A new combination function in evidence theory

This paper studies the combination of basic probability assignment (bpa) in evidence theory. After introducing an interpretation of the mass function we show that given two bpa Dempster's rule of combination does not build a coherent bpa with respect to the interpretation. Next we give a new combination function that overcomes this problems and study some of its properties. 0. Introduction One of the models of approximate reasoning is evidence theory8,9 where the knowledge over a frame of discernment θ is expressed by means of belief and plausibility measures. They are functions from (θ) (i.e., parts of θ) into [0,1]. In particular, a belief measure, Bel, should satisfy the following axioms7: (i) Bel(Ø)=0 and Bel(θ)=1 (ii) For every A, B Œ (θ), if A∏B then Bel(A)=Bel(B) (iii) Bel(A1 ≈ A2 ≈ ... ≈ An) = ? i Bel(Ai) ? i<j Bel(Ai ↔ Aj) +...+ (-1) n+1 Bel(A1↔A2↔...↔An), for all nŒM. On the other hand, a plausibility measure, Pl, should satisfy (i), (ii) and also (iii)': (iii)' Pl(A1 ↔ A2 ↔ ... ↔ An) = ? i Pl(Ai) ? i<j Pl(Ai ≈ Aj) +...+ (-1) n+1 Pl(A1≈A2≈...≈An), for all nŒM. In fact, belief and plausibility measures are related to each other. For each belief measure Bel, it can be defined a plausibility measure Pl in the following way: Pl(A)=1 Bel(Ac) for all A in (A), where Ac is the complement of A.