Boolean Logic

To be or not to be... a member of a set.

Crisp Set Theory

:

Either true or false

Either black or white

Either 0 or 1

Either tall or short

Boolean is used when there is an

absolute certainty

about a value, and there are only

two possible values

.

Boolean Math

**Cloud Computing Risk Analysis**

**Fuzzy Applications**

**Boolean Applications**

set operators AND, OR and NOT

Examples

Turning 18

Height: Tall or not?

On and off

True or false

Action potential in a neuron

Why Cloud Computing?

**By: Ankita Prakash Amajuri**

A2305213525, 3CSE2X

A2305213525, 3CSE2X

Fuzzy

Math

NOT Operator

AND Operator

OR Operator

If Fuzzy Statement A is m is true, then the statement

“Not A” is (1.0 – m) true

(where m is a number between 0.0 and 1.0 inclusive).

Ex: if A = .2,

then NOT A = (1 - .2) = .8

Equivalent Set Theory Operation

Equivalent Set Theory operation: If an object A has m

membership in Fuzzy Set S, then it must have membership (1.0 – m) in Fuzzy Set Not-S.

Ex: {A} = {(a, .2), (b, .9), (c, .5)...}

{NOT A} = {(a, .8), (b, .1), (c, .5)...}

If the Fuzzy Statement A is m is true, and Fuzzy Statement B is n is true, then the Fuzzy Statement “A and B” is k true, where

k = min(m, n)

. (Here, m, n and k are numbers between 0.0 and 1.0 inclusive.)

Example: (.1 AND .9) = min ( .1, .9) = .1

If Fuzzy Statement A is m is true, and Fuzzy Statement B is n is true, then the Fuzzy Statement “A or B” is k true, where

k = max(m,n)

. (Here, m, n and k are numbers between 0.0 and 1.0 inclusive.)

Fuzzification

Rule Evaluation

Defuzzification

Fuzzy Control

Using membership functions to graphically describe a situation.

Here, each member is assigned a "degree of membership" in all the sets being considered.

Application of fuzzy rules.

Here, one defines the functions (using members and operators) that will be used to determine the results.

Obtaining Crisp or actual results.

This is where you are no longer "fuzzy" because a "YES OR NO" answer has been reached.

Ex: (.3 OR .7) = max( .3 , .7) = .7

Have I used the Cloud before?

Sendai Subway system in Sendai, Japan.

Energy Saving Air Conditioner Controls and thermostats

Adaptive Heating System Control

Rice Cooker

NeuroFuzzy Signal Analysis in Washing Machines

Artificial intelligence

Artificial Life

Artificial Neural Networks

Data Mining

Genetic Algorithms

Intelligent User Interfaces

Robotics

Artificial or computer based systems which exhibit life like behavior.

Visual pattern recognition

Differentiating human faces

Speech and handwriting recognition

Using a computer to examine and locate information that may have complex parameter connectivity(specifications that you are looking for).

Data sets(populations) attempt to mimic natures adaptive way of solving problems by the survival of the fittest.

When all of the population has been tested, various operators are used to select a new population.

Learning systems are designed to interact with the learner to provide a learning environment which suites the individual and is constantly revised and customized based on "fuzzy" inputs regarding an array of related topics.

Robots that are designed to act like humans and have human-like intelligence use "fuzzy" inputs to make intelligent decisions.

Circuits

Parallel Circuits

Parallel circuits use OR gates with 0s and 1s, OFF and ON.

Series Circuits

Series circuits use AND gates with 0s and 1s, OFF and ON.

Users in

Asia

:

China

Japan

India

Singapore

All major Japanese companies spend $2-3 bn on integrating fuzzy logic.

Fuzzy logic technologies are largely ignored by

USA

In

Europe

, France and Germany conduct fuzzy logic research

Binary Search

We want more memory!!!

Physical Storage Devices:

Floppy disks

CDs

USB Drives

External Hard Drives

Physical storage can also get VERY EXPENSIVE!!!