Hemisphere Philosophy did not arouse great interest in vagueness or vagueness in academic circles at that time. This is not because the question is unimportant, nor because the article is not profound, but because it is not yet time. For a long time, people have always regarded vagueness as a derogatory term, and only paid tribute to accuracy and strictness. At the beginning of the 20th century, the development of society, especially the development of science and technology, did not need the study of fuzziness. In fact, fuzzy theory is the product of the era of electronic computers. It is the invention and wide application of this very precise machine that makes people more deeply aware of the limitations of precision and promotes people's research on its opposite or its "other half"-fuzziness.

The concept of precision can be described by the usual set. Fuzzy concepts should be described by corresponding fuzzy sets. Zadeh, an American cybernetic expert, grasped this point and made a breakthrough in the quantitative description of fuzzy sets, laying the foundation for fuzzy theory and its application. 1965, Zadeh published a paper entitled "Fuzzy Sets", and put forward the concept of fuzzy sets for the first time. He pointed out: "in the field of human knowledge, the only department where non-fuzzy concepts play a major role is classical mathematics." "If we deeply study the cognitive process of human beings, we will find that the use of vague concepts is a great wealth rather than a burden for human beings. This is the key to understanding the profound difference between human intelligence and machine intelligence. "

Set is the foundation of modern mathematics. Once fuzzy sets were put forward, the concept of "fuzzy" also penetrated into many branches of mathematics. The development speed of fuzzy mathematics is also quite fast. Judging from the published papers, it is almost exponential growth. It involves pure mathematics, applied mathematics, natural science, humanities and management science. It has been widely used in image recognition, artificial intelligence, automatic control, information processing, economics, psychology, sociology, ecology, linguistics, management, medical diagnosis, philosophical research and other fields. Fuzzy mathematics theory is applied to decision-making research, and fuzzy decision-making technology is formed. As long as we study it carefully, we will find that in most cases, the decision-making objectives and constraints are fuzzy, especially for the decision-making process of complex large-scale systems. In this case, the application of fuzzy decision technology will be more natural and get better results.