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Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

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the degree to which the current evidence supports A, the Disbelief (A) is the<br />

degree to which the current evidence supports ¬ A <strong>and</strong> Uncertainty (A) is the<br />

degree to which we believe nothing one way or the other about proposition A.<br />

As new evidences are collected, the remaining uncertainty will decrease [5],<br />

<strong>and</strong> each piece of length that it loses will be given to Belief (A), or Disbelief<br />

(A). The concept can be best described by fig. 9.9. We denote Belief (A),<br />

Disbelief (A), Plausibility (A) <strong>and</strong> Uncertainty (A) by Bel (A), Disbel (A), Pl<br />

(A) <strong>and</strong> U (A) respectively.<br />

Further, Pl (A) = Bel (A) + U (A)<br />

<strong>and</strong> D (A) = Disbel (A) + U (A).<br />

It can be easily shown that<br />

i) Pl (A) ≥ Bel (A)<br />

ii) Pl (A) + Pl (¬ A) ≥ 1<br />

iii) Bel (A) + Bel (¬ A) ≤1.<br />

Further, for A being a subset of B,<br />

Bel (A) ≤ Bel (B) <strong>and</strong><br />

Pl (A) ≤ Pl (B).<br />

0 j k 1<br />

|-----------------------------------------------------|<br />

|--Belief-------|---Uncertainty--|--Disbelief--- |<br />

(Bel) (U) (Disbel)<br />

|---------Plausibility-------------|<br />

(Pl)<br />

|---------------Doubt--------------|<br />

(D)<br />

Fig. 9.9: The belief interval.

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