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A descriptive (linguistic) fuzzy model captures qualitative knowledge in the form of if‐then rules [106]:

(4.31)

Here, is the input (antecedent) linguistic variable, and A_i are the antecedent descriptive (linguistic) terms (constants). Similarly, is the output (consequent) linguistic variable, and B_i are the consequent linguistic terms. The values of and the linguistic terms A_i(B_i) are fuzzy sets defined in the domains of their respective base variables: x ∈ X ⊂ R^p and y ∈ Y ⊂ R^q. The membership functions of the antecedent (consequent) fuzzy sets are then the mappings: μ(x) : X → [0, 1], μ(y) : Y → [0, 1]. Fuzzy sets A_i define fuzzy regions in the antecedent space, for which the respective consequent propositions hold. The linguistic terms A_i and B_i are usually selected from sets of predefined terms, such as Small, Medium, and so on. By denoting these sets by and , respectively, we have and . The rule base and the sets and constitute the knowledgebase of the linguistic model.