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NNFL-Unit 4

This document provides an introduction to classical and fuzzy sets. It begins with an overview of classical set theory, including properties, operations, and relations of classical sets. It then introduces fuzzy set theory, explaining that fuzzy sets allow for partial membership rather than crisp membership as in classical sets. Membership is defined through membership functions that assign a value between 0 and 1. The document outlines some basic fuzzy set operations and properties of fuzzy sets, including fuzzy relations. It discusses applications of fuzzy logic in areas like control systems and decision making. Finally, it provides advantages and disadvantages of fuzzy logic systems.

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244 views58 pages

NNFL-Unit 4

This document provides an introduction to classical and fuzzy sets. It begins with an overview of classical set theory, including properties, operations, and relations of classical sets. It then introduces fuzzy set theory, explaining that fuzzy sets allow for partial membership rather than crisp membership as in classical sets. Membership is defined through membership functions that assign a value between 0 and 1. The document outlines some basic fuzzy set operations and properties of fuzzy sets, including fuzzy relations. It discusses applications of fuzzy logic in areas like control systems and decision making. Finally, it provides advantages and disadvantages of fuzzy logic systems.

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CRR EEE3Y2
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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R1632025

NEURAL NETWORKS & FUZZY LOGIC

UNIT-4: CLASSICAL & FUZZY SETS

S R SAGAR
DEPARTMENT OF EEE
COURSE INFORMATION-UNIT 4
Unit 3 Syllabus
Unit-4: Classical & Fuzzy Sets
Introduction to classical sets - properties, Operations and relations; Fuzzy sets,
Membership, Uncertainty, Operations, properties, fuzzy relations, cardinalities,
membership functions.
Text Book
TEXT Neural Networks, Fuzzy logic, Genetic algorithms: synthesis and applications by S
BOOK Rajasekaran and Vijayalakshmi Pai – PHI Publication.
T1

Unit 3 Learning or Course Outcome


CO Classify classical and fuzzy sets and explain properties, operations, and
PO2,PO3
32025.3 relations of fuzzy sets.

Prerequisites:
Knowledge of Set Theory, Logic, and Engineering Mathematics
Introduction
Introduction
The word fuzzy refers to things which are not clear or are vague.
Fuzzy Logic resembles the human decision-making methodology and
deals with vague and imprecise information.

Fuzzy Logic was introduced in 1965 by Lofti A. Zadeh in his research


paper “Fuzzy Sets”. He is considered as the father of Fuzzy Logic.
Unit 4 Part 1
Classical Set Theory
Classical sets - properties, operations and relations
Unit 4 Part 2
Fuzzy set Theory
Traditional representation of logic

Slow Fast
Speed = 0 Speed = 1

CODE:
bool speed;
get the speed
if ( speed == 0)
{
// speed is slow
}
else
{
// speed is fast
}
Fuzzy logic representation

 For every problem Slowest


must represent in [ 0.0 – 0.25 ]
terms of fuzzy sets.

 What are fuzzy Slow


sets? [ 0.25 – 0.50 ]

Fast
[ 0.50 – 0.75 ]

Fastest
[ 0.75 – 1.00 ]
Fuzzy logic representation, cont.

Slowest Slow Fast Fastest


float speed;
get the speed
if ((speed >= 0.0)&&(speed < 0.25)) {
// speed is slowest
}
else if ((speed >= 0.25)&&(speed < 0.5))
{
// speed is slow
}
else if ((speed >= 0.5)&&(speed < 0.75))
{
// speed is fast
}
else // speed >= 0.75 && speed < 1.0
{
// speed is fastest
}
Fuzzy logic is a convenient way to map an input space to an output space
Advantages of Fuzzy Logic System
•This system can work with any type of inputs whether it is imprecise, distorted or noisy
input information.
•The construction of Fuzzy Logic Systems is easy and understandable.
•Fuzzy logic comes with mathematical concepts of set theory and the reasoning of that is
quite simple.
•It provides a very efficient solution to complex problems in all fields of life as it resembles
human reasoning and decision making.
•The algorithms can be described with little data, so little memory is required.

Disadvantages of Fuzzy Logic Systems


•There is no systematic approach to solve a given problem through fuzzy logic.
•Proof of its characteristics is difficult or impossible in most cases because every time we
do not get mathematical description of our approach.
•As fuzzy logic works on precise as well as imprecise data so most of the time accuracy is
compromised.
Application
•It is used in the aerospace field for altitude control of spacecraft and satellite.
•It has used in the automotive system for speed control, traffic control.
•It is used for decision making support systems and personal evaluation in the large
company business.
•It has application in chemical industry for controlling the pH, drying, chemical
distillation process.
•Fuzzy logic are used in Natural language processing and various intensive
applications in Artificial Intelligence.
•Fuzzy logic are extensively used in modern control systems such as expert
systems.
•Fuzzy Logic is used with Neural Networks as it mimics how a person would make
decisions, only much faster. It is done by Aggregation of data and changing into
more meaningful data by forming partial truths as Fuzzy sets.
Fuzzy sets
Classical set

Fuzzy set
Basic Fuzzy Set Operations
Properties of Fuzzy Sets
Fuzzy relations

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