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# Boolean and Fuzzy Logic

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## Jyoshitha Tella

on 2 September 2014

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#### Transcript of Boolean and Fuzzy Logic

Fuzzy Logic Around the World
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

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
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!!!
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