Fuzzy logic is a form of logic that deals with reasoning that is approximate rather than fixed and exact. It allows for partial truth and handles incomplete or ambiguous data. Fuzzy logic originated with Lotfi Zadeh's 1965 proposal of fuzzy set theory and has since been applied to fields like control systems and artificial intelligence. It represents values through fuzzy sets defined by membership functions rather than binary variables. This allows for linguistic variables like "temperature is cold" that can be evaluated to degrees between true and false. Fuzzy logic uses IF-THEN rules to model human reasoning and has been used in applications like temperature controllers and anti-lock braking systems.
How can you deal with Fuzzy Logic. Fuzzy logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact. In contrast with traditional logic theory, where binary sets have two-valued logic: true or false, fuzzy logic variables may have a truth value that ranges in degree
between 0 and 1
Fuzzy logic is a form of many-valued logic that allows intermediate values between conventional assessments like true/false, yes/no, or 0/1. It is used to model imprecise concepts and has applications in control systems, image processing, decision making, and more. Fuzzy logic uses linguistic variables and IF-THEN rules to relate inputs to outputs. Membership functions assign a degree of truth between 0 and 1 to indicate how strongly an element belongs to a set. Fuzzy logic provides an effective way to deal with uncertainty and imprecision in real-world problems.
Fuzzy Logic
Where did it begin?
What is Fuzzy Logic?
Fuzzy Logic in Control Systems
Fuzzy Logic in Other Fields
Fuzzy Logic vs. Neural Networks
Fuzzy Logic Benefits
Fuzzy logic is a form of logic that deals with reasoning that is approximate rather than precise. It allows intermediate values to be defined between conventional evaluations like true/false, and uses a continuum of truth values between 0 and 1. Fuzzy logic is useful for problems with imprecise or uncertain data, and can represent human reasoning that uses approximate terms like "warm" or "fast". It has been applied in various systems to control variables like temperature, speed, and focus based on fuzzy linguistic rules.
Fuzzy logic is a form of logic that deals with reasoning that is approximate rather than precisely defined. It was first developed in 1965 and allows for modeling of systems with imprecise or uncertain inputs. Fuzzy logic controllers use fuzzy sets and membership functions to model linguistic variables like "temperature is high" and control systems using if-then rules. The main components of a fuzzy logic controller are fuzzification, a knowledge base of rules, an inference strategy, and defuzzification. Fuzzy logic has been applied to control systems like temperature controllers and ABS braking to handle imprecise inputs more effectively than traditional binary logic.
Fuzzy logic is a form of multivalued logic that deals with approximate reasoning rather than binary logic. It allows intermediate values between conventional evaluations like true/false, yes/no, or 0/1. Fuzzy logic variables can have membership values between 0 and 1 and are not constrained to two truth values. It has been applied to fields like control theory and artificial intelligence. Fuzzy logic uses IF-THEN rules to represent knowledge with linguistic terms rather than precise quantitative values and allows for gradual transitions between categories.
Logika Fuzzy merupakan suatu logika yang memiliki nilai kekaburan atau kesamaran (fuzzyness) antara benar atau salah. Dalam logika klasik dinyatakan bahwa segala hal dapat
diekspresikan dalam istilah binary (0 atau 1, hitam atau putih, ya atau tidak), sedangkan logika fuzzy memungkinkan nilai keanggotaan antara 0 dan 1, tingkat keabuan dan juga hitam dan putih, dan dalam bentuk linguistik, konsep tidak pasti seperti "sedikit", "lumayan" dan "sangat". Logika ini berhubungan dengan himpunan fuzzy dan teori kemungkinan. Logika fuzzy ini diperkenalkan oleh Dr. Lotfi Zadeh dari Universitas California, Berkeley pada 1965. Logika fuzzy dapat digunakan dalam bidang teori kontrol, teori keputusan, dan beberapa bagian dalam managemen sains. Selain itu, kelebihan dari logika fuzzy adalah kemampuan dalam proses penalaran secara bahasa (linguistic reasoning), sehingga dalam perancangannya tidak memerlukan persamaan matematik dari objek yang dikendalikan.
