fuzzy, neurális és genetikus mesterséges intelligencia ... · 2008 1. oldal fuzzy, neurÆlis Øs...

Fuzzy, neurális és genetikus mesterséges intelligencia módszereka (VIVG9115) c. tárgy hallgatói részére

Az előadások illusztrációi 2008 tavaszán

Gail Cocker-Bogusz: The Fuzzy FlagGail Cocker-Bogusz: The Fuzzy Flag

2008 1. oldal

Fuzzy, neurális és genetikus mesterséges intelligencia módszerek (VIVG9115)TEMATIKA

Fuzzy rendszerekBevezetés A fuzzy koncepcióA fuzzy rendszerek matematikai alapjaiFuzzy halmazok

Alapfogalmak: A fuzzy fogalom. A klasszikus halmazok. Fuzzy halmazok. Jelölési módok. Gyakori tagsági függvénytípusok. A tagsági függvények.

Műveletek halmazokkal: Klasszikus halmazok alapfogalmai. Műveletek klasszikus halmazokkal. Fuzzy halmazokkapcsolatai, műveletei. Fuzzy egyenlőség, fuzzy részhalmazok. A fuzzy halmazok struktúra tulajdonságai.

Fuzzy halmazok további műveletei: A t- és s-normák. Parametrizált t- és s-normák. Kompenzátoros paraméter-operátorok.Átlagoló és kompenzátoros operátorok.

Fuzzy relációk: Klasszikus relációk. Fuzzy relációk. Fuzzy reláció műveletek.A kiterjesztési elvFuzzy számok és fuzzy aritmetika

Nyelvi-lingvisztikai változók és HA-AKKOR szabályokNumerikus változóktól nyelvi változókig.Nyelvi kordonok: koncentráció, dilatáció.HA-AKKOR szabályok.

Fuzzy logika és közelítő következtetésA klasszikus logikától a fuzzy logikáig.A fuzzy logika alapelvei: Az éles logikai következtetés. A fuzzy logikai következtetés. A közelítő következtetés "pontosabb"

vizsgálata.A fuzzy szabályozás áttekintése: Fuzzy szabályozók áttekintése.

Fuzzy rendszerekFuzzy szabály-bázis

A szabály-bázis struktúrája. A szabály-készlet tulajdonságai.

A fuzzy inferencia gépA kompozíció alapú inferencia.Individuális szabályok alapú inferencia.Néhány inferencia gép.

Fuzzifikátorok és defuzzifikátorok Fuzzifikátorok. Defuzzifikátorok.A defuzzifikátorok összehasonlítása.

Fuzzy rendszerek mint nemlineáris leképzésekFuzzy rendszerek néhány osztályának képletei.Fuzzy rendszerek mint univerzális approximátorok.

Fuzzy rendszerek tervezéséről

2008 2. oldal

Neurális hálózatokBevezetés és áttekintés Miért használjuk őket. Hogyan működnek. Hátrányok. Néhány alkalmazási terület.Alapvető koncepciók, modellekNeuron modellek

A McCullock-Pitts neuron modell.Az általános neuron szimbólum.A perceptron.

Neurális hálózat modellekAz előrecsatolt hálózat.A visszacsatolt hálózat.

Neurális processzálásTanulás és adaptáció

Tanulás mint approximáció.Felügyelt és nem felügyelt tanulás.

Neurális hálózatok tanulási szabályaiAz általánosított tanulási szabály.A Hebb-féle tanulási szabály.Az eredeti - Rosenblatt féle- perceptron tanulási szabály.A delta szabály folytonos perceptronra.A korrelációs tanulási szabály.A győztes - mindent - elvisz tanulási szabály.

Többréteges előrecsatolt hálózatokNeurális hálózatok összefoglaló áttekintéseEgy perceptronos hálózat tanulása

A diszkrét perceptron.A folytonos perceptron.

A többréteges hálózatokAz egyréteges hálózat.Kétréteges egyszerű hálózat.Az általános kétréteges hálózat.Többréteges előrecsatolt hálózat mint univerzális approximátor.Tanulási tényezők.

Radiális bázisfüggvényes hálózatokLokális és globális osztályozás.Az RBF hálózatok formális modellje.Az RBF hálózatok tanulási módjai.

Kohonen önszervező térképAz önszervező algoritmus általános képe.A súly adaptálás.Tanuló vektorkvantálás.

Genetikus algoritmusokMi és milyen a genetikus algoritmus.Egyszerű genetikus algoritmus.A hasonló mintázatok (szkémák).A genetikus algoritmus alaptörvénye.

