View by Category

The presentation will start after a short

(15 second) video ad from one of our sponsors.

Hot tip: Video ads won’t appear to registered users who are logged in. And it’s free to register and free to log in!

(15 second) video ad from one of our sponsors.

Hot tip: Video ads won’t appear to registered users who are logged in. And it’s free to register and free to log in!

Loading...

PPT – Fuzzy Sets and Basic Operations on Fuzzy Sets PowerPoint presentation | free to download - id: d0ca5-YmNkN

The Adobe Flash plugin is needed to view this content

About This Presentation

Write a Comment

User Comments (0)

Transcript and Presenter's Notes

Fuzzy Sets and Basic Operations on Fuzzy Sets

- Ch. 2

Example Cars in Berkeley

- U all the cars in Berkeley, CA
- some sets
- X cylinder cars (X 4, 6, 8, ??, etc.)
- foreign cars
- American cars
- Write in set notation
- Write in discrimination function notation.

- Questions
- What car manufacturers are American?
- how many US-made parts are required for a car to

be classified as Made-in-America? - Are there clear set boundaries?

Classical vs. Fuzzy Sets

- Classical (or crisp) set theory is used when the

set boundaries are clear and easy to distinguish.

(black and white) - Fuzzy set theory is used when the set boundaries

are not clear and easy to distinguish. (shades of

gray)

Classical Sets Fuzzy Sets

- U is the
- universal set or
- universe of discourse
- Recall that a classical set A or a (crisp set) in

the universe of discourse can be defined by - listing all of its members
- specifying the properties that members must have

- Membership, Characteristic (or discrimination)

function

Fuzzy Sets Representation

- A fuzzy set in a universe of discourse U is

characterized by a membership function that takes

values in the interval 0, 1. - Representations

Cars in Berkeley (cont.)

- D is the set of domestic (I.e. American) cars in

Berkeley. - How do you quantify the domesticity of a car?
- p(x)

- F is the set of foreign cars in Berkeley. F is

the set of non domestic cars in Berkeley.

(No Transcript)

Numbers close to ZERO

Numbers Close to ZERO

Comments

- Fuzzy sets characterize fuzzy properties
- Close to zero, hot, cold, fast, slow
- How to determine membership functions?
- Use human experts
- Use sensor data
- Are humans sensors?
- The Gaussian and Triangular membership functions

that described close to zero defined different

fuzzy sets even though they tried to describe the

same concept.

Basic Concepts of Fuzzy Sets

- Consider a fuzzy set A in the universe of

discourse U - The support is the crisp set that contains all of

the elements in U that have non zero membership

values

- If the support of a fuzzy set is empty, it is

called the empty fuzzy set. - A fuzzy singleton is a fuzzy set whose support is

a single point in U.

Activity Define hot warm comfortable

cool cold

Basic Concepts of Fuzzy Sets

- The following fuzzy sets help motivate the

concept of the center of a fuzzy set.

- For A2 the center is clear it is where the

function peaks - For A3 it is the center of the plateau.
- For A1, and A4 it is where the function becomes a

max that is closest to the origin.

Basic Concepts of Fuzzy Sets

- The crossover point(s) of a fuzzy set is(are) the

point(s) in U whose membership value equals .5. - The height of a fuzzy set is the largest

membership value attained by any point. - A normal fuzzy set has height of 1.
- An alpha-cut of a fuzzy set is a crisp set that

contains all the elements in U that have

membership values greater than alpha

Multi-Dimensional Fuzzy Sets

- IF Temperature is HOT and Humidity is LOW THEN

set cooling-level ______ and fan-speed ________

Operations on Fuzzy Sets

- Assume that A and B are fuzzy sets in the same

Universe of Discourse, U.

- Equality
- containment
- complement
- union
- intersection

Example

- Given fuzzy sets Close-to-zero and Close-to-one,

determine the union and intersection.

- Is one contained in the other?
- Draw a fuzzy set contained in another fuzzy set.

Example

- Given fuzzy sets, close-to-0 and determine its

complement

Crisp vs. Fuzzy Set Theory

- The basic definitions and operations of set

theory determine what Theorems are true. - Question Are any of the Theorems of Crisp set

Theory true in Fuzzy Set Theory? - Ans Yes
- Question Are all of the Theorems of Crisp Theory

true in Fuzzy Set Theory? - Ans No
- How do we Tell?
- Try to Prove them.
- Is this good?
- Yes. Different Theorems allow us to solve

different problems.

DeMorgans Laws

- Very useful theorems in Crisp set Theory and

Logic. (Remember from Boolean Algebra?) - Do they hold in Fuzzy Set Theory?
- Translate into Fuzzy Set Theory
- Express in terms of membership functions

- DeMorgans Law is valid provided the following

equality is valid

Proof of DeMorgans LAW

- We break this up into 2 simpler cases that

describe all possible situations - The left is easy once we know which membership

function is largest

Homework/Quiz

- Read
- Exercises 2.1, 2.2, 2.3, 2.5, 2.6, 2.7
- Quiz One of the parts in exercise 2.3

- Comments
- Read about alpha-cuts, projections (and

hyperplanes) - Failure of Law of Excluded Middle in Fuzzy Set

Theory (Exercise 2.6) is a major distinction

between Crisp and Fuzzy Set Theory - These differences allow the theories to solve

different problems

About PowerShow.com

PowerShow.com is a leading presentation/slideshow sharing website. Whether your application is business, how-to, education, medicine, school, church, sales, marketing, online training or just for fun, PowerShow.com is a great resource. And, best of all, most of its cool features are free and easy to use.

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

Recommended

«

/ »

Page of

«

/ »

Promoted Presentations

Related Presentations

Page of

Page of

CrystalGraphics Sales Tel: (800) 394-0700 x 1 or Send an email

Home About Us Terms and Conditions Privacy Policy Contact Us Send Us Feedback

Copyright 2017 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

Copyright 2017 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

The PowerPoint PPT presentation: "Fuzzy Sets and Basic Operations on Fuzzy Sets" is the property of its rightful owner.

Do you have PowerPoint slides to share? If so, share your PPT presentation slides online with PowerShow.com. It's FREE!

Committed to assisting Mercer University and other schools with their online training by sharing educational presentations for free