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This lecture was delivered by Dr. Asif Ullah at Pakistan Institute of Engineering and Applied Sciences, Islamabad (PIEAS) for Fuzzy Intelligence course. It includes: Introduction, Complexity, Credibility, Uncertainty, Traditional, Modern, Logic, Probability
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Department of Computer & Information SciencesPakistan Institute of Engineering and Applied Sciences
CIS-524 Fuzzy Intelligence
Lecture 01
Umar Faiz
http://www.pieas.edu.pk/umarfaiz/cis
CIS-524 Fuzzy Intelligence
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In general practice, we deal with problems in terms ofsystems that are constructed as modelssystems that are constructed as models.
The purpose of constructing models is to understand
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some phenomenon of reality, be it natural or man-made.
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Uncertainty has a pivotal role in any effort tomaximize the usefulness of systems modelsmaximize the usefulness of systems models.
Uncertainty becomes very valuable when considered in
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connection to the other characteristics of the systemsmodels.
The concept of uncertainty in science and mathematicsis manifested by two views
Traditional View
Modern View
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Traditional View:
According to traditional view science should strive for
According to traditional view, science should strive forcertainty in all its manifestations (precision, specificity,sharpness, consistency, etc) and uncertainty (imprecision, non-
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specificity, vagueness, inconsistency, etc) is considered asunscientific.
Modern View:
According to modern view, uncertainty is considered essential
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Fuzzy Logic
Fuzzy or multi valued logic was introduced in the 1930s by
Fuzzy, or multi-valued logic, was introduced in the 1930s byJan Lukasiewicz, a Polish philosopher.
While classical logic operates with only two values 1 (true)While classical logic operates with only two values 1 (true) and 0 (false), Lukasiewicz introduced logic that extended therange of truth values to all real numbers in the intervalbetween 0 and 1.
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In 1965 Lotfi Zadeh, published his famous paper“Fuzzy sets” Zadeh extended the work on possibility
Fuzzy sets. Zadeh extended the work on possibility theory into a formal system of mathematical logic, andintroduced a new concept for applying naturalintroduced a new concept for applying naturallanguage terms.
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This new logic for representing and manipulating fuzzyterms was called fuzzy logic.
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The word fuzzy means blurred, fluffy, frayed orindistinctindistinct.
Fuzzy logic is not logic that is fuzzy, but logic that is
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used to describe fuzziness.
Fuzziness is deterministic uncertainty.
Fuzziness is connected with the degree to which eventsoccur rather than the likelihood of their occurrence(probability).
For example, the degree to which a person is young is afuzzy event rather than a random event.
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Fuzzy sets are functions that map each member in a setto a real number in [0 1] to indicate the degree ofto a real number in [0, 1] to indicate the degree ofmembership of that member.
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The ambiguity of real world definitions
Javaid is OLD
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"OLD" i
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60?
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ow "OLD" is old? 40 years, 50, or 60?
Daud is TALL
How "TALL" is tall? 5 feet, 6 feet, or 7 feet?
Every thing is a matter of degree
The "degrees" of being old or tall can be quantitativelyillustrated using quantified meaning.
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Replacement of a skilled human operator by a fuzzyrule based systemrule based system
Sendal subway (Hitachi)
Cement kiln (F L Smith)
Cement kiln (F.L. Smith)
Elevator Control (Fujitec, Hitachi, Toshiba)
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Sugeno s model car and model helicopter
Hirota's robotN
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uclear Reactor Control (Hitachi, Bernard)
Automobile automatic transmission (Nissan, Subaru)B lld
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ulldozer Control (Terano)
Ethanol Production (Filev)
Appliance control – Washing machine, microwave ovens, ricecookers, vacuum cleaners, camcorders, TVs, thermal rugs,heaters
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Replacement of a human expert by a fuzzy logicbased decision making systembased decision making system
Medical – CADIAG
Securities (Yamaichi Hitachi)
Securities (Yamaichi, Hitachi)
Credit Worthiness (Zimmermann)
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Damage assessment (Yao, Hadipriono)
Fault Diagnosis (Guangzhou)P
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roduction planning (Turksen)
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A Neural Network generally maps a set of inputs to aset of outputsset of outputs
Number of inputs/outputs is variable
The network itself is composed of an arbitrary numberof nodes with an arbitrary topology
Input 0
Input 1
Input n
Output 0
Output 1
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Neuron vs. Node
Illustration of a biological and artificial neuron (perception)
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Has a potential to solve difficult problems currentmethods can not solve well (realistic reasons):methods can not solve well (realistic reasons):
Pattern classification: hand-written characters, facialexpression engine diagnosis etcexpression, engine diagnosis, etc.
Non-linear time series modeling, forecasting: Stock price,utility forecasting, ecg/eeg/emg, speech, etc.
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Adaptive control, machine learning: robot arm, autonomousvehicle
Requires massive parallel implementation with opticaldevices, analog ICs.devices, analog ICs.
Performance degrades gracefully when portions of thenetwork are faultynetwork are faulty.
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The study of neural networks started by the publicationof Mc Culloch and Pitts [1943]of Mc Culloch and Pitts [1943].
The single-layer networks, with threshold activation functions,were introduced by Rosenblatt [1959] These types ofwere introduced by Rosenblatt [1959]. These types ofnetworks were called perceptrons.
In the 1960s it was experimentally shown that perceptrons
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could solve many problems, but many problems could not besolved.
These limitations of one-layer perceptron weremathematically shown by Minsky and Papert in their
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book Perceptron [1969].
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