Discrete (Set) Derivatives and "Algebraic" Fuzzy Logic Operations

Authors

Bernadette Bouchon-Meunier
Hung T. Nguyen
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

9-2001

Comments

UTEP-CS-01-12a.

Published in Proceedings of the 10th IEEE International Conference on Fuzzy Systems FUZZ-IEEE'2001, Melbourne, Australia, December 2-5, 2001, Vol. 1, pp. 420-423.

Abstract

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 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*b and a+b-a*b.