On some bisymmetric functions on closed intervals

The author presents some technical results concerning binary operations on closed intervals of real numbers. The main goal is to develop a unified approach to t-norms, t-conorms, and means. Although t-norms, t-conorms, and means are quite different operations with respect to their properties, there is a particular common property which they share. It is called bisymmetry. The class of quasi-linear functions satisfying the bisymmetry condition is completely described. These functions are important tools in modeling generalized implication functions in the framework of fuzzy logic