This document discusses fuzzy logic, beginning with its origins in ancient Greece and formalization in 1965 by Lotfi Zadeh. It explains fuzzy logic represents concepts with overlapping membership functions rather than binary logic. Fuzzy logic and neural networks both model human reasoning but fuzzy logic uses linguistic rules while neural networks learn from examples. Fuzzy logic has applications in control systems like temperature controllers and anti-lock braking systems to handle nonlinear dynamics. It is used in other fields like business and expert systems to represent subjective concepts.
How can you deal with Fuzzy Logic. Fuzzy logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact. In contrast with traditional logic theory, where binary sets have two-valued logic: true or false, fuzzy logic variables may have a truth value that ranges in degree
between 0 and 1
Fuzzy logic is a form of many-valued logic that allows intermediate values between conventional assessments like true/false, yes/no, or 0/1. It is used to model imprecise concepts and has applications in control systems, image processing, decision making, and more. Fuzzy logic uses linguistic variables and IF-THEN rules to relate inputs to outputs. Membership functions assign a degree of truth between 0 and 1 to indicate how strongly an element belongs to a set. Fuzzy logic provides an effective way to deal with uncertainty and imprecision in real-world problems.
Fuzzy Logic
Where did it begin?
What is Fuzzy Logic?
Fuzzy Logic in Control Systems
Fuzzy Logic in Other Fields
Fuzzy Logic vs. Neural Networks
Fuzzy Logic Benefits
Fuzzy logic is a form of logic that deals with reasoning that is approximate rather than precise. It allows intermediate values to be defined between conventional evaluations like true/false, and uses a continuum of truth values between 0 and 1. Fuzzy logic is useful for problems with imprecise or uncertain data, and can represent human reasoning that uses approximate terms like "warm" or "fast". It has been applied in various systems to control variables like temperature, speed, and focus based on fuzzy linguistic rules.
Fuzzy logic is a form of logic that deals with reasoning that is approximate rather than precisely defined. It was first developed in 1965 and allows for modeling of systems with imprecise or uncertain inputs. Fuzzy logic controllers use fuzzy sets and membership functions to model linguistic variables like "temperature is high" and control systems using if-then rules. The main components of a fuzzy logic controller are fuzzification, a knowledge base of rules, an inference strategy, and defuzzification. Fuzzy logic has been applied to control systems like temperature controllers and ABS braking to handle imprecise inputs more effectively than traditional binary logic.
Fuzzy logic is a form of multivalued logic that deals with approximate reasoning rather than binary logic. It allows intermediate values between conventional evaluations like true/false, yes/no, or 0/1. Fuzzy logic variables can have membership values between 0 and 1 and are not constrained to two truth values. It has been applied to fields like control theory and artificial intelligence. Fuzzy logic uses IF-THEN rules to represent knowledge with linguistic terms rather than precise quantitative values and allows for gradual transitions between categories.
Logika Fuzzy merupakan suatu logika yang memiliki nilai kekaburan atau kesamaran (fuzzyness) antara benar atau salah. Dalam logika klasik dinyatakan bahwa segala hal dapat
diekspresikan dalam istilah binary (0 atau 1, hitam atau putih, ya atau tidak), sedangkan logika fuzzy memungkinkan nilai keanggotaan antara 0 dan 1, tingkat keabuan dan juga hitam dan putih, dan dalam bentuk linguistik, konsep tidak pasti seperti "sedikit", "lumayan" dan "sangat". Logika ini berhubungan dengan himpunan fuzzy dan teori kemungkinan. Logika fuzzy ini diperkenalkan oleh Dr. Lotfi Zadeh dari Universitas California, Berkeley pada 1965. Logika fuzzy dapat digunakan dalam bidang teori kontrol, teori keputusan, dan beberapa bagian dalam managemen sains. Selain itu, kelebihan dari logika fuzzy adalah kemampuan dalam proses penalaran secara bahasa (linguistic reasoning), sehingga dalam perancangannya tidak memerlukan persamaan matematik dari objek yang dikendalikan.