Káosz neurális és fuzzy rendszerkbenBevezetésNeurális hálózatok és káoszFuzzy rendszerek és káosz

A témához kapcsolódó irodalom:1. Retter Gyula: Fuzzy, neurális genetikus, kaotikus rendszerek (Bevezetés a "lágy számítás" módszereibe) Akadémiai Kiadó, 2006.2. Borgulya István: Neurális hálók és fuzzy rendszerek. Dialog Campus K., 1998.3. Horváth Gábor szerk.: Neurális hálózatok és műszaki alkalmazásaik. Műegyetemi Kiadó, 1995.4. Kóczy T. László, Tikk Domonkos: Fuzzy Rendszerek. Typotex Kft., 2000.5. Várkonyiné Kóczy Annamária szerk.: Genetikus algoritmusok. Typotex Kft., 2002.

2008 3. oldal

Applications of Fuzzy LogicSource: Fuzzy Logic Laboratorium, Linz.http://www.flll.uni-linz.ac.at/aboutus/whatisfuzzy/applications01.html

First, we shall look at the fitness of Fuzzy Control in general terms.The employment of Fuzzy Control is commendable...

for very complex processes, when there is no simple mathematical modelfor highly nonlinear processesif the processing of (linguistically formulated) expert knowledge is to be performed

The employment of Fuzzy Control is no good idea if...conventional control theory yields a satisfying resultan easily solvable and adequate mathematical model already existshe problem is not solvable

Now let's look at some examples where Fuzzy Control actually has been applied.

Here are some examples of how Fuzzy Logic has been applied in reality:Automatic control of dam gates for hydroelectric-powerplants (Tokio Electric Pow.)Simplified control of robots (Hirota, Fuji Electric, Toshiba, Omron)Camera aiming for the telecast of sporting events (Omron)Substitution of an expert for the assessment of stock exchange activities (Yamaichi, Hitachi)Preventing unwanted temperature fluctuations in air-conditioning systems (Mitsubishi, Sharp)Efficient and stable control of car-engines (Nissan)Cruise-control for automobiles (Nissan, Subaru)Improved efficiency and optimized function of industrial control applications (Aptronix, Omron,Meiden, Sha, Micom, Mitsubishi, Nisshin-Denki, Oku-Electronics)Positioning of wafer-steppers in the production of semiconductors (Canon)Optimized planning of bus time-tables (Toshiba, Nippon-System, Keihan-Express)Archiving system for documents (Mitsubishi Elec.)Prediction system for early recognition of earthquakes (Inst. of Seismology Bureau of Metrology, Japan)Medicine technology: cancer diagnosis (Kawasaki Medical School)Combination of Fuzzy Logic and Neural Nets (Matsushita)Recognition of handwritten symbols with pocket computers (Sony)Recognition of handwriting, objects, voice (CSK, Hitachi, Hosai Univ., Ricoh)Recognition of motives in pictures with video cameras (Canon, Minolta)Automatic motor-control for vacuum cleaners with recognition of surface condition and degree ofsoiling (Matsushita)Back light control for camcorders (Sanyo)Compensation against vibrations in camcorders (Matsushita)Single button control for washing-machines (Matsushita, Hitatchi)Flight aid for helicopters (Sugeno)Simulation for legal proceedings (Meihi Gakuin Univ, Nagoy Univ.)Software-design for industrial processes (Aptronix, Harima, Ishikawajima-OC Engeneering)Controlling of machinery speed and temperature for steel-works (Kawasaki Steel, New-Nippon Steel,NKK)Controlling of subway systems in order to improve driving comfort, precision of halting and powereconomy (Hitachi)Improved fuel-consumption for automobiles (NOK, Nippon Denki Tools)Improved sensitiveness and efficiency for elevator control (Fujitec, Hitachi, Toshiba)Improved savety for nuklear reactors (Hitachi, Bernard, Nuclear Fuel div.)

2008 4. oldal

The Helicopter that does what it's told

Mastering a remote-controlled aircraft can take more than 70 hours training. But now the Japanese have built amini-helicopter that anyone can fly - as long as they can talk.

The little aircraft is designed to carry microphones,cameras and otherequipment into places too hazardous for human pilots to visit.The pilot on the ground steers the helicopter in the air simply by speaking anyof 14 commands into a microphone,such as "up", "down", "hover", and "turn".A camera aboard the aircraft relays the view from the nose to a monitor infront of the pilot.But a helmet with a screen inside and with camera controls operated by

movements of the pilot's head is being developed.The voice-controlled system uses "fuzzy logic" to help identify the command. Fuzzy logic is a type of computerprogram in which a microprocessor makes choices and takes action on the basis of probabilities - in this casethe likeliest voice command.

