Definition of evidence fusion rules based on referee functions

This chapter defines a new concept and framework for constructing fusion rules for evidences. This framework is based on a referee function, which does a decisional arbitrament conditionally to basic decisions provided by the several sources of information. A simple sampling method is derived from this framework. The purpose of this sampling approach is to avoid the combinatorics which are inherent to the definition of fusion rules of evidences. This definition of the fusion rule by the means of a sampling process makes possible the construction of several rules on the basis of an algorithmic implementation of the referee function, instead of a mathematical formulation. Incidentally, it is a versatile and intuitive way for defining rules. The framework is implemented for various well known evidence rules. On the basis of this framework, new rules for combining evidences are proposed, which takes into account a consensual evaluation of the sources of information. 185 186 Chapter 6: Definition of evidence fusion rules based on referee functions Notations • I [b], function of Boolean b, is defined by I [true] = 1 and I [false] = 0 . Typically, I [x = y] has value 1 when x = y, and 0 when x = y, • Let be given a frame of discernment Θ. Then, the structure G denotes any lattice constructed from Θ. In particular, G may be a distributive lattice like the hyper-power set D; or G may be a Boolean algebra like the power set 2, the super-power set S, or the free Boolean algebra generated by Θ, • x1:n is an abbreviation for the sequence x1, · · · , xn , • max{x1, · · · , xn}, or max{x1:n} , is the maximal value of the sequence x1:n . Similar notations are used for min , • maxx∈X{f(x)}, or max{f(x) / x ∈ X}, is the maximal value of f(x) when x ∈ X . Similar notations are used for min 6.