This document discusses fuzzy logic, beginning with its origins in ancient Greece and formalization in 1965 by Lotfi Zadeh. It explains fuzzy logic represents concepts with overlapping membership functions rather than binary logic. Fuzzy logic and neural networks both model human reasoning but fuzzy logic uses linguistic rules while neural networks learn from examples. Fuzzy logic has applications in control systems like temperature controllers and anti-lock braking systems to handle nonlinear dynamics. It is used in other fields like business and expert systems to represent subjective concepts.
Fuzzy logic is a form of knowledge representation that allows for notions that cannot be precisely defined but depend on context. It originated in the 1960s from Lotfi Asker Zadeh and was first implemented commercially in control systems in the 1980s. Fuzzy logic uses fuzzy sets and membership functions to model imprecise data, as opposed to traditional binary logic that uses true and false. It has been applied in control systems like temperature controllers and anti-lock braking systems to improve efficiency over conventional control methods.
Presentation on fuzzy logic and fuzzy systemsShreyaSahu20
Fuzzy logic is a form of many-valued logic that allows intermediate values between conventional evaluations like true/false, yes/no, or black/white. It employs the concept of fuzzy sets, where elements have degrees of membership as opposed to full membership. Fuzzy logic has applications in areas like control systems, pattern recognition, and decision making where precise probabilities or crisp boundaries are not easily determined.
The document discusses using fuzzy logic to determine thesis preceptors and examiners based on lecturer skills. It describes collecting data on lecturer skills in various areas and processing it using fuzzy logic methods to assign the most appropriate lecturers. Lecturers are given weights from 0-100 in different skill areas and these weights are mapped to fuzzy sets of low, mid, and high. The lecturers with the highest total weights are selected as preceptors and examiners to best match their skills to thesis topics.
- Fuzzy logic was developed by Lotfi Zadeh to address applications involving subjective or vague data like "attractive person" that cannot be easily analyzed using binary logic. It allows for partial truth values between completely true and completely false.
- Fuzzy logic controllers mimic human decision making and involve fuzzifying inputs, applying fuzzy rules, and defuzzifying outputs. This allows systems to be specified in human terms and automated.
- Fuzzy logic has many applications from industrial process control to consumer products like washing machines and microwaves. It offers an intuitive way to model real-world ambiguities compared to mathematical or logic-based approaches.
This presentation contains my one day lectures which introduces fuzzy set theory, operations on fuzzy sets, some engineering control applications using Mamdamn model.
This document presents a summary of fuzzy logic and its applications to computer aided manufacturing. It introduces fuzzy logic as a way to process imprecise data and mimic human control logic. The basic concepts are explained, including fuzzy sets that have partial truth values between 0 and 1. An example is provided of how fuzzy logic can be used for temperature regulation. The steps in fuzzy logic control are outlined as fuzzification, rule specification, and defuzzification. Applications discussed include anti-lock braking systems, flight control, and using fuzzy logic controllers to adjust feed rates and position presses in manufacturing.
Fuzzy logic is a form of knowledge representation that allows for notions that cannot be defined precisely but depend on context. It uses fuzzy sets where elements have a partial degree of membership between 0 and 1 rather than full membership. Fuzzy logic operators like AND, OR, and NOT are defined for fuzzy sets. Fuzzy logic can be applied to control systems through IF-THEN rules to efficiently and flexibly model imprecise variables like temperature, providing a more resourceful approach than traditional binary logic. Examples of applications include temperature controllers, automotive systems like anti-lock braking, and more.
fuzzy logic,proposition with types and examplestellan7
This document provides an introduction to fuzzy logic and its applications in geographical information analysis. It explains that fuzzy logic allows for vagueness and partial set membership to better represent real-world phenomena that are not strictly binary. It then discusses fuzzy sets, fuzzy logic models, and how these models work. Finally, it provides examples of how fuzzy logic has been used in fields like spatial interaction modeling, remote sensing, land evaluation, and physical geography applications like climate classification and flood forecasting.
