On a functional equation characterizing two binary operations on the space of membership functions
Let * and \(\Delta\) be continuous, abelian semi-group operations on the fuzzy subsets of X with the topology of pointwise convergence. Assume that 1 and 0 are the respective units and that the sections of the binary operations are non-decreasing. The author characterizes the solutions of the functional equation \[ A*B+A\Delta B=A+B \] in terms of families of t-norms and t-conorms discovered by \textit{M. J. Frank} [Aequationes Math. 19, 194-226 (1979; Zbl 0444.39003)].
scientific article; zbMATH DE number 4115187