Fundamental unit structures: A theory of ratio scalability☆

A theory of nonassociative measurement structures is developed which produces a natural generalization of associative measurement (i.e., extensive structures), and representation and uniqueness theorems are established for these generalized structures, and it is shown that in many cases these representations are ratio scales. The methods of proof strongly relate the structure of the automorphism group of the nonassociative structure to its underlying concatenation operation.