Introduction to Rule-Based Systems, Expert Systems, Fuzzy ... · `Fuzzification- rule evaluation- defuzzification' inference ... •mean of maxima ... Introduction to Rule-Based Systems,

Introduction to Rule-Based

Systems, Expert Systems, Fuzzy

Systems

(sections 2.7, 2.8, pp. 118-132; and

partially 3.1 and 3.4)

N. Kasabov, Foundations of Neural Networks, Fuzzy Systems, and Knowledge Engineering, MIT Press, 1996

Sub-topics:

Production rules and production systems

How to program in rules?

Advantages and limitations of the production systems

Expert systems

Fuzzy sets

Fuzzy rules and fuzzy inference

Fuzzy information retrieval and fuzzy databases

Fuzzy expert systems


Production Rules and

Production Systems

A production rule consists of two parts: condition

(antecedent) part and conclusion (action, consequent) part,

i.e: IF (conditions) THEN (actions)

Example

IF Gauge is OK AND [TEMPERATURE] > 120

THEN Cooling system is in the state of overheating



Production Systems...

This rule consists of 2 propositions given on separate lines

(2 condition elements) and a conclusion. The second

condition element contains a variable. Condition elements in

a rule can be connected by different connectives, the most

used being AND, OR, NOT.




A production system consists of:

• Working memory (facts memory)

• Production rules memory

• Inference engine, it cycles through three steps:

– match facts against rules

– select a rule

– execute the rule





Figure

2.25:

A

production

system

cycle

How to Program in Production

Rules?


Figure 2.27:

A program

written in a

production

language for the

family

relationship

problem

Advantages and Limitations of

the Production Systems (PS):

PS are universal computational mechanism

PS are universal function approximators

readability

explanation

expressiveness

modularity


Expert Systems


They are information systems for solving a specific

problem which provides an expertise similar to those of

experts in the problem area.

An ES contains expert knowledge.

Expert Systems...


A typical ES architecture consists of:

• knowledge base module

• working memory module (for the current data)

• inference engine

• forward chaining (inductive, data driven)

• backward chaining (deductive, goal driven)

• user interface (possibly a NLI, menu, windows, etc)

• explanation module

Expert Systems...


Figure 2.29:

An expert system architecture

Expert Systems...

`How' and `Why' explanations in ES


Figure 2.30

HOW and

WHY

explanation

for The Car

Monitoring

Production

System

Data Analysis...


Expert systems design

• identification

• conceptualization

• formalization

• realization

• validation

The knowledge acquisition problem:

• interview experts

• learning from data

• literature

• agents on the Web

Fuzzy Sets


Figure 3.1

Membership

functions

representing

three fuzzy

sets for the

variable

"height".

Fuzzy Sets...


Figure 3.2

Representin

g crisp and

fuzzy sets

as subsets

of a domain

(universe)

U

Fuzzy Sets...


Figure 3.3

Support of a

fuzzy set A

see also fig 3.21 for an example of fuzzy sets definitions

for the The Bank Loan Decision problem.

Building Fuzzy Expert System

A typical process in developing the fuzzy expert

system incorporates the following steps:

1. Specify the problem and define linguistic

variables.

2. Determine fuzzy sets.

3. Elicit and construct fuzzy rules.

4. Encode the fuzzy sets, fuzzy rules and

procedures to perform fuzzy inference into the

expert system.

5. Evaluate and tune the system.

Fuzzy Rules and Fuzzy

Inference


Rule 1: IF (CScore is high) and (CRatio is good) and

(CCredit is good)

then (Decision is approve)

Rule 2: IF (CScore is low) and (CRatio is bad) or (CCredit

is bad)

then (Decision is disapprove)


Inference...


Inputs to a fuzzy system can be:

• fuzzy, e.g. (Score = Moderate), defined by membership

functions

• exact, e.g.: (Score = 190); (Theta = 35), defined by

crisp values.

Outputs from a fuzzy system can be:

• fuzzy, i.e. a whole membership function, or

• exact, i.e. a single value is produced on the output.


Inference...


Fuzzy inference methods:

`Fuzzification- rule evaluation- defuzzification' inference

see Figure 3.27 for an illustration of "crisp input data

rules evaluation defuzzification" inference for a

particular crisp input data for the Bank Loan

Decision system.


Inference...


Methods for defuzzification:

• center of gravity

• mean of maxima

see Figure 3.26

Methods of defuzzification: the

centre of gravity method (COG),

and the mean of maxima method

(MOM) applied over the same

membership function for a fuzzy

output variable y. They calculate

different crisp output values.

Fuzzy Information Retrieval

and Fuzzy Databases


Fuzzy interfaces to standard databases

(see fig 3.32)

Fuzzy databases (see fig. 3.33)

Fuzzy expert system shells (see fig. 3.36, 3.37)

Fuzzy Information Retrieval

and Fuzzy Databases...


Fuzzy expert systems

Figure 3.35:

A block diagram

of a fuzzy expert

system.

Fuzzy Expert Systems

Fuzzy systems are:

• easy to develop and debug

• easy to understand

• easy and cheap to maintain


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Introduction to Rule-Based Systems, Expert Systems, Fuzzy ... · `Fuzzification- rule evaluation- defuzzification' inference ... •mean of maxima ... Introduction to Rule-Based Systems,