%0 Journal Article
%T Lattice induced threshold functions and Boolean functions
%A Eszter K. Horv¨˘th
%A Branimir Seselja
%A Andreja Tepavcevic
%J Mathematics
%D 2013
%I arXiv
%X Lattice induced threshold function is a Boolean function determined by a particular linear combination of lattice elements. We prove that every isotone Boolean function is a lattice induced threshold function and vice versa. We also represent lattice valued up-sets on a finite Boolean lattice in the framework of cuts and lattice induced threshold functions. In terms of closure systems we present necessary and sufficient conditions for a representation of lattice valued up-sets on a finite Boolean lattice by linear combinations of elements of the co-domain lattice.
%U http://arxiv.org/abs/1307.1318v1