June 1994 p30

Symbol Technologies Symbol LS 3000 ScannerSeries

The Symbol LS 3000 Barcode Scanner Series are designed to meet theexacting requirements of rugged outdoor and industrial workenvironments.The Symbol LS 3603 Barcode Scanner Series features Symbol'spatented "fuzzy logic" technology with artificial intelligence for "smart"scanning of all types of difficult-to-read and damaged barcodes. Noother scanner is better at reading low-contrast and poorly printedbarcodes, including high-density and dot matrix symbols. Forrás: http://www.racoindustries.com/syls3000.htm

AEG LAV86741 - Factsheet

Front Loading Washing Machine. Advanced Rinse Technology. Advanced Fuzzy Logicintelligence. VARIOMATIC spin cycles. Microprocessor update facility. Child safety doorlock. Aqua Control flood protection and Aqua Lock. Variable spin. 3 time save options.LED showing programme length/wash time remaining.

Forrás: http://www.comparestoreprices.co.uk/washing-machines/aeg-lav86741.asp

The Small camera that gets you close to the action

The Samsung ECX-1 is for camera users who want the benefits of a decent zoom lens but in compact design.Designed by Porsche, the camera has a 4x zoom lens that ranges from 35mm to a full140mm for real telephoto work. You don't have to worry about camera shake orunderexposed shots: the built in microcomputer works out and adjusts the zoom,shutterspeed and flash when the camera is in fuzzy logic mode.Other modes include one for professional - looking portraits,and a step zoom,whichautomatically shoots the same subject in up to three focal lengths.The dioptre adjuster on the viewfinder setsthe camera to your individual eyesight requirement.

July 1994 p62

2008 5. oldal

Three ways of controlling a train.

Forrás: Reinfark, M.: Fuzzy Control Systems: Clear Advantages. Siemens Review Vol. 58, 6/91, pp. 28-32.

2008 6. oldal

Applications of neural networksNeural Networks in Practice

(by Christos Stergiou and Dimitrios Siganos)

Forrás:http://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Neural%20networks%20in%20medicine

Given this description of neural networks and how they work, what real world applications are theysuited for? Neural networks have broad applicability to real world business problems. In fact, they have alreadybeen successfully applied in many industries.

Since neural networks are best at identifying patterns or trends in data, they are well suited forprediction or forecasting needs including:

- sales forecasting- industrial process control- customer research- data validation- risk management- target marketingBut to give you some more specific examples; ANN are also used in the following specific paradigms:

recognition of speakers in communications; diagnosis of hepatitis; recovery of telecommunications from faultysoftware; interpretation of multimeaning Chinese words; undersea mine detection; texture analysis; three-dimensional object recognition; hand-written word recognition; and facial recognition.

Neural networks in medicineArtificial Neural Networks (ANN) are currently a 'hot' research area in medicine and it is believed that

they will receive extensive application to biomedical systems in the next few years. At the moment, theresearch is mostly on modelling parts of the human body and recognising diseases from various scans (e.g.cardiograms, CAT scans, ultrasonic scans, etc.).

Neural networks are ideal in recognising diseases using scans since there is no need to provide a specificalgorithm on how to identify the disease. Neural networks learn by example so the details of how to recognisethe disease are not needed. What is needed is a set of examples that are representative of all the variations of thedisease. The quantity of examples is not as important as the 'quantity'. The examples need to be selected verycarefully if the system is to perform reliably and efficiently.

Modelling and Diagnosing the Cardiovascular SystemNeural Networks are used experimentally to model the human cardiovascular system. Diagnosis can be

achieved by building a model of the cardiovascular system of an individual and comparing it with the real timephysiological measurements taken from the patient. If this routine is carried out regularly, potential harmfulmedical conditions can be detected at an early stage and thus make the process of combating the disease mucheasier.

A model of an individual's cardiovascular system must mimic the relationship among physiologicalvariables (i.e., heart rate, systolic and diastolic blood pressures, and breathing rate) at different physical activitylevels. If a model is adapted to an individual, then it becomes a model of the physical condition of thatindividual. The simulator will have to be able to adapt to the features of any individual without the supervisionof an expert. This calls for a neural network.

Another reason that justifies the use of ANN technology, is the ability of ANNs to provide sensor fusionwhich is the combining of values from several different sensors. Sensor fusion enables the ANNs to learncomplex relationships among the individual sensor values, which would otherwise be lost if the values wereindividually analysed. In medical modelling and diagnosis, this implies that even though each sensor in a setmay be sensitive only to a specific physiological variable, ANNs are capable of detecting complex medicalconditions by fusing the data from the individual biomedical sensors.

