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.
Keywords. Family of compatible frames, Birkhoff lattice, linear dependence, conflict.
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Authors addresses:
Fabio Cuzzolin
Dipartimento di Elettronica e Informatica
Via Ognissanti 72
35131 Padova
Italy
Ruggero Frezza
Dipartimento di Elettronica e Informatica
Via Ognissanti 72
35131 Padova
Italy
E-mail addresses:
| Fabio Cuzzolin | cuzzolin@dei.unipd.it |
| Ruggero Frezza | frezza@dei.unipd.it |