AI - a Guide to Intelligent Systems.pdf - Member of EEPIS

CERTAINTY FACTORS THEORY AND EVIDENTIAL REASONING
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Thus, if we assume that
cf ðE 1 Þ¼cf ðE 2 Þ¼1:0
then from Eq. (3.32) we get:
cf 1 ðH; E 1 Þ¼cf ðE 1 Þcf 1 ¼ 1:0 0:8 ¼ 0:8
cf 2 ðH; E 2 Þ¼cf ðE 2 Þcf 2 ¼ 1:0 0:6 ¼ 0:6
and from Eq. (3.35) we obtain:
cf ðcf 1 ; cf 2 Þ¼cf 1 ðH; E 1 Þþcf 2 ðH; E 2 Þ½1
¼ 0:8 þ 0:6 ð1 0:8Þ ¼0:92
cf 1 ðH; E 1 ÞŠ
This example shows an incremental increase of belief in a hypothesis and also
confirms our expectations.
Consider now a case when rule certainty factors have the opposite signs.
Suppose that
cf ðE 1 Þ¼1 and cf ðE 2 Þ¼ 1:0;
then
cf 1 ðH; E 1 Þ¼1:0 0:8 ¼ 0:8
cf 2 ðH; E 2 Þ¼ 1:0 0:6 ¼ 0:6
and from Eq. (3.35) we obtain:
cf 1 ðH; E 1 Þþcf 2 ðH; E 2 Þ
cf ðcf 1 ; cf 2 Þ¼
1 min ½jcf 1 ðH; E 1 Þj; jcf 2 ðH; E 2 ÞjŠ ¼ 0:8 0:6
1 min ½0:8; 0:6Š ¼ 0:5
This example shows how a combined certainty factor, or in other words net
belief, is obtained when one rule, Rule 1, confirms a hypothesis but another,
Rule 2, discounts it.
Let us consider now the case when rule certainty factors have negative signs.
Suppose that:
cf ðE 1 Þ¼cf ðE 2 Þ¼ 1:0;
then
cf 1 ðH; E 1 Þ¼ 1:0 0:8 ¼ 0:8
cf 2 ðH; E 2 Þ¼ 1:0 0:6 ¼ 0:6