2008 7. oldal

Electronic nosesANNs are used experimentally to implement electronic noses. Electronic noses have several potential

applications in telemedicine. Telemedicine is the practice of medicine over long distances via a communicationlink. The electronic nose would identify odours in the remote surgical environment. These identified odourswould then be electronically transmitted to another site where an door generation system would recreate them.Because the sense of smell can be an important sense to the surgeon, telesmell would enhance telepresentsurgery.

Instant PhysicianAn application developed in the mid-1980s called the "instant physician" trained an autoassociative

memory neural network to store a large number of medical records, each of which includes information onsymptoms, diagnosis, and treatment for a particular case. After training, the net can be presented with inputconsisting of a set of symptoms; it will then find the full stored pattern that represents the "best" diagnosis andtreatment.

Neural Networks in businessBusiness is a diverted field with several general areas of specialisation such as accounting or financial

analysis. Almost any neural network application would fit into one business area or financial analysis.There is some potential for using neural networks for business purposes, including resource allocation

and scheduling. There is also a strong potential for using neural networks for database mining, that is, searchingfor patterns implicit within the explicitly stored information in databases. Most of the funded work in this areais classified as proprietary. Thus, it is not possible to report on the full extent of the work going on. Most workis applying neural networks, such as the Hopfield-Tank network for optimization and scheduling.Marketing

There is a marketing application which has been integrated with a neural network system. The AirlineMarketing Tactician (a trademark abbreviated as AMT) is a computer system made of various intelligenttechnologies including expert systems. A feedforward neural network is integrated with the AMT and wastrained using back-propagation to assist the marketing control of airline seat allocations. The adaptive neuralapproach was amenable to rule expression. Additionaly, the application's environment changed rapidly andconstantly, which required a continuously adaptive solution. The system is used to monitor and recommendbooking advice for each departure. Such information has a direct impact on the profitability of an airline andcan provide a technological advantage for users of the system. [Hutchison & Stephens, 1987]

While it is significant that neural networks have been applied to this problem, it is also important to seethat this intelligent technology can be integrated with expert systems and other approaches to make a functionalsystem. Neural networks were used to discover the influence of undefined interactions by the various variables.While these interactions were not defined, they were used by the neural system to develop useful conclusions.It is also noteworthy to see that neural networks can influence the bottom line.Credit Evaluation

The HNC company, founded by Robert Hecht-Nielsen, has developed several neural networkapplications. One of them is the Credit Scoring system which increase the profitability of the existing model upto 27%. The HNC neural systems were also applied to mortgage screening. A neural network automatedmortgage insurance underwritting system was developed by the Nestor Company. This system was trained with5048 applications of which 2597 were certified. The data related to property and borrower qualifications. In aconservative mode the system agreed on the underwritters on 97% of the cases. In the liberal model the systemagreed 84% of the cases. This is system run on an Apollo DN3000 and used 250K memory while processing acase file in approximately 1 sec.

2008 8. oldal

Applications of Genetic Algorithms(by Naranker Dulay)

Forrás:http://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/tcw2/report.html

Genetic Algorithms (GAs) are adaptive heuristic search algorithm premised on the evolutionaryideas of natural selection and genetic. The basic concept of GAs is designed to simulate processes in naturalsystem necessary for evolution, specifically those that follow the principles first laid down by Charles Darwinof survival of the fittest. As such they represent an intelligent exploitation of a random search within a definedsearch space to solve a problem.

If the conception of a computer algorithms being based on the evolutionary of organism issurprising, the extensiveness with which this algorithms is applied in so many areas is no less thanastounishing. These applications, be they commercial, educational and scientific, are increasingly dependent onthis algorithms, the Genetic Algorithms. Its usefulness and gracefulness of solving problems has made it the amore favourite choice among the traditional methods, namely gradient search, random search and others. GAsare very helpful when the developer does not have precise domain expertise, because GAs possess the ability toexplore and learn from their domain.

GA on optimisation and planning: Travelling Salesman ProblemThe TSP is interesting not only from a theoretical point of view, many practical applications can

be modelled as a travelling salesman problem or as variants of it, for example, pen movement of a plotter,drilling of printed circuit boards (PCB), real-world routing of school buses, airlines, delivery trucks and postalcarriers. Researchers have tracked TSPs to study biomolecular pathways, to route a computer networks' parallelprocessing, to advance cryptography, to determine the order of thousands of exposures needed in X-raycrystallography and to determine routes searching for forest fires (which is a multiple-salesman problempartitioned into single TSPs). Therefore, there is a tremendous need for algorithms.