This document provides an introduction to fuzzy logic and its applications in geographical information analysis. It explains that fuzzy logic allows for vagueness and partial set membership to better represent real-world phenomena that are not strictly binary. It then discusses fuzzy sets, fuzzy logic models, and how these models work. Finally, it provides examples of how fuzzy logic has been used in fields like spatial interaction modeling, remote sensing, land evaluation, and physical geography applications like climate classification and flood forecasting.
Fuzzy logic is a form of logic that accounts for partial truth and intermediate values between true and false. It is used in control systems to mimic how humans apply fuzzy concepts like "cold" or "hot" temperature. Some key applications of fuzzy logic include temperature controllers, washing machines, air conditioners, and anti-lock braking systems. Fuzzy logic controllers use if-then rules to determine outputs based on fuzzy inputs and degrees of membership rather than binary logic.
Is there any a novel best theory for uncertainty? Andino Maseleno
The document discusses several uncertainty modeling techniques including fuzzy logic, Dempster-Shafer theory, neural networks, and genetic algorithms. It provides background on each technique, how they were developed and applied to problems. Fuzzy logic allows for imprecise variables rather than binary true/false. Dempster-Shafer theory generalizes probability to assign beliefs to sets rather than individual outcomes. Neural networks learn from examples via weighted connections. Genetic algorithms use evolutionary principles to optimize solutions. These soft computing methods complement each other and help model real-world uncertainty.
Fuzzy logic is a form of logic that accounts for intermediate values between true and false. It is used in control systems to mimic how humans apply fuzzy concepts like "cold" or "hot" temperature. Some key applications of fuzzy logic include temperature controllers, washing machines, air conditioners, and anti-lock braking systems. Fuzzy logic controllers use if-then rules to determine outputs based on fuzzy inputs and degrees of membership rather than binary logic.
This document discusses fuzzy logic and how it can be applied to databases. Fuzzy logic uses degrees of truth rather than binary true/false values and allows partial truth. It describes fuzzy sets which assign membership values between 0 and 1 to elements. Basic fuzzy set operations like union and intersection are also covered. The document gives an example of how fuzzy values could be used in a database to describe attributes like age and time spent in partially true ways rather than discrete values.
Fuzzy logic is a form of logic that accounts for partial truth and intermediate values between true and false. It extends conventional binary logic which has only true and false values. Fuzzy logic is used in fuzzy expert systems where rules use linguistic variables and fuzzy membership functions rather than binary logic. A fuzzy expert system fuzzifies inputs, applies inference rules to fuzzy subsets assigned by rules, composes the fuzzy subsets into single fuzzy subsets for outputs, and may defuzzify outputs into crisp values.
Fuzzy logic is a form of logic that accounts for partial truth and vagueness. It is used in control systems and decision support systems. The document discusses the history of fuzzy logic and its applications in areas like automotive, robotics, manufacturing, medical, and more. Fuzzy logic controllers combine fuzzy linguistic variables and rules to automate tasks like speed control in vehicles and temperature control in air conditioners and washing machines.
This presentation includes what is fuzzy logic, characteristics, membership function with example, fuzzy set theory, De-Morgans Law, Fuzzy logic V/S probability, advantages and disadvantages and application areas of fuzzy logic. This is a presentation is useful for IT students.
