1. CHAPTER 5
Handling Uncertainty
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2. INTRODUCTION Standard statistical methods are based on
the assumption that an uncertainty is the
probability that an event (or fact) is true or
false. In certainty theory, as well as in fuzzy
logic, uncertainty is represented as a degree
of belief. There are two steps in using every
non-probabilistic method of uncertainty.
Uncertainty is an important component in
ES. It is treated as a three-step process in
AI.
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3. INTRODUCTION In Step 1, an expert provides inexact
knowledge. In Step 2, the inexact knowledge
of the basic set of events can be directly used
to draw inferences in simple cases (Step 3). In
Step 3, knowledge-based system is to draw
inferences.
1st,it is necessary to be able to express
the degree of belief. 2nd, it is to manipulate
(combine, for example) degrees of belief when
using knowledge - based systems.
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4. CERTAINTY THEORY Certainty theory relies on the use of certainty
factors. Certainty factors (CFs) express belief
in an event (or fact or hypothesis) based on
evidence (or on the expert’s assessment).
There are several methods of using certainty
factors in handling uncertainty in knowledge-
based systems. One way is to use 1.0 or 100
for absolute truth (complete confidence) and
0 for certain falsehood. These certainty
factors are not probabilities.
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5. BAYES THEORY Bayesian mathematical model is the oldest
method for modeling subjective degree of
belief. If we have probabilistic measures with
unknown values, then we must choose a
different and appropriate model.
The belief functions are a bridge between
various models handling different forms of
uncertainty. The conjunctive rules of Bayes
builds a new set of posteriori probability
when two random variables make inference.
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6. FUZZY LOGIC Fuzzy logic is derived from fuzzy set theory
dealing with reasoning that is approximate
rather than precisely deduced from classical
predicate logic. It can be thought of as the
application side of fuzzy set theory dealing
with well thought out real world expert
values for a complex problem (Klir 1997).
Fuzzy logic allows for set membership
values to range (inclusively) between 0 and 1
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7. FUZZY LOGIC In linguistic form, fuzzy logic refers to
imprecise concepts like "slightly", "quite" and
"very". Specifically, it allows partial
membership in a set. It is related to fuzzy sets
and possibility theory.
It extends the notion of logic beyond a simple
true / false to allow for partial (or even
continuous) truths. In fuzzy logic, the value of
true or false is replaced by the degree of set
membership.
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