In a set, ￠ means "not included" (not "not included"), such as A￠B means "A set is not included in B set", that is, one or some elements in a set are not included in B.

Therefore, the subordinate relationship between each object and the set is also clear, either one or the other. But there are still many vague concepts in people's minds, such as young, old, warm, late and so on. The object attributes described by these concepts cannot be simply answered with "yes" or "no", and a fuzzy set refers to the whole object with the attributes described by a fuzzy concept.

Because the concept itself is not clear, the definition is not clear, so the subordinate relationship between object and set is not clear, either one or the other. This concept was first put forward in 1965 by L.A. Zadeh, a cybernetic expert at the University of California.

The appearance of the concept of fuzzy set enables mathematical ideas and methods to deal with fuzzy phenomena, thus forming the basis of fuzzy set theory (commonly known as fuzzy mathematics in China).