Some algebraic and analytical properties of a class of two-place functions.

This article deals with the formula f (− 1) (F (f (x) , f (y))) generated by a one-place function f : [ 0 , 1 ] → [ 0 , 1 ] and a binary function F : [ 0 , 1 ] 2 → [ 0 , 1 ]. When the f is a strictly increasing function and F is a continuous, non-decreasing and associative function with neutral element in [ 0 , 1 ] , the following algebraic and analytical properties of the formula are studied: idempotent elements, the continuity (resp. left-continuity/right-continuity), the associativity and the limit property. Relationship among these properties is investigated. Some necessary conditions and some sufficient conditions are given for the formula being a triangular norm (resp. triangular conorm). In particular, a necessary and sufficient condition are expressed for obtaining a continuous Archimedean triangular norm (resp. triangular conorm). When the f is a non-decreasing surjective function and F is a non-decreasing associative function with neutral element in [ 0 , 1 ] , we investigate the associativity of the formula. [ABSTRACT FROM AUTHOR]