Fuzzy logic is a form of multivalued logic that allows intermediate values between conventional evaluations like true/false, yes/no, or 0/1. It provides a mathematical framework for representing uncertainty and imprecision in measurement and human cognition. The document discusses the history of fuzzy logic, key concepts like membership functions and linguistic variables, common fuzzy logic operations, and applications in fields like control systems, home appliances, and cameras. It also notes some drawbacks like difficulty in tuning membership functions and potential confusion with probability theory.
The document provides an overview of fuzzy logic and fuzzy sets. It discusses how fuzzy logic can handle imprecise data unlike classical binary sets. Membership functions assign degrees of membership values between 0 and 1. Fuzzy logic systems use if-then rules and linguistic variables. An example shows how fuzzy logic is used to estimate project risk levels based on funding and staffing levels. Fuzzy logic has been applied in various domains due to its ability to model human reasoning.
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Fuzzy logic is a form of knowledge representation that allows for notions that cannot be precisely defined but depend on context. It originated in the 1960s from Lotfi Asker Zadeh and was first implemented commercially in control systems in the 1980s. Fuzzy logic uses fuzzy sets and membership functions to model imprecise data, as opposed to traditional binary logic that uses true and false. It has been applied in control systems like temperature controllers and anti-lock braking systems to improve efficiency over conventional control methods.
Presentation on fuzzy logic and fuzzy systemsShreyaSahu20
Fuzzy logic is a form of many-valued logic that allows intermediate values between conventional evaluations like true/false, yes/no, or black/white. It employs the concept of fuzzy sets, where elements have degrees of membership as opposed to full membership. Fuzzy logic has applications in areas like control systems, pattern recognition, and decision making where precise probabilities or crisp boundaries are not easily determined.
The document discusses using fuzzy logic to determine thesis preceptors and examiners based on lecturer skills. It describes collecting data on lecturer skills in various areas and processing it using fuzzy logic methods to assign the most appropriate lecturers. Lecturers are given weights from 0-100 in different skill areas and these weights are mapped to fuzzy sets of low, mid, and high. The lecturers with the highest total weights are selected as preceptors and examiners to best match their skills to thesis topics.
- Fuzzy logic was developed by Lotfi Zadeh to address applications involving subjective or vague data like "attractive person" that cannot be easily analyzed using binary logic. It allows for partial truth values between completely true and completely false.
- Fuzzy logic controllers mimic human decision making and involve fuzzifying inputs, applying fuzzy rules, and defuzzifying outputs. This allows systems to be specified in human terms and automated.
- Fuzzy logic has many applications from industrial process control to consumer products like washing machines and microwaves. It offers an intuitive way to model real-world ambiguities compared to mathematical or logic-based approaches.
This presentation contains my one day lectures which introduces fuzzy set theory, operations on fuzzy sets, some engineering control applications using Mamdamn model.
This document presents a summary of fuzzy logic and its applications to computer aided manufacturing. It introduces fuzzy logic as a way to process imprecise data and mimic human control logic. The basic concepts are explained, including fuzzy sets that have partial truth values between 0 and 1. An example is provided of how fuzzy logic can be used for temperature regulation. The steps in fuzzy logic control are outlined as fuzzification, rule specification, and defuzzification. Applications discussed include anti-lock braking systems, flight control, and using fuzzy logic controllers to adjust feed rates and position presses in manufacturing.
Fuzzy logic is a form of knowledge representation that allows for notions that cannot be defined precisely but depend on context. It uses fuzzy sets where elements have a partial degree of membership between 0 and 1 rather than full membership. Fuzzy logic operators like AND, OR, and NOT are defined for fuzzy sets. Fuzzy logic can be applied to control systems through IF-THEN rules to efficiently and flexibly model imprecise variables like temperature, providing a more resourceful approach than traditional binary logic. Examples of applications include temperature controllers, automotive systems like anti-lock braking, and more.
fuzzy logic,proposition with types and examplestellan7
This document provides an introduction to fuzzy logic and its applications in geographical information analysis. It explains that fuzzy logic allows for vagueness and partial set membership to better represent real-world phenomena that are not strictly binary. It then discusses fuzzy sets, fuzzy logic models, and how these models work. Finally, it provides examples of how fuzzy logic has been used in fields like spatial interaction modeling, remote sensing, land evaluation, and physical geography applications like climate classification and flood forecasting.
