GENERALIZED INFORMATION THEORY AND DECOMPOSABILITY OF SYSTEMS

Abstract

Properties of the lattice or symmetric relations on a reference space Ω properties of the valued boolean lattices and an association between a random vector and an equivalence relation on tl are used to show how most or the formulae given by different authors concerning joint information of random vectors may easily be interpreted through introduction or a random object denoted A:B (A and B being random vectors).

R_A:Bis defined as the reflexive and symmetric relation associated with A:B.

R_A:B=R_Awhere R_A: equivalence relation associated with A R_B: equivalence relation associated with B.

A distance between random variables and a similarity relation having good independence properties are derived. These results are then extended to more complex structures of random objects.

INDEX TERMS:

• Structure
• reconstruct ability
• constraint
• multivariate analysis
• information
• relations
• lattices
• system
• modelling
• decomposition