Dempster shafer theory in AI (Artificial Intelligence)

Dempster Shafer Theory:

This refers to original conception of the theory by Dempster and Shafer theory.

Need Of Dempster Theory:

There is some information that probability cannot describe ignorance.

Dempster-Shafer theory can effectively solve this problem. For the scenario of ignorance, the belief of HEAD and TAIL would be 0.

For the fair coin scenario, the belief of HEAD and TAIL would be 0.5.

The basic idea in representing uncertainty in this model is:          
1) Set up a confidence interval.
2) The belief brings together all the evidence that would lead to believe in P with some certainty.

   3)The plausibility brings together the evidence that is compatible with P and is not consistent with it.

   4)This method allows for further addition to set of knowledge and does not assume disjoint outcomes.

If Ω = set of possible outcomes then a mass probability, M is defined for each member of set 2Ω and takes values in range [0,1].

The NULL set is also a member of 2Ω.

M = Probability density function for all subsets.

So Ω is set ( FLU(F), COLD(C), PNEUMONIA(P))

Then 2 Ω is set { ϕ ,(F),(C),(P),(F,C),(F,P),(C,P),(F,C,P)}.

The confidence interval is defined as [B(E),PL(E)] where

B(E) = ∑M , A is subset of E

PL (E) = 1-B(¬E)

           = 1-∑M

Where ¬L is subset of ¬E i.e. all the evidence that contradicts P.

Characteristics:

·        It assigns the part of the probability to the entire universe to make the aggregate of all events to 1. This part is called ignorance level.

·        As more and more evidence is added, the ignorance level reduces.

·        Evidence is combined using a combination rule.

·        Evidence against a hypothesis is considered to be evidence for its negation.

Advantages:

·        The uncertainty interval becomes narrower with additional information.

·        Representation of diagnose hierarchies.

·        Ignorance is lowered as more information is added.

·        Uncertainty is included in model.

·        More freedom is allowed.

Disadvantage:

Computation effort is high as 2**n sets are to be considered where n is size of power set (number of subsets in the set).