CHAPTER 5 Handling Uncertainty BIC 3337 EXPERT SYSTEM

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. BIC 3337 EXPERT SYSTEM

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. BIC 3337 EXPERT SYSTEM

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. BIC 3337 EXPERT SYSTEM

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. BIC 3337 EXPERT SYSTEM

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 BIC 3337 EXPERT SYSTEM

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. BIC 3337 EXPERT SYSTEM