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Consider the effect of adding irrelevance relations, in particular
the statement that the nondescendants of a variable are irrelevant
to the variable given the parents of the variable. Four constraints
represent this statement regarding credal sets:
and
.
To simplify the calculation of lower and upper bounds,
Theorem 2 can be used.
The upper bound is obtained by solving the program:
and
(w1 = p(f,b),
w2 = p(f,bc),
w3 = p(fc,b),
w4 = p(fc,bc)). This program
produces the upper bound 0.4509. By minimization, the lower bound
0.3818 is obtained. Note that these bounds are different from the
bounds obtained by type-1 extension.
Fabio Gagliardi Cozman
1998-07-03