On order invariant synthesizing functions.
The author offers several characterizations of lattice polynomials [see \textit{G. Birkhoff}, Lattice theory, AMS, Providence (1967; Zbl 0153.02501) and \textit{S. Ovchinnikov}, Order 14, 365--371 (1998; Zbl 0910.06001)]. The author calls them Boolean max-min functions -- they are indeed composed of a set function with 0 or 1 as values and of several maximum and minimum functions. Essential characterizing properties are, in addition to continuity, order invariance and, eventually, idempotence \((M(x,\dots ,x)=x)\). Order statistics, medians, and projection functions are considered as particular cases and characterized in corollaries.
scientific article; zbMATH DE number 1901017