In the last two decades an enormous progress has been made with respect to solving travellingsalesman problems to optimality which, of course, is the ultimate goal of every researcher. One of landmarks inthe search for optimal solutions is a 3038-city problem. This progress is only party due to the increasinghardware power of computers. Above all, it was made possible by the development of mathematical theory andof efficient algorithms.

GA in Business and Their Supportive Role in Decision MakingGenetic Algorithms have been used to solve many different types of business problems in

functional areas such as finance, marketing, information systems, and production/ operations. Within thesefunctional areas, GAs have performed a variety of applications such as tactical asset allocation, job scheduling,machine-part grouping, and computer network design.

Finance ApplicationsModels for tactical asset allocation and international equity strategies have been improved with

the use of GAs. They report an 82% improvement in cumulative portfolio value over a passive benchmarkmodel and a 48% improvement over a non-GA model designed to improve over the passive benchmark.

Information Systems ApplicationsDistributed computer network topologies are designed by a GA, using three different objective

functions to optimise network reliability parameters, namely diameter, average distance, and computer networkreliability. The GA has successfully designed networks with 100 order of nodes.

GA has also been used to determine file allocation for a distributed system. The objective is to maximisethe programs' abilities to reference the file s located on remote nodes.

Production/Operation ApplicationsGenetic Algorithm has been used to schedule jobs in a sequence dependent setup environment

for a minimal total tardiness. All jobs are scheduled on a single machine; each job has a processing time and adue date. The setup time of each job is dependent upon the job which immediately precedes it. The GA is ableto find good, but not necessarily optimal schedules, fairly quickly.

2008 9. oldal

GA is also used to schedule jobs in non-sequence dependent setup environment. The jobs arescheduled on one machine with the objective of minimising the total generally weighted penalty for earliness ortardiness from the jobs' due dates. However, this does not guarantee that it will generate optimal solutions forall schedules.

GA is developed for solving the machine-component grouping problem required for cellularmanufacturing systems. GA provides a collection of satisfactory solutions for a two objective environment(minimising cell load variation and minimising volume of inter cell movement), allowing the decision maker tothen select the best alternative.

Learning Robot behaviour using Genetic AlgorithmsRobot has become such an prominent tools that it has increasingly taken a more important role in many

different industries. As such, it has to operate with great effieciency and accuracy. This may not sound verydifficult if the environment in which the robot operates remain unchanged, since the behaviours of the robotcould be pre-programmed. However, if the environment is ever-changing, it gets extremely difficult, if notimpossible, for programmers to figure out every possible behaviours of the robot. Applying robot in a changingenvironment is not only inevitable in modern technology, but is also becoming more frequent. This hasobviously led to the development of a learning robot.

The approach to learning behaviours, which lead the robot to its goal, described here reflects aparticular methodology for learning via simulation model. The motivation is that making mistakes on realsystem can be costly and dangerous. In addition, time constraints may limit the extent of learning in real world.Since learning requirs experimenting with behaviours that might occassionally produce undesriable results ifapplied to real world. Therefore, as shown in the diagram, the current best behaviour can be place in the real,on-line system, while learning continues in the off-line system.

Genetic Algorithms for Object Localisation in a Complex SceneIn order to provide machines with the ability to interact in complex, real-world environments,

sensory data must be presented to the machine. One such module dealing with sensory input is the visual dataprocessing module, also known as the computer vision module. A central task of this computer vision module isto recognise objects from images of the environment.

There are two different parts to computer vision modules, namely segmentation and recognition.Segmentation is the process of finding interested objects while recognition works to see if the located objectmatches the predefined attributes. Since images cannot be recognised until they have been located andseparated from the background, it is of paramount importance that this vision module is able to locate differentobjects of interest for different systems with great efficiency.

Artificial LifeGenetic algorithms are currently the most prominent and widely used computational models of

evolution in artificial-life systems. This decentralised models provide a basis for understanding many othersystems and phenomena in the world. Researches on GAs in alife give illustrative examples in which thegenetic algorithm is used to study how learning and evolution interact, and to model ecosystems, immunesystem, cognitive systems, and social systems.

2008

Applications of chaos

Applications Of Chaos Theory To Real-Life SituationsForrás: http://library.thinkquest.org/3493/noframes/chaos.html

Much like physics, chaos theory provides a foundation for the study of all other scientific disciplines. Itis acually a tool box of methods for incorporating nonlinear dynamics into the study of science. For manypeople, the work in chaos represents the reunification of the sciences.

