Common Sense Reasoning in Diagnostic Systems - Efficient Decision Support Systems: Practice and Challenges from Current to Future - page 115

b.  J  Envs(x): J  SingleNogood < SingleNogood. The cardinality of SingleNogood is
more than the cardinality of a set obtaining as result of an intersection SingleNogood
with a set from Envs(x). We evaluate this version as max | J  SingleNogood | i.e. the

JEnvsx  ()

more of components from SingleNogood are intersected with any environment from
Envs(x), the more priority of a choice of the given measurement point for the
observation.
c.  J  Envs(x): SingleNogood  J. The SingleNogood includes in a set from Envs(x). We
evaluate this version as min (| | | J  i gleNogood |) i.e. the less a difference between

JEnvsx  ()

SingleNogood and Envs(x), the more priority of a choice of the given measurement point
for the current observation.
d.  J  Envs(x) : J  SingleNogood = , i.e. no-one of the most probable faulty candidates
includes in environments Envs(x) supporting predictions at the point x. We
evaluate this version as the least priority choice, i.e. 0 in the numerical
equivalent.
Also to the version (d) there are referred other methods of definition of current
measurement point priorities which happen when SingleNogood = . Thus in the
estimations of a choice priority a numerical value returned as a result of call of other method
is accepted. We call it by ResultD(x).
At appearance of the greater priority choosing between versions (b) and (c), heuristically we
accept the version (b) as at this choice the refinement of faulty candidates is produced better.
Note for various supporting sets of the same Envs ( x ), the availability both the version (b)
and the version (c) is also possible. In this case, as a resulting estimation for the given
Envs ( x ) the version (b) is also accepted.
Continuing the example, we obtain the following:
Nogood = {{And2,Inv1}, {And2,Inv2,Inv5}, {And2,Inv3}}
SingleNogood = {And2}

min (| | | J  SingleNogood |)

< R3, version (c), = 2>

JEnvsx  ()

< R1, version (c), min (| | | J  SingleNogood |) = 2>

JEnvsx  ()

< O6, version (c), min (| | | J  i le d |) = 1>

JEnvsx  ()

< O5, version (a) >

< O4, version (c), min (| | | J  i le d |) = 1>

JEnvsx  ()

< O3, version (a) >

< O2, version (c), min (| | | J  i le d |) = 1>

JEnvsx  ()

< O1, version (a) >.