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Soft computing (SC)

Objective:

Mimic human (linguistic) reasoning

Main constituents:

- Fuzzy systems

- Neural networks

- Evolutionary computing

- Probabilistic reasoning

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Constituents of SC

• Fuzzy systems => imprecision

• Neural networks => learning

• Probabilistic reasoning => uncertainty

• Evolutionary computing => optimization

Over 24 000 publications today

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SC: a user-friendly interface

Soft computing approach

Linguistic worldSoft data

InterpretationsUnderstandingExplanations

Qualitative methodsBivalent or multivalent

reasoning

Mathematical worldHard data

Quantitative methodsBivalent reasoning

Phenomenon under study

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Advantages of SC

• Models base on human reasoning.

• Models can be- linguistic - simple (no number crunching),- comprehensible (no black boxes), - fast when computing, - good in practice.

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SC today (Zadeh)

• Computing with words (CW)

• Theory of information granulation (TFIG)

• Computational theory of perceptions (CTP)

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Possible SC data & operations

• Numeric data:5, about 5, 5 to 6, about 5 to 6

• Linguistic data: cheap, very big, not high, medium or bad

• Functions & relations:f(x), about f(x), fairly similar, much greater

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Neural networks (NN, 1940's)

• Neural networks offer a powerful method to explore, classify, and identify patterns in data.

• Website of Matlab

• Neuron: y=wixi

InputsNeurons(1 layer)

Outputs

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Machine learning (supervised)

• Pattern recognition based on training data.

• Classification supervised by instructor.

• Neural (crisp or fuzzy), neuro-fuzzy and fuzzy models.

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Plum?

Instructor

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Machine learning (unsupervised)

• Pattern recognition based on training data.

• Classification based on structure of data (clustering).

• Neural (crisp or fuzzy), neuro-fuzzy and fuzzy models.

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Nectarine

Labeling

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Machine learning (unsupervised)

• Self-organized maps (Kohonen).

• Fuzzy c-means (Bezdek).

• Subclust (Yager, Chiu).

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LabelingWebsomSelf-Organizing

Maps for Internet Exploration

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Fuzzy systems (Zadeh, 1960's)• Deal with imprecise entities in automated environments

(computer environments)

• Base on fuzzy set theory and fuzzy logic.

• Most applications in control and decision making

Omron’s fuzzy processor

Omron Electronics

Matlab's Fuzzy Logic Toolbox

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SC applications: control

• Heavy industry (Matsushita, Siemens, Stora-Enso)

• Home appliances (Canon, Sony, Goldstar, Siemens)

• Automobiles (Nissan, Mitsubishi, Daimler-Chrysler, BMW, Volkswagen)

• Spacecrafts (NASA)

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SC applications: business

•hospital stay prediction,•TV commercial slot evaluation, •address matching, •fuzzy cluster analysis,•sales prognosis for mail order house, •multi-criteria optimization etc.•(source: FuzzyTech)

•supplier evaluation for sample testing,•customer targeting, •sequencing, •scheduling, •optimizing R&D •projects, •knowledge-based prognosis, •fuzzy data analysis

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SC applications: finance

• Fuzzy scoring for mortgage applicants,

• creditworthiness assessment,

• fuzzy-enhanced score card for lease risk assessment,

• risk profile analysis,

• insurance fraud detection,

• cash supply optimization,

• foreign exchange trading,

• insider

• trading surveillance,

• investor classification etc.

• Source: FuzzyTech

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SC applications: robotics

Fukuda’s lab

Joseph F. Engelberger

We are proud to announce that the HelpMate Robotic Courier has been acquired by Pyxis Corporation.

Entertainment robot AIBO

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SC applications: others

•Statistics

•Social sciences

•Behavioural sciences

•Biology

•Medicine

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(Neuro)-fuzzy system construction

Training data

ExpertsFuzzy rules(SOM, c-means etc.)

Control data

System evaluation(errors)

Tuning(NN)

New system

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Model construction (mathematical)

• Mathematical models are functions. Deep knowledge on mathematics.• If non-linear (eg. NN), laborious calculations and computing.• Linear models can be too simplified.• How can we find appropriate functions?

Y=1-1./(1 + EXP(-2*(X-5)))

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Model construction (trad. rules )

If 0<x<1, then y=1If 1<x<2, then y=0.99:If 8<x<10, then y=0

If 0<x<1, then y=f(x)If 1<x<2, then y=g(x):If 8<x<10, then y=h(x)

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- Rule for each input. => Large rule bases.- Only one rule is fired for each input. - Coarse models.

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Model construction (SC/fuzzy)

If x0, then y1If x5, then y0.5If x10, then y0

- Approximate values- Rules only describe typical cases (no rule for each input). => Small rule bases.- A group of rules are partially fired simultaneously.

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SC and future

SC and conventional methods should be used in combination.