In mathematics, the use of strange attractors, fractals, and cellular automata, and other nonlinear,graphical models are used for studying data that was previously thought of as random. Mathematicalapplications of chaos theory actually began being developed 100 years ago by the French mathematician HenrePoincare.

In biology, chaos is used in the identification of new evolutionary processes leading to understandingthe genetic algorithim, artificial life simulations, better understanding of learning processes in systemsincluding the brain, and studies of such previously unresearchable areas as consciousness and the mind. Thisstrain can be traced back to the work of Charles Darwin, and is a significant new understanding of evolutionaryprocesses. Darwin's work also appears in direct conflict with Newton's because it changes our understanding ofthe nature of time, demonstrating that some time is not reversible.

In physics, thermodynamics in particular, chaos is applied in the study of turbulence leading to theunderstanding of self-organizing systems and system states (equilibrium, near equilibrium, the edge of chaos,and chaos). Prigogine explains that the concept of entropy is actually the physicists application of the conceptof evolution to physical systems. The greater the entropy of a system, the more highly evolved the system is.Chaos theory is also having a major impact on quantum physics and attempts to reconcile the chaos of quantumphysics with the predictability of Newton's universe. The push for such unification cam from Einstein. Chaostheory is causing most quantum physicists to accept what Einstein rejected, that God probably did play dicewith the universe.

Chaos theory is already affecting the critical aspects of our lives. It greatly impacts all sciences. Forexample, it is answering previously unsolvable problems in quantum mechanics and cosmology. Theunderstanding of heart arrhthmias and brain function has been revolutionized by chaos research. There havebeen games and toys developed from chaos research, such as the SimAnt, SimLife, SimCity, etc. series ofcomputer games. Fractal mathematics are critiical to improved information compression and encryptionschemese needed for computer networking and telecommunications. Genetic algorithims are being applied toeconomic research and stock predictions. Engineering applications range from factory scheduling to productdesign, with pioneering work being done at places such as DuPont and Deere & Co.

Peter Stavroulakis: Chaos Applications in TelecommunicationsForrás: http://www.telecommunicationsnetbase.com/ejournals/books/book_summary/summary.asp?id=3000

The concept of transmitting information from one chaotic system to another derives from the observation of thesynchronization of two chaotic systems. Having developed two chaotic systems that can be synchronized,scientists can modulate on one phase signal the information to be transmitted, and subtract (demodulate) theinformation from the corresponding phase signal of the coupled chaotic system.Chaos Applications in Telecommunications demonstrates this technique in various applications ofcommunication systems. This book details methods of transmitting information at much higher levels ofsecurity than what is available by current techniques. Following a detailed introduction, the book demonstrateshow chaotic signals are generated and transmitted. It then details the design of chaotic transmitters andreceivers, and describes chaos-based modulation and demodulation techniques. The text describes how a chaos-based spreading sequence outperforms classical pseudorandom sequences in selective and nonselectivechannels. It also develops channel equalization techniques designed for chaotic communications systems byapplying knowledge of systems dynamics, linear time-invariant representations of chaotic systems, andsymbolic dynamics representations of chaotic systems. The final chapter explains a specific application foroptical communications.

2008

Jason Putorti: Chaos and the Logistic MapForrás:http://pear.math.pitt.edu/mathzilla/Examples/chaos/studentReports/JasonPutorti.html

Applications of Chaos TheoryI found several several little tidbits around the Internet that show chaos theory applied to the world around us.The most obvious I already knew about was fractals, I have explored fractal systems for quite some time andthey are truly remarkable application of mathematics. Worlds within worlds, the closer you look, the more yousee, constantly changing and seemingly random patterns emerging before your eyes. Mandelbrot himself foundan interesting application that I found amusing:

How long is the coastline of Britain? His mathematical colleagues were miffed, to say the least, at suchan annoying waste of their time on such insignificant problems. Theof their time on such insignificantproblems. They told him to look it up. Of course, Madelbrot had a reason for his peculiar question, quite aninteresting reason. Look up the coastline of Britain yourself, in some encyclopedia. Whatever figure you get, itis wrong. Quite simply, the coastline of Britain is infinite. You protest that this is impossible. Well, considerthis. Consider looking at Britain on a very large-scale map. Draw the simplest two-dimensional shape possible,a triangle, which circumscribes Britain as closely as possible. The perimeter of this shape approximates theperimeter of Britain. However, this area is of course highly inaccurate. Increasing the amount of vertices of theshape going around the coastline, and the area will become closer. The more vertices there are, the closer thecircumscribing line will be able to conform to the dips and the protrusions of Britain's rugged coast. There isone problem, however. Each time the number of vertices increases, the perimeter increases. It must increase,because of the triangle inequality. Moreover, the number of vertices never reaches a maximum. There is nopoint at which one can say that a shape defines the coastline of Britain. After all, exactly circumscribing thecoast of Britain would entail encircling every rock, every tide pool, and every pebble that happens to lie on theedge of Britain. Thus, the coastline of Britain is infiritain is infinite.” –The Chaos Experience, Thinkquest.org

