Fuzzy Logic - Introduction Computers are useless, they can only give you answers. Pablo Picasso...
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Transcript of Fuzzy Logic - Introduction Computers are useless, they can only give you answers. Pablo Picasso...
Fuzzy Logic - Introduction
Computers are useless, they can only give you answers.
Pablo Picasso
Adriano CruzNCE e IM/UFRJ
@2001 Adriano Cruz NCE e IM - UFRJ No. 2
IntroductionIntroduction
Adriano Cruz NCE-IM UFRJ [email protected]
Light travels faster than sound. That is the reason why some people look brighter until they start talking.
Linux Journal
@2001 Adriano Cruz NCE e IM - UFRJ No. 3
Bibliography 1Bibliography 1
J. Yen, R. Langari, “Fuzzy Logic: Intelligence, Control and Information”, Prentice Hall, 1999
J. R. Jang, C. Sun, E. Mizutani, “Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence, Prentice Hall, 1997
Slides and notes: http://equipe.nce.ufrj.br/adriano/fuzzy/bibliogr-ic.htm
C. von Altrock, “Fuzzy Logic & NeuroFuzzy Applications Explained”, Prentice Hall PTR, 1995
@2001 Adriano Cruz NCE e IM - UFRJ No. 4
Bibliography 2Bibliography 2
H. T. Nguyen, E. A. Walker, “A First Course in Fuzzy Logic”, Chapman & Hall/CRC, 2000
Bart Kosko, “Fuzzy Thinking”, Harper Collins Publishers, 1994, ISBN 0-00-654713-3
L. H. Tsoukalas, R. E. Uhig, “Fuzzy and Neural Approaches in Engineering”, John Wiley and Sons, Inc, 1997
@2001 Adriano Cruz NCE e IM - UFRJ No. 5
SummarySummary
Introduction Fuzzy Sets Fuzzy Set Operations Fuzzy Systems
@2001 Adriano Cruz NCE e IM - UFRJ No. 6
Artificial Intelligence?Artificial Intelligence?
“AI is the activity of providing such machines as computers with the ability to display behaviours that would be regarded as intelligent if it were observed in humans” (R. McLeod)
“AI is the study of agents that exist in an environment, perceive and act.” (S. Russel and P. Norvig)
@2001 Adriano Cruz NCE e IM - UFRJ No. 7
Artificial Intelligence?Artificial Intelligence?
AI emphasizes symbolic processing Acts on higher levels of intelligence AI seeks to understand
@2001 Adriano Cruz NCE e IM - UFRJ No. 8
Computational IntelligenceComputational Intelligence
Acts on lower levels of Intelligence Uses learning extensively Pattern recognition and heuristics play
important roles
@2001 Adriano Cruz NCE e IM - UFRJ No. 9
Computational IntelligenceComputational Intelligence
Fuzzy Logic
Artificial Neural Networks
Evolutionary Systems
Swarm Intelligence
Hybrid Systems
@2001 Adriano Cruz NCE e IM - UFRJ No. 10
Computational IntelligenceComputational Intelligence
Fuzzy Logic
Artificial Neural Networks
Evolutionary Systems
Swarm Intelligence
Hybrid Systems
@2001 Adriano Cruz NCE e IM - UFRJ No. 11
Fuzzy LogicFuzzy Logic
Logic that deals mathematically with imprecise information usually employed by humans.
Multi-valued logic that extends Boolean logic usually employed in computer science.
@2001 Adriano Cruz NCE e IM - UFRJ No. 12
Fuzzy Logic Fuzzy Logic
Used to alleviate difficulties in developing and analysing complex control systems.
Function approximator
Decision systems
@2001 Adriano Cruz NCE e IM - UFRJ No. 13
Fuzzy LogicFuzzy Logic
Who is greater than 1.80 m?
Who is tall?
Who weighs more than 100 kg?
Who is heavy?
The driver was heavy and tall.
@2001 Adriano Cruz NCE e IM - UFRJ No. 14
Computational IntelligenceComputational Intelligence
Fuzzy Logic
Artificial Neural Networks
Evolutionary Systems
Swarm Intelligence
Hybrid Systems
@2001 Adriano Cruz NCE e IM - UFRJ No. 15
Artificial Neural NetworksArtificial Neural Networks
Computational models that try to emulate the structure of the human brain wishing to reproduce at least some of its flexibility and power.
ANN consist of many simple computing elements – usually simple nonlinear summing operations – highly connected by links of varying strength.
