Fuzzy logic - Discrete Mathematics - Computer Science

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Fuzzy Logic And Its
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2. Why Fuzzy Logic is its
self?• For Examples
• Engineers can use the package to research,
model, test, and visualize real systems from the
most basic to the highly complex.
• Researchers can use the package's
comprehensive set of Fuzzy Logic tools to
investigate applications of fuzzy theory and new
ideas in the field.
• Educators can use Fuzzy Logic to teach
concepts, basic theory, and applications of Fuzzy
Logic, using the package alone or as a
complement to a class text.
• Students can use the examples in the package to
help solve a large variety of problems in step-by-
step detail.
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Fuzzy Logic And Its
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3. Learning Object
• What is The Fuzzy Concepts?
• What is a Fuzzy Set?
• What is a Fuzzy Logic?
• What are some applications of fuzzy logic?
• How is it that fuzzy systems have been successfully
applied to such a wide variety of applications?
• How are fuzzy sets defined in Fuzzy Logic?
• What are fuzzy relations, and does Fuzzy Logic support
them?
• Can fuzzy relations be graphed like fuzzy sets?
• How are Fuzzy Sets created in Fuzzy Logic?
• Can Fuzzy Logic participate in the digital revolution?
• What's New in Fuzzy Logic?
• Lotfi Zadeh In Lines.
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Fuzzy Logic And Its
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4. What Is a Fuzzy
Concepts?• In classical sets, objects either belong to a set or do
not belong to a set; there is no other choice. By
defining a set using a membership function, it is
possible for an element to belong partially to a set.
and Common Sense: analysis of a
experience.
• In France Say : “C’est une Femme est très La
Vache”.
• In Arabic Say : “‫ات‬َ‫ه‬َّ‫م‬ُ‫األ‬ ِ‫ام‬َ‫د‬‫أق‬ َ‫ت‬ْ‫ح‬َ‫ت‬ ُ‫ة‬َّ‫ن‬‫.”الج‬
• In English Say : “if my feet in your shoes”.
• These is Called : Fuzzy Thinking.
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Fuzzy Logic And Its
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5. What is a Fuzzy Set?
• A Fuzzy Set is a set that is defined by a membership
function. A membership function assigns to each element
in the set under consideration (the universal space) a
membership grade, which is a value in the interval [0, 1].
• In Classical Sets, objects either belong to a set or do not
belong to a set; there is no other choice.
• By defining a set using a membership function, it is
possible for an element to belong partially to a set.
• For Example: if a door is slightly ajar, one might say that
the door is open, with a membership grade of 0.2 to
indicate that the door is slightly open. We might also say
that the door is closed, with a membership grade of 0.8.
• By using a Fuzzy Set, we are able to indicate that the
door is partially open or partially closed.
• Using Classical Logic, we would not be able to do this; the
door would be considered either open or closed with no
in-between.
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Fuzzy Logic And Its
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6. What is a ?
• Fuzzy Logic is an extension of classical logic and uses
Fuzzy Sets rather than Classical Sets. There are a few
different explanations of what Fuzzy Logic is, so rather
than add our own explanation, we will quote one
explanation put forth by Lotfi A. Zadeh.
• The Father of Fuzzy Logic. Zadeh says: "In its narrow sense, Fuzzy
Logic is a logic of approximate reasoning which may be viewed as
a generalization and extension of multi-valued Logic. But in a
broader and much more significant sense, Fuzzy Logic is
coextensive with the theory of Fuzzy Sets, that is, classes of
objects in which the transition from membership to non membership
is gradual rather than abrupt.
• In its wider sense, Fuzzy Logic has many branches ranging from
fuzzy arithmetic and fuzzy automata to fuzzy pattern recognition,
fuzzy languages, and fuzzy expert systems."
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Fuzzy Logic And Its
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7. • The use of for creating decision-
support and expert systems has grown in popularity
among management and financial decision-modeling
experts.
• Still others are putting it to work in pattern
recognition, economics, data analysis, and other
areas that involve a high level of uncertainty,
complexity, or nonlinearity.
• There are presently numerous applications that
incorporate control.
• Some of the more prominent applications are
electronically stabilized camcorders, autofocus
cameras, washing machines, air conditioners,
automobile transmissions, subway trains, and
cement kilns.
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Fuzzy Logic And Its
Applications