Chaos theory has been used to explain nearly every aspect of human life; the famous butterfly effectdetails how a seemingly miniscule force could affect storms on the other side of the planet. Edward Lorenzshowed how the bifurcation effect that we looked at earlier is consistent with attempts to predict the weather inany amount of time into the future. Why is the weather [forecast] right sometimes and off others? We put all thevariables into the system and what happens? 1/1000 decimal place in the results dramatically diverged theresults.

Another interesting fact I came across had to do with stock markets and their relation to the tree-likefractals:

While the branches get smaller and smaller, each is similar in structure to the larger branches and thetree as a whole. Similarly, in market price action, as you look at monthly, weekly, daily, and intra day barcharts, the structure has a similar appearance. Just as with natural objects, as you move in closer and closer, yousee more and more detail. Another characteristic of chaotic markets is called "sensitive dependence on initialconditions." This is what makes dynamic market systems so difficult to predict. Because we cannot accuratelydescribe the current situation band because errors in the description are hard to f description are hard to finddue to the system's overall complexity, accurate predictions become impossible. Even if we could predicttomorrow's stock market change exactly (which we can't), we would still have zero accuracy trying to predictonly twenty days ahead. A number of thoughtful traders and experts have suggested that those trading withintra day data such as five-minute bar charts are trading random noise and thus wasting their time. Over time,they are doomed to failure by the costs of trading. At the same time these experts say that longer-term priceaction is not random. Traders can succeed trading from daily or weekly charts if they follow trends. Thequestion naturally arises how can short-term data be random and longer-term data not be in the same market? Ifshort-term (random) data accumulates to form long-term data, wouldn't that also have to be random? As it turnsout, such a paradox can exist.” –The Chaos Experience, Thinkquest.org

Note Chaos theory is undoubtedly a hot, if not the hottest topic in modern mathematics. Ever readJurrasic Park? The possibilities for explanation of natural phenomena are endless including religion. Trulyfascinating!

Fuzzy rendszerek 2008 10. oldal

Neurális és fuzzy rendszerek képies bemutatása

A genetikus algoritmus vázlata

Idempotencia A∩A=A,A∪A=AInvolució A A=Kommutativitás A∩B=B∩A, A∪B=B∪AAsszociativitás (A∪B)∪C=A∪(B∪C)

(A∩B)∩C=A∩(B∩C)Disztributivitás A∪(B∩C)=(A∪B)∩(A∪C)

A∩(B∪C)=(A∩B)∪(A∩C)Elnyelés A∪(A∩B)=A

A∩(A∪B)=AA komplementum elnyelés A∪( A ∩B)=A∪B

A∩( A ∪B)=A∩BA DeMorgan törvények A B A B∪ = ∩

A B A B∩ = ∪

Halmaz műveletek alaptulajdonságai.


0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

A B

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

A B

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

A B

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

A B

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

A B

A és B fuzzy halmaz drasztikus összeg korlátos összeg algebrai összeg maximum

Az A és B fuzzy halmaz néhány s-normája

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

A B

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

A B

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

A B

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

A B

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

A B

A és B fuzzy halmaz minimum algebrai szorzat korlátos szorzat drasztikus szorzat

Az A és B fuzzy halmaz néhány t-normája

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

A Balgs

algt

a)

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

A Balgs

algt

b)

a) A és B fuzzy halmaz, b) a két halmaz algebrai összege és szorzata

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

A Bkorls

korlt

a)

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

A Bdras

drat

b)

A és B fuzzy halmaz a) korlátos, b) drasztikus összege és szorzata


0 0.5 10

0.2

0.4

0.6

0.8

1µ(x)

x 0 0.5 10

0.2

0.4

0.6

0.8

1µ(y)

y

0 0.5 10

0.5

10

0.5

1

yx 0 0.5 10

0.5

10

0.5

1

yx 0 0.5 10

0.5

10

0.5

1

yx

0 0.5 10

0.5

10

0.5

1

yx

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0.8 0.8 0.8 0.8 0.8 0.8 1 0.8 0.8 0.84 0.88 0.92 0.96 1 0.8 0.8 1 1 1 1 1 0.8 0.8 1 1 1 1 1

