The characterizations of monotone functions which generate associative functions

Chen Meng, Yun-Mao Zhang, Xue-ping Wang

Associativity of a two-place function $T:[0,1{]}^2\to [0,1]$ defined by $T(x,y)=f^{(-1)}(F(f(x),f(y)))$ where $F:[0,\infty {]}^2\to [0,\infty ]$ is an associative functio…