Consider the following models: \(𝑀_1\): Mamdani model \(𝑀_2\): Takagi –…

Answer: Only the Takagi–Sugeno–Kang model and Kosko’s additive model are additive rule models.

Key idea: An additive rule model produces numeric outputs from each rule and combines those outputs by addition or a weighted sum/average to obtain the overall system output.

• Takagi–Sugeno–Kang model: consequents are numeric functions (often linear) of the inputs; the final output is computed as a weighted average of these numeric rule outputs, which is an additive combination.

• Kosko’s additive model (SAM): each rule contributes a numeric output and the system sums these contributions to form the overall output; the model is explicitly additive.

• Mamdani model: consequents are fuzzy sets; outputs are aggregated as fuzzy sets and then defuzzified. This is not an additive combination of numeric rule outputs.

Therefore, the correct choice is the one that lists the Takagi–Sugeno–Kang model and Kosko’s additive model.