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

[email protected]

@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


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


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


SummarySummary

Introduction Fuzzy Sets Fuzzy Set Operations Fuzzy Systems


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)


Artificial Intelligence?Artificial Intelligence?

AI emphasizes symbolic processing Acts on higher levels of intelligence AI seeks to understand


Computational IntelligenceComputational Intelligence

Acts on lower levels of Intelligence Uses learning extensively Pattern recognition and heuristics play

important roles



Fuzzy Logic

Artificial Neural Networks

Evolutionary Systems

Swarm Intelligence

Hybrid Systems



Fuzzy Logic



Swarm Intelligence

Hybrid Systems


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.


Fuzzy Logic Fuzzy Logic

Used to alleviate difficulties in developing and analysing complex control systems.

Function approximator

Decision systems


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.



Fuzzy Logic



Swarm Intelligence

Hybrid Systems


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.


ANNsANNs

ANNs are able to learn from examples.

Function approximators.

Solutions not always correct.

ANNs are able to generalize the acquired knowledge.


NeuronsNeurons


Neural NetworksNeural Networks


StructureStructure

Inputs Inputlayer

Weight

Matrix 1

Weight

Matrix 2

Hiddenlayer

Outputlayer

Outputs


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.



Fuzzy Logic



Swarm Intelligence

Hybrid Systems


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.


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.


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.


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.


GA FluxGA Fluxbegin

Initial Population

EvaluatesSelectsParents

Currentgeneration

GeneratesSons

Mutation

Crossing

NextGeneratio

OK?No

Randomly



Fuzzy Logic



Swarm Intelligence

Hybrid Systems


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.


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.


MotivationsMotivations

Robust nature of animal problem-solving– simple creatures exhibit complex behaviour;– behaviour modified by dynamic

environment. Emergent behaviour observed in:

– bacteria– ants– bees– ...


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.



Fuzzy Logic



Swarm Intelligence

Hybrid Systems


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.


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


Why do we reason as we do?Why do we reason as we do?


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.


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.


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


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


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


How to classify?How to classify?

Happy people Small rooms High temperatures Faster cars High tax rates High people


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.


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.


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


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


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


Fuzzy ThinkingFuzzy Thinking

YesYes

NoNo NoNo

YesYes


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


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


Fuzzy SystemsFuzzy Systems

XX Y=F(X)Y=F(X)

Function F(x) is unknownFunction F(x) is unknown


Approximation of FunctionsApproximation of Functions

X

Y patches


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


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


Fuzzy SystemsFuzzy Systems

Inference Engine

Data Management

Rules Sets Operators

Fu

zzyf

ier

Def

fuzz

ifie

r


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


DisadvantagesDisadvantages

Need more tests and simulation

Do not learn easily

Difficult to establish correct rules

Lack of precise mathematical model


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.


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


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


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.

Fuzzy Logic - Introduction Computers are useless, they can only give you answers. Pablo Picasso...

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