@2001 Adriano Cruz NCE e IM - UFRJ No. 16
ANNsANNs
ANNs are able to learn from examples.
Function approximators.
Solutions not always correct.
ANNs are able to generalize the acquired knowledge.
@2001 Adriano Cruz NCE e IM - UFRJ No. 17
NeuronsNeurons
@2001 Adriano Cruz NCE e IM - UFRJ No. 18
Neural NetworksNeural Networks
@2001 Adriano Cruz NCE e IM - UFRJ No. 19
StructureStructure
Inputs Inputlayer
Weight
Matrix 1
Weight
Matrix 2
Hiddenlayer
Outputlayer
Outputs
@2001 Adriano Cruz NCE e IM - UFRJ No. 20
TrainingTraining
Weight values change during the training process
Values are presented at the inputs and outputs are compared to the desired values.
Wrong outputs cause weights to change in order to reduce the error
Process is repeated with different inputs till the ANN is able to give the correct answers
Hopefully the ANN will be able to give the correct answer even to inputs that were not trained.
@2001 Adriano Cruz NCE e IM - UFRJ No. 21
Computational IntelligenceComputational Intelligence
Fuzzy Logic
Artificial Neural Networks
Evolutionary Systems
Swarm Intelligence
Hybrid Systems
@2001 Adriano Cruz NCE e IM - UFRJ No. 22
Evolutionary SystemsEvolutionary Systems
ES are global search and optimization algorithms modelled from natural genetic principles such as natural selection.
They are stochastic searching methods. Good solutions will survive and be
combined by the natural selection process.
At the end the most fit will survive.
@2001 Adriano Cruz NCE e IM - UFRJ No. 23
The MetaphorThe Metaphor
The metaphor that lays behind GAs is the natural selection.
The problem of each species in the nature is seek for the best adaptations in order to survive in a hostile environment that is in constant modification.
@2001 Adriano Cruz NCE e IM - UFRJ No. 24
AdaptationAdaptation The sets of characteristics of an
individual, that distinguishes from everybody else, defines its survival capacity.
These characteristics are determined by its genetic material.
@2001 Adriano Cruz NCE e IM - UFRJ No. 25
MechanismsMechanisms
The competition for scarce resources makes the apts survive and reproduce.
Through reproduction the genes from individuals are transmitted to their descendants.
This continuous process of selection and reproduction of the best individuals may conduct to more adpated individuals.
@2001 Adriano Cruz NCE e IM - UFRJ No. 26
GA FluxGA Fluxbegin
Initial Population
EvaluatesSelectsParents
Currentgeneration
GeneratesSons
Mutation
Crossing
NextGeneratio
OK?No
Randomly
@2001 Adriano Cruz NCE e IM - UFRJ No. 27
Computational IntelligenceComputational Intelligence
Fuzzy Logic
Artificial Neural Networks
Evolutionary Systems
Swarm Intelligence
Hybrid Systems
@2001 Adriano Cruz NCE e IM - UFRJ No. 28
Swarm IntelligenceSwarm Intelligence
Swarm Intelligence (SI) is the property of a system whereby the collective behaviours of (unsophisticated) agents interacting locally with their environment cause coherent functional global patterns to emerge.
SI provides a basis with which it is possible to explore collective (or distributed) problem solving without centralized control or the provision of a global model.
@2001 Adriano Cruz NCE e IM - UFRJ No. 29
Characteristics of a swarmCharacteristics of a swarm
Distributed, no central control or data source;
No (explicit) model of the environment; Perception of environment, i.e. sensing; Ability to change environment.
@2001 Adriano Cruz NCE e IM - UFRJ No. 30
MotivationsMotivations
Robust nature of animal problem-solving– simple creatures exhibit complex behaviour;– behaviour modified by dynamic
environment. Emergent behaviour observed in:
– bacteria– ants– bees– ...
@2001 Adriano Cruz NCE e IM - UFRJ No. 31
Ant ColoniesAnt Colonies
Ants are behaviourally unsophisticated; collectively perform complex tasks.
Ants have highly developed sophisticated sign-based stigmergy– communicate using pheromones;– trails are laid that can be followed by other ants.
Stigmergy is a method of indirect communication in a self-organising emergent system where its individual parts communicate with one another by modifying their local environment.
