Characterizations of monotone right continuous functions which generate associative functions

Yun-Mao Zhang, Xue-ping Wang

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