On the paradoxical success of Mamdani's minimum-based inference

Marcin Detyniecki (1) , Benjamin Moubêche , Bernadette Bouchon-Meunier (1)

1 MALIRE - Machine Learning and Information Retrieval

Mamdani’s inference has an incredible success, especially in areas such as decision making and control. Yet, it is well known that it uses a min-based implication that does not verify classical boolean logic requirements. This contribution aims at, in the one hand, exploring Mamdani’s choice from a practical point of view, and in the other hand, explaining the success of Mamdani’s inference from a logical perspective, by introducing a simple variant of the Generalized Modus Ponens (GMP) that uses standard fuzzy implications. In addition, this new formulation opens the way for new methods of inference that have the same benefits as Mamdani’s.

Domaines: Informatique [cs]

Marcin Detyniecki, Benjamin Moubêche, Bernadette Bouchon-Meunier. On the paradoxical success of Mamdani's minimum-based inference. Combining Experimentation and Theory: A Hommage to Abe Mamdani, 271, Springer, pp.259-270, 2012, Studies in Fuzziness and Soft Computing, ⟨10.1007/978-3-642-24666-1_19⟩. ⟨hal-01269705⟩