This document provides an introduction to fuzzy logic and its applications in geographical information analysis. It explains that fuzzy logic allows for vagueness and partial set membership to better represent real-world phenomena that are not strictly binary. It then discusses fuzzy sets, fuzzy logic models, and how these models work. Finally, it provides examples of how fuzzy logic has been used in fields like spatial interaction modeling, remote sensing, land evaluation, and physical geography applications like climate classification and flood forecasting.
Fuzzy logic is a form of logic that accounts for partial truth and intermediate values between true and false. It is used in control systems to mimic how humans apply fuzzy concepts like "cold" or "hot" temperature. Some key applications of fuzzy logic include temperature controllers, washing machines, air conditioners, and anti-lock braking systems. Fuzzy logic controllers use if-then rules to determine outputs based on fuzzy inputs and degrees of membership rather than binary logic.
Is there any a novel best theory for uncertainty? Andino Maseleno
The document discusses several uncertainty modeling techniques including fuzzy logic, Dempster-Shafer theory, neural networks, and genetic algorithms. It provides background on each technique, how they were developed and applied to problems. Fuzzy logic allows for imprecise variables rather than binary true/false. Dempster-Shafer theory generalizes probability to assign beliefs to sets rather than individual outcomes. Neural networks learn from examples via weighted connections. Genetic algorithms use evolutionary principles to optimize solutions. These soft computing methods complement each other and help model real-world uncertainty.
Fuzzy logic is a form of logic that accounts for intermediate values between true and false. It is used in control systems to mimic how humans apply fuzzy concepts like "cold" or "hot" temperature. Some key applications of fuzzy logic include temperature controllers, washing machines, air conditioners, and anti-lock braking systems. Fuzzy logic controllers use if-then rules to determine outputs based on fuzzy inputs and degrees of membership rather than binary logic.
This document discusses fuzzy logic and how it can be applied to databases. Fuzzy logic uses degrees of truth rather than binary true/false values and allows partial truth. It describes fuzzy sets which assign membership values between 0 and 1 to elements. Basic fuzzy set operations like union and intersection are also covered. The document gives an example of how fuzzy values could be used in a database to describe attributes like age and time spent in partially true ways rather than discrete values.
Fuzzy logic is a form of logic that accounts for partial truth and intermediate values between true and false. It extends conventional binary logic which has only true and false values. Fuzzy logic is used in fuzzy expert systems where rules use linguistic variables and fuzzy membership functions rather than binary logic. A fuzzy expert system fuzzifies inputs, applies inference rules to fuzzy subsets assigned by rules, composes the fuzzy subsets into single fuzzy subsets for outputs, and may defuzzify outputs into crisp values.
Fuzzy logic is a form of logic that accounts for partial truth and vagueness. It is used in control systems and decision support systems. The document discusses the history of fuzzy logic and its applications in areas like automotive, robotics, manufacturing, medical, and more. Fuzzy logic controllers combine fuzzy linguistic variables and rules to automate tasks like speed control in vehicles and temperature control in air conditioners and washing machines.
This presentation includes what is fuzzy logic, characteristics, membership function with example, fuzzy set theory, De-Morgans Law, Fuzzy logic V/S probability, advantages and disadvantages and application areas of fuzzy logic. This is a presentation is useful for IT students.
Fuzzy logic is a form of multivalued logic that allows intermediate values between conventional evaluations like true/false, yes/no, or 0/1. It provides a mathematical framework for representing uncertainty and imprecision in measurement and human cognition. The document discusses the history of fuzzy logic, key concepts like membership functions and linguistic variables, common fuzzy logic operations, and applications in fields like control systems, home appliances, and cameras. It also notes some drawbacks like difficulty in tuning membership functions and potential confusion with probability theory.
