Tags:analogical proportion, analogical proportion between numerical values, boolean analogical proportion, frank s triangular norms, piaget s logical proportions, triangular co-norm and triangular norm
Abstract:
Starting from the Boolean notion of logical proportion in Piaget’s sense, which turns out to be equivalent to analogical proportion, this note pro- poses a definition of analogical proportion between numerical values based on triangular norms (and dual co-norms). Frank’s family of triangular norms is par- ticularly interesting from this perspective. The article concludes with a compara- tive discussion with another very recent proposal for defining analogical propor- tions between numerical values based on the family of generalized means.
Frank’s Triangular Norms in Piaget’s Logical Proportions