@2001 Adriano Cruz NCE e IM - UFRJ No. 32
Computational IntelligenceComputational Intelligence
Fuzzy Logic
Artificial Neural Networks
Evolutionary Systems
Swarm Intelligence
Hybrid Systems
@2001 Adriano Cruz NCE e IM - UFRJ No. 33
Hybrid SystemsHybrid Systems
Each intelligent technique has its particular strengths and weakness and cannot be applied to universally to every problem.
Mixing together these techniques systems improve the quality of the solutions and allows application to different tasks.
@2001 Adriano Cruz NCE e IM - UFRJ No. 34
HistoryHistory
EAFLANNsAI
50s 57 Perceptron56 AI
40s 43 Neuron Model47 Cybernetics
60s 65 Fuzzy SetsAdaline - Madaline
60 Lisp
70s Genetic Algorithm74 Fuzzy Control74 Back-Propagation
Expert Systems
80s Immune modelling85 Fuzzy modelling(TSK model)
80 Self orgazing map82 Hopfield83 Boltzmann Mach
90sGenetic programming
Neuro-Fuzzy modelling
@2001 Adriano Cruz NCE e IM - UFRJ No. 35
Why do we reason as we do?Why do we reason as we do?
@2001 Adriano Cruz NCE e IM - UFRJ No. 36
AristotleAristotle
Macedonian philosopher who lived between 384 e 322 AC
Studied under Plato in the Academy Creator of formal logic His father Nichomachus was court physician
to King Amyntas Associates the spirit of observation and a
classification instinct He was considered during the middle ages
the philosopher He shaped much of the western mind.
@2001 Adriano Cruz NCE e IM - UFRJ No. 37
Limitations of the Aristotle’s LogicLimitations of the Aristotle’s Logic
Objects are separated on very clear categories
One object either belongs to a category or another
Either you are or not Helps to separate objects into well
defined categories.
@2001 Adriano Cruz NCE e IM - UFRJ No. 38
Aristotle X BuddhaAristotle X Buddha Everything must either be or not be,
whether in the present or in the future.Aristotle
I have not explained that the world is eternal or not eternal. I have not explained that the world is finite or infinite.
The Buddha
@2001 Adriano Cruz NCE e IM - UFRJ No. 39
Why fuzzy logic?Why fuzzy logic? Every language is vague. All traditional logic habitually assumes that
precise symbols are being employed. It is therefore not applicable to this terrestrial life, but only to an imagined celestial one.
Everything is vague to a degree you do not realize till you have tried to make it precise.
Bertrand Russel
@2001 Adriano Cruz NCE e IM - UFRJ No. 40
Why fuzzy logic?Why fuzzy logic?
As far as the laws of Mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.
Albert Einstein
@2001 Adriano Cruz NCE e IM - UFRJ No. 41
How to classify?How to classify?
Happy people Small rooms High temperatures Faster cars High tax rates High people
@2001 Adriano Cruz NCE e IM - UFRJ No. 42
To be or not to be?To be or not to be? Bertrand Russel, while trying to formalize
Mathematic had difficulties due to the liar’s paradox.
“I am lying.” If Eubulides‘ statement was true, then he is
lying when he says “I am lying” and so he isn't, i.e. his statement is false.
If his statement is false, then he isn't lying when he tells us he is, and so his statement is true.
@2001 Adriano Cruz NCE e IM - UFRJ No. 43
Answer: To be and not to be.Answer: To be and not to be.
Consider the set of all sets that are not members of its own set. Is it a member of this set?
If it is a member then it is not, but if it is not then it is.
@2001 Adriano Cruz NCE e IM - UFRJ No. 44
The DetractorsThe Detractors
Fuzzy theory is wrong, wrong, and pernicious. What we need is more logical thinking, not less. The danger of fuzzy logic is that it will encourage the sort of imprecise thinking that has brought us so much trouble. Fuzzy logic is the cocaine of the science.
Prof. William Kaham - U. Cal - Berkeley
@2001 Adriano Cruz NCE e IM - UFRJ No. 45
The DetractorsThe Detractors
“Fuzzification” is a kind of scientific permissiveness. It tends to result in socially appealing slogans unaccompanied by the discipline of hard scientific work and patient observation.
Prof. Rudolf Kalam - U. Florida - Gainesville
@2001 Adriano Cruz NCE e IM - UFRJ No. 46
The BeginningThe Beginning
Lotfy Zadeh. “Fuzzy Sets”, Information na Control, 1965
Principle of Incompatibility– As the complexity of a system increases, our
ability to make precise yet significant descriptions about its behaviour diminishes until a threshold is reached beyond which precision and significance (or relevance) become almost mutually exclusive characteristics.
