Uncertainty reasoning methods (1, 2)

4. Uncertainty Reasoning Methods

4.1 Basic issues in uncertainty reasoning

Uncertainties and their types:

(Narrow sense) Uncertainty: (uncertainty) means that the authenticity of a proposition cannot be completely certain, but can only give some estimate of the possibility of its being true. For example: Team A may win this game.
(Fuzziness) Inexactness: The meaning of certain words in a proposition is not precise enough. For example: Xiao Ming is a tall man.
Incompleteness: For something, the information or knowledge about it is incomplete, incomplete, and insufficient. eg: Certain stages of the criminal investigation process often require reasoning based on incomplete evidence.
Inconsistency: Inconsistent conclusions occur during the reasoning process

4.1.1 Representation and measurement of uncertainty

三种不确定性：
    ①关于知识的不确定性
    ②关于证据的不确定性
    ③关于结论的不确定性

The representation of knowledge is closely related to reasoning. Different reasoning methods require corresponding knowledge representation models.

Measurement of knowledge
Static strength: In expert systems, a numerical value is usually used to represent the degree of uncertainty of the corresponding knowledge.
Dynamic strength: The uncertainty of the evidence is also usually represented by a numerical value to represent the degree of uncertainty of the corresponding evidence.

4.1.2 Uncertainty matching algorithm and threshold selection

Uncertainty matching algorithm: an algorithm used to calculate the similarity between matching parties

Threshold: used to indicate the "limit" of similarity

4.1.3 Combined evidence uncertainty algorithm

Maximum and minimum method
C(E1∧E2) = min{C(E1),C(E2)}
C(E1∨E2) = max{C(E1),C(E2)}
Probability method
C(E1∧E2) = C(E1)×C(E2)
C(E1∨E2) = C(E1)+C(E2)−C(E1)×C(E2)
Bounded method
C(E1∧E2) = max{0, C (E1)+C(E2)−1}
C(E1∨E2) = min{1, C(E1)+C(E2)}

4.1.4 Uncertainty transfer algorithm

Given the uncertainty C(E) of the premise E and the rule strength f(H,E), find the uncertainty of the conclusion H
That is, define function f1 such that C(H)=f1(C(E),f(H,E))

4.1.5 Synthesis of conclusion uncertainty

Find the uncertainty C1(H) and C2(H) of hypothesis H obtained from two independent pieces of evidence E1 and E2. Find the uncertainty of hypothesis H caused by the combination of evidence E1 and E2.
That is, define the function C(H)=f2(C1(H),C2(H))