0.6 0.6 0.6 0.6 0.6 0.8 1 0.6 0.6 0.68 0.76 0.84 0.92 1 0.6 0.6 0.8 1 1 1 1 0.6 0.6 1 1 1 1 1

0.4 0.4 0.4 0.4 0.6 0.8 1 0.4 0.4 0.52 0.64 0.76 0.88 1 0.4 0.4 0.6 0.8 1 1 1 0.4 0.4 1 1 1 1 1

0.2 0.2 0.2 0.4 0.6 0.8 1 0.2 0.2 0.36 0.52 0.68 0.84 1 0.2 0.2 0.4 0.6 0.8 1 1 0.2 0.2 1 1 1 1 1

0 0 0.2 0.4 0.6 0.8 1 0 0 0.2 0.4 0.6 0.8 1 0 0 0.2 0.4 0.6 0.8 1 0 0 0.2 0.4 0.6 0.8 1

↑→yx

0 0.2 0.4 0.6 0.8 1 ↑→yx

0 0.2 0.4 0.6 0.8 1 ↑→yx

0 0.2 0.4 0.6 0.8 1 ↑→yx

0 0.2 0.4 0.6 0.8 1

max algs korls dras

s-norma felületek és vetületeik

0 0.5 10

0.2

0.4

0.6

0.8

1µ(x)

x 0 0.5 10

0.2

0.4

0.6

0.8

1µ(y)

y

0 0.5 10

0.5

10

0.5

1

yx 0 0.5 10

0.5

10

0.5

1

yx 0 0.5 10

0.5

10

0.5

1

yx 0 0.5 10

0.5

10

0.5

1

yx

1 0 0.2 0.4 0.6 0.8 1 1 0 0.2 0.4 0.6 0.8 1 1 0 0.2 0.4 0.6 0.8 1 1 0 0.2 0.4 0.6 0.8 1

0.8 0 0 0 0 0 0.8 0.8 0 0 0.2 0.4 0.6 0.8 0.8 0 0.16 0.32 0.48 0.64 0.8 0.8 0 0.2 0.4 0.6 0.8 0.8

0.6 0 0 0 0 0 0.6 0.6 0 0 0 0.2 0.4 0.6 0.6 0 0.12 0.24 0.36 0.48 0.6 0.6 0 0.2 0.4 0.6 0.6 0.6

0.4 0 0 0 0 0 0.4 0.4 0 0 0 0 0.2 0.4 0.4 0 0.08 0.16 0.24 0.32 0.4 0.4 0 0.2 0.4 0.4 0.4 0.4

0.2 0 0 0 0 0 0.2 0.2 0 0 0 0 0 0.2 0.2 0 0.04 0.08 0.12 0.16 0.2 0.2 0 0.2 0.2 0.2 0.2 0.2

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

↑→yx

0 0.2 0.4 0.6 0.8 1 ↑→yx

0 0.2 0.4 0.6 0.8 1 ↑→yx

0 0.2 0.4 0.6 0.8 1 ↑→yx

0 0.2 0.4 0.6 0.8 1

drat korlt algt min

t-norma felületek és vetületeik


A fuzzy aggregációs operátorok teljes befutási tartománya.

A Hamacher operátorok tartományai.

Kompenzátoros paraméteres operátorok befutási tartományai.


Az inferencia kompozíciós szabálya

02

46

810

0

10

20

30

400

0.5

1

XY

a) fuzzy reláció X és Y alaphalmazon0

510

0

10

20

30

400

0.5

1

XY

B

b) X-en definiált "B" halmaz hengereskiterjesztése

05

10

0

10

20

30

400

0.5

1

XY

"a)" és "b)" minimuma0

510

0

10

20

30

400

0.5

1

XY

"c)" vetítése az Y tengelyre

Fuzzy relációk kompozíciójának �szemléletes� bemutatása

Fuzzy módszerek 2008 17. oldal


a) b)a) rács, b) fa particionálás

a) b) c)

a) rács, b) klaszter alapú, c) "sorbaállítós" particionálás

A Mamdami és a Lukasiewicz inferencia összehasonlítása

Neurális hálózatok 2008 21. oldal

Alapvető neurális hálózati topológiák

Felügyelt tanulás blokkdiagramja

Nem felügyelt tanulás blokk-vázlata

Megerősítő tanulás blokk-diagrammja


A hiba-visszaterjesztéses módszer

Kaotikus rendszerek 2008 33. oldal

A logisztikai egyenlet különbözõ paraméter értékeknél

A logisztikai egyenlet viselkedése a p bifurkációs paraméter függvényében

fuzzy, neurális és genetikus mesterséges intelligencia ... · 2008 1. oldal fuzzy, neurÆlis Øs...

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