Discrete set derivatives and algebraic fuzzy logic operations

Bernadette Bouchon-Meunier (1) , Hung T. Nguyen , Vladik Kreinovich

1 APA - Apprentissage et Acquisition des connaissances

We propose a new way to generalize logical operations from the discrete classical logic to a continuous fuzzy logic, namely we propose to define derivatives for the discrete case, and then to use these derivatives to derive the continuous operations. We show that this natural approach leads to "algebraic" fuzzy operations a/spl middot/b and a+b-a/spl middot/b.

Domaines: Informatique [cs]

Bernadette Bouchon-Meunier, Hung T. Nguyen, Vladik Kreinovich. Discrete set derivatives and algebraic fuzzy logic operations. FUZZ-IEEE'2001 Conference, Dec 2001, Melbourne, Australia. pp.420-423, ⟨10.1109/FUZZ.2001.1007338⟩. ⟨hal-01570841⟩