Lattice structure of the families of compatible frames of discernment.
Fabio Cuzzolin, R. Frezza · 2001
One of the central ideas in Shafer's mathematical theory of evidence is the concept of different level of knowledge of a given phenomenon, embodied into the notion of compatible frames of discernment. In this work we are going to analyze the concept of family of frames from an algebraic point of view, distinguish among finite and general families and introduce the internal operation of maximal coarsening, originating the structure of semimodular lattice. We will show the equivalence between the classical independence of frames and the independence of frames as elements of a locally finite Birkhoff lattice, eventually prefiguring a solution to the conflict problem based on a pseudo Gram-Schmidt algorithm.