The document provides an overview of fuzzy logic and fuzzy sets. It discusses how fuzzy logic can handle imprecise data unlike classical binary sets. Membership functions assign degrees of membership values between 0 and 1. Fuzzy logic systems use if-then rules and linguistic variables. An example shows how fuzzy logic is used to estimate project risk levels based on funding and staffing levels. Fuzzy logic has been applied in various domains due to its ability to model human reasoning.
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2. OVERVIEW
What is Fuzzy Logic?
Where did it begin?
Fuzzy Logic vs. Neural Networks
Fuzzy Logic in Control Systems
Fuzzy Logic in Other Fields
Future
3. WHAT IS FUZZY LOGIC?
Definition of fuzzy
⚫ Fuzzy – “not clear, distinct, or precise; blurred”
Definition of fuzzy logic
⚫ A form of knowledge representation suitable for
notions that cannot be defined precisely, but which
depend upon their contexts.
4. What is Fuzzy Logic?
Fuzzy logic is a form of many-valued logic; it
deals with reasoning that is approximate
rather than fixed and exact. In contrast with
traditional logic theory, where binary sets
have two-valued logic: true or false, fuzzy
logic variables may have a truth value that
ranges in degree
5. What is Fuzzy Logic?
Fuzzy logic has been extended to handle the
concept of partial truth, where the truth
value may range between completely true
and completely false. Furthermore,
when linguistic variables are used, these
degrees may be managed by specific
functions
6. Fuzzy Logic began
Fuzzy logic began with the 1965 proposal
of fuzzy set theory by Lotfi Zadeh Fuzzy logic
has been applied to many fields, from control
theory to artificial intelligence
7. Fuzzy Data- Crisp Data
• he reasoning in fuzzy logic is similar to
human reasoning
• It allows for approximate values
and inferences as well as
incomplete or
ambiguous data
8. Fuzzy Data- Crisp Data
• Fuzzy logic is able to process
incomplete data and provide
approximate solutions to problems
other methods find difficult to solve.
9. Fuzzy Data- Crisp Data
• Terminology used in fuzzy logic not used in
other methods are: very high, increasing,
somewhat decreased, reasonable and very
low.
10. Degrees of Truth
Fuzzy logic and probabilistic logic are
mathematically similar – both have truth
values ranging between 0 and 1 – but
conceptually distinct, due to different
interpretations—see interpretations of
probability theory..
11. Degrees of Truth
Fuzzy logic corresponds to "degrees of truth",
while probabilistic logic corresponds to
"probability, likelihood"; as these differ, fuzzy
logic and probabilistic logic yield different
models of the same real-world situations.
12. Degrees of Truth
Both degrees of truth and probabilities range
between 0 and 1 and hence may seem similar
at first. For example, let a 100 ml glass
contain 30 ml of water. Then we may consider
two concepts: Empty and Full. The meaning
of each of them can be represented by a
certain fuzzy set.
13. Degrees of Truth
Then one might define the glass as being 0.7
empty and 0.3 full. Note that the concept of
emptiness would be subjective and thus
would depend on the observer or designer.
14. Degrees of Truth
Another designer might equally well design a
set membership function where the glass
would be considered full for all values down
to 50 ml. It is essential to realize that fuzzy
logic uses truth degrees as a mathematical
model of the vagueness phenomenon while
probability is a mathematical model of
ignorance.
15. Applying the Values
A basic application might characterize
subranges of a continuous variable. For
instance, a temperature measurement
for anti-lock brakes might have several
separate membership functions defining
particular temperature ranges needed to
control the brakes properly.
16. Applying the Values
Each function maps the same temperature
value to a truth value in the 0 to 1 range.