8. How is it that have been
successfully applied to such a wide variety of
applications?• Fuzzy "if-then" rules are often employed to
capture the imprecise modes of reasoning that
play an essential role in the human ability to
make decisions in uncertain and imprecise
environments. These Fuzzy "if-then" rules are
used extensively in both Fuzzy modeling and
control.
• “if-then” : ‫المشروط‬ ‫التفرع‬ ‫تعليمة‬
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Fuzzy Logic And Its
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9. How are defined in
?
• In , are defined
on a discrete universal space.
are characterized by pairs, {{x1,
u1}, {x2, u2}, ..., {xn, un}}, which consist
of the elements of the , x1,
x2, ..., xn, and the membership grades of
the elements, u1, u2, ..., un (membership
grades are from the range [0, 1]).
• The discrete universal space allows for
quick calculations and provides unique
visualization opportunities.
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Fuzzy Logic And Its
Applications

10. What are , and does
support Them?
• A represents the degree
of strength of the association or
interaction between the elements of two
or more sets. contains a
wide array of functions for creating and
operating on or with .
• In fact, most of the functions that work
with also work with
.
Fuzzy Logic And Its
Applications 10
Figure is a Random Fuzzy
Relation

11. Can be graphed like
?
• Yes, they can.
contains plotting functions for
producing different types of three-
dimensional plots of
.
• There are discrete, surface, and
wire frame-type plots. In addition,
can be viewed as
membership matrices, which are
also supported by .
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Fuzzy Logic And Its
Applications

12. How are created in
?• There are numerous ways to create
in .
• The package provides functions for creating
using some common
membership functions such as ,
, or .
• Also, can be created with
functions, provided the
functions return membership grades in the
range [0, 1].
• Also, there is a function for creating a
collection of that are evenly
distributed over the universal space.
• If you don't want to use a function at all, you
can also create a manually by
defining the individual elements and
membership grades.
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Fuzzy Logic And Its
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13. How are created in
?• Figure (Fuzzy Sets are Created in Fuzzy
Logic)…
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Fuzzy Logic And Its
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Gaussian Fuzzy
SetTrapezoidal Fuzzy
SetUser-Defined Fuzzy
SetTriangular Fuzzy
Set

14. Can participate in the
digital revolution?
• It definitely can. provides functions for
creating digital with different numbers
of the membership grade levels.
• These digital create the opportunity to
process digital images and to apply them to multi-
valued logic. With the advance of VLSI
technologies, we expect that fuzzy chips will play an
increasingly important role in control automation.
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Fuzzy Logic And Its
Applications

15. What’s New In ?
• Universal space now defined
with three numbers that
specify the start and end of the
universal space and the
increment between elements,
giving users a greater flexibility
in choosing the universal
space
• Membership functions to
create special types of fuzzy
sets, including bell-shaped,
sigmoid, two-sided Gaussian,
and digital fuzzy sets
• Visualization tool, fuzzy graph,
to show what a set of fuzzy
rules looks like
Fuzzy Logic And Its
Applications 15

16. Lotfi Zadeh In Lines
• The was introduced by
Professor Lotfi Zadeh in and can be
seen as an infinite - valued logic. Lotfi Zadeh
is currently serving as a director of BISC
(Berkeley Initiative in Soft Computing). Prior
to Zadeh's work had been centered on
system theory and decision analysis. Since
then, his research interests have shifted to
the theory of Fuzzy Sets and its applications
to artificial intelligence, linguistics, logic,
Decision Analysis, Control Theory, Expert
Systems and Neural Networks. Currently, his
research is focused on , soft
computing, computing with words, and the
newly developed computational theory of
perceptions and natural language.
Fuzzy Logic And Its
Applications 16

17. • 1.^ http://www.wolfram.com/products/applications/anm/features.html
• 2.^ http://www.math.psu.edu/simpson/courses/math557/logic.pdf
• 3.^ http://www.wolfram.com/products/applications/fuzzylogic/for.html
• 4.^ http://www.wolfram.com/products/applications/fuzzylogic/newin2/
• 5.^ http://www.wolfram.com/products/applications/fuzzylogic/qanda.html
• 6.^ http://www.wolfram.com/products/applications/fuzzylogic/examples/
• 7.^ http://www.wolfram.com/products/applications/fuzzylogic/for.html
• 8.^ http://www.adalta.it/Pages/160.asp
• 9.^ http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TY8-42RVSF8-
• 10.^
http://www.google.com/search?hl=en&source=hp&q=Math+logic+is+very+Great+.pdf&aq=o&
oq=&aqi=
• 11.^ http://image.google.com/Lotfi _Zadeh/image.png/image.jpg
• 12.^ The Film Is Collected By Tarek Kala’ajy – Type WMV
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