Fuzzy mathematical model In practice, the mathematical models we deal with reality can be divided into three categories: the first category is deterministic mathematical model, that is, the background of the model is certain and there is an inevitable relationship between objects. The second is a stochastic mathematical model, that is, the background of the model is random and accidental. The third category is fuzzy model, that is, the background and relationship of the model are fuzzy.

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Fuzzy sets and membership functions

Any mapping μ: X→ [0, 1] A X→μ (x) A from the universe X of1to the closed interval of [0, 1] determines a fuzzy set A on X, μ is called the membership function of A, and μ (x) is called the membership of A A X to fuzzy set A. When μ (x) {0, 1}, A degenerates into an A A ordinary set.