These truth values can then be used to
determine how the brakes should be
controlled
18. Applying the Values
In this image, the meaning of the
expressions cold, warm, and hot is
represented by functions mapping a
temperature scale. A point on that scale has
three "truth values"—one for each of the three
functions.
19. Applying the Values
The vertical line in the image represents a
particular temperature that the three arrows
(truth values) gauge. Since the red arrow
points to zero, this temperature may be
interpreted as "not hot". The orange arrow
(pointing at 0.2) may describe it as "slightly
warm" and the blue arrow (pointing at 0.8)
"fairly cold"
21. FUZZY LOGIC REPRESENTATION
For every problem
must represent in
terms of fuzzy sets.
What are fuzzy
sets?
Slowest
[ 0.0 – 0.25 ]
Fastest
[ 0.75 – 1.00 ]
Slow
[ 0.25 – 0.50 ]
Fast
[ 0.50 – 0.75 ]
22. FUZZY LOGIC REPRESENTATION
CONT.
Slowest Fastest
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
}
Slow
float speed;
get the speed
Fast
23. Linguistic Variables
While variables in mathematics usually take
numerical values, in fuzzy logic applications,
the non-numeric linguistic variables are
often used to facilitate the expression of rules
and facts
24. Linguistic Variables
A linguistic variable such as age may have a
value such as young or its antonym old.
However, the great utility of linguistic
variables is that they can be modified via
linguistic hedges applied to primary terms.
The linguistic hedges can be associated with
certain functions
25. Examples
Fuzzy set theory defines fuzzy operators on
fuzzy sets. The problem in applying this is that
the appropriate fuzzy operator may not be
known. For this reason, fuzzy logic usually
uses IF-THEN rules, or constructs that are
equivalent, such as fuzzy associative matrices
Rules are usually expressed in the form:
IF variable IS property THEN action
26. that uses a fan might look like
this:
IF temperature IS very cold THEN stop fan
IF temperature IS cold THEN turn down fan
IF temperature IS normal THEN maintain
level
IF temperature IS hot THEN speed up fan
There is no "ELSE" – all of the rules are evaluated,
because the temperature might be "cold" and
27. ORIGINS OF FUZZY LOGIC
Traces back to Ancient Greece
Lotfi Asker Zadeh ( 1965 )
⚫ First to publish ideas of fuzzy logic.
Professor Toshire Terano ( 1972 )
⚫ Organized the world's first working group on fuzzy
systems.
F.L. Smidth & Co. ( 1980 )
⚫ First to market fuzzy expert systems.
28. FUZZY LOGIC VS. NEURAL
NETWORKS
How does a Neural Network work?
Both model the human brain.
⚫ Fuzzy Logic
⚫ Neural Networks
Both used to create behavioral
systems.
29. FUZZY LOGIC IN CONTROL
SYSTEMS
Fuzzy Logic provides a more efficient and
resourceful way to solve Control Systems.
Some Examples
⚫ Temperature Controller
⚫ Anti – Lock Break System ( ABS )
30. TEMPERATURE CONTROLLER
The problem
⚫ Change the speed of a heater fan, based off the room
temperature and humidity.
A temperature control system has four settings
⚫ Cold, Cool, Warm, and Hot
Humidity can be defined by:
⚫ Low, Medium, and High
Using this we can define
the fuzzy set.
32. ANTI LOCK BREAK SYSTEM ( ABS )
Nonlinear and dynamic in nature
Inputs for Intel Fuzzy ABS are derived from
⚫ Brake
⚫ 4 WD
⚫ Feedback
⚫ Wheel speed
⚫ Ignition
Outputs
⚫ Pulsewidth
⚫ Error lamp
33. FUZZY LOGIC IN OTHER FIELDS
Business
Hybrid Modelling
Expert Systems
34. CONCLUSION
Fuzzy logic provides an alternative way to
represent linguistic and subjective attributes of
the real world in computing.
It is able to be applied to control systems and
other applications in order to improve the
efficiency and simplicity of the design process.