Lofty Zadeh
@2001 Adriano Cruz NCE e IM - UFRJ No. 47
Fuzzy ThinkingFuzzy Thinking
YesYes
NoNo NoNo
YesYes
@2001 Adriano Cruz NCE e IM - UFRJ No. 48
Fuzzy ThinkingFuzzy Thinking
If the interest rate is high and the deficit is high then there will be a recession
If rush hour then diminish the interval between busses
If the tyre skids then loose the brake a bit
If the soil is very dry then water it for very long time
@2001 Adriano Cruz NCE e IM - UFRJ No. 49
FuzzifyingFuzzifying
Measure Fuzzified Measure Temp = 35º Temp = high, µhigh(t)=0.8 Temp = 48º Temp = high, µhigh(t)=1.0 Age = 35 Idade = middle, µmiddle(i)=0.8 Grade = 10.0 Grade = A, µA(t)=1.0 Grade = 8.5 Grade = A, µA(t)=0.87
@2001 Adriano Cruz NCE e IM - UFRJ No. 50
Fuzzy SystemsFuzzy Systems
XX Y=F(X)Y=F(X)
Function F(x) is unknownFunction F(x) is unknown
@2001 Adriano Cruz NCE e IM - UFRJ No. 51
Approximation of FunctionsApproximation of Functions
X
Y patches
@2001 Adriano Cruz NCE e IM - UFRJ No. 52
Fuzzy Aproximation TheoremFuzzy Aproximation Theorem
Patches are pieces of knowledge about a problem
Every patch corresponds to a rule or proposition
If the speed is high then step on the break
@2001 Adriano Cruz NCE e IM - UFRJ No. 53
Fuzzy Aproximation TheoremFuzzy Aproximation Theorem
An additive fuzzy system F:X->Y uniformly approximates f:X->Y if X is compact and f is continuous.
Bart Kosko
@2001 Adriano Cruz NCE e IM - UFRJ No. 54
Fuzzy SystemsFuzzy Systems
Inference Engine
Data Management
Rules Sets Operators
Fu
zzyf
ier
Def
fuzz
ifie
r
@2001 Adriano Cruz NCE e IM - UFRJ No. 55
AdvantagesAdvantages
Use rules that express imprecision of the real world.
Easy to understand, test and maintain Easy to be prototyped Robust. They operate even when there is
lack of rules or wrong rules. Need less rules Parallel evaluation of rules Accumulate evidences in favour and against
@2001 Adriano Cruz NCE e IM - UFRJ No. 56
DisadvantagesDisadvantages
Need more tests and simulation
Do not learn easily
Difficult to establish correct rules
Lack of precise mathematical model
@2001 Adriano Cruz NCE e IM - UFRJ No. 57
Commercial ProductsCommercial Products
Sendai subway: 16 stations and 13,5 km route, designed by Hitachi
Washing machines that measure weight, saturation time and water clarity in order to program cycles
Portable camcorders with automatic focus and anti-jitter
Vacuum cleaners that measure air dust to set suction power
Microwave ovens that measure temperature, humidity, weight of food to set time and power.
@2001 Adriano Cruz NCE e IM - UFRJ No. 58
Commercial ProductsCommercial Products Sugeno designed a voice controlled system to
operate an unmanned helicopter Anti-Lock Braking Systems: Nissan, Mitsubishi.
Honda, Mazda, Hyunday, BMW, Bosch and Peugeot
Suspension, transmission and fuel injector systems are usual.
Hitachi uses approximately 150 rules to trade in Japanese bonds and futures
Yamaichi Securities uses hundreds of rules to manage a stock fund
Anaesthesia Control and Fuzzy Data Analysis for Cardio-Anaesthesia
@2001 Adriano Cruz NCE e IM - UFRJ No. 59
ProductsProducts
Air conditioning
Mitsubishi, Hitachi, Sharp
Avoids temperature oscillations and saves energy
Electronic fuel injection
NOK/Nissan Injection based on throttle, O2 tax, water temperature, RPM, etc
Steel Nippon Steel Mix inputs and controls time and temperature
Golf Maruman Golf Club
Chooses clubs
Lifts Fujitec Improves response time based on traffic
@2001 Adriano Cruz NCE e IM - UFRJ No. 60
Questions?Questions?
Is fuzzy logic probability ?
Find a fuzzy product description.
Find fuzzy development tools.
Fuzzy Logic is a multi values logic. Find other examples.