Multi Attribute Utility Functions g(Y)=G(91y,g2(y2),) where G{u1u2….U=G(u1,G(u2…un) G(u1)=G(u1,1 Example: Diagnosis gi(mode j =P(y;=modei) G(u,, uxu 3/17/2004 copyright Brian Williams, 2002 Mutual Preferential Independence For any subset WcY our preference between two assignments to w is independent of the assignment to the remaining variables W-Y Assignment 0, is preferred over 02 if g(01)<g(02) Example: Diagnosis If M1=G is more likely than M1=U, a Then {M1=G,M2=G,M3=U,A1=G,A2=G} Is preferred to {M1=U,M2=G,M3=U,A1=G,A2=G} copyright Brian Williams, 20023/17/2004 copyright Brian Williams, 2002 7 Multi Attribute Utility Functions g(Y) = G(g1(y1), g2(y2), . . .) where G(u1, u2 … un) = G(u1,G(u2 … un)) G(u1) = G(u1, IG) Example: Diagnosis gi (modeij) = P(yi = modeij) G(u1,u2) = u1 x u2 IG = 1 3/17/2004 copyright Brian Williams, 2002 8 Mutual Preferential Independence For any subset W ⊆ Y our preference between two assignments to W is independent of the assignment to the remaining variables W – Y. Assignment δ1 is preferred over δ2 if g(δ1) < g(δ2) Example: Diagnosis ƒ If M1 = G is more likely than M1 = U, ƒ Then, {M1 = G, M2 = G, M3 = U, A1 = G, A2 = G} ƒIs preferred to {M1 = U, M2 = G, M3 = U, A1 = G, A2 = G}