Department of Computer Science, Department of Computer Science,
(UBIT)(UBIT)
University of KarachiUniversity of Karachi
Artificial Intelligence: Artificial Intelligence: Logic Systems for Logic Systems for
ReasoningReasoning
(First National Conference on (First National Conference on Mathematical Sciences)Mathematical Sciences)
2222––MarchMarch––2010 2010
MERITORIOUS PROFESSOR DR. S.M. AQIL BURNEYDepartment of Computer Science at UBIT
University of KarachiEmail: [email protected]
www.drburney.net
2222––MarchMarch––2010 2010
•• Hard Approach : Precise Truth values Hard Approach : Precise Truth values available for modeling and computingavailable for modeling and computing
Modeling and ComputingModeling and Computing
•• Soft Approach : Imprecise Truth valuesSoft Approach : Imprecise Truth values
What is Intelligence?What is Intelligence?
�� IntelligenceIntelligence is the ability to understand is the ability to understand and learn things. and learn things.
�� IntelligenceIntelligence is the ability to think and is the ability to think and �� IntelligenceIntelligence is the ability to think and is the ability to think and understand instead of doing things by understand instead of doing things by instinct or automatically.instinct or automatically.
((Essential English DictionaryEssential English Dictionary, Collins, London, , Collins, London, 1990)1990)
Definition of Artificial Definition of Artificial
IntelligenceIntelligence�� “Artificial intelligence is the study of how to make “Artificial intelligence is the study of how to make
computers do things at which, at the moment, people are computers do things at which, at the moment, people are better”.better”.
�� “ Artificial intelligence is the branch of Computer Science “ Artificial intelligence is the branch of Computer Science that deals with ways of representing knowledge using that deals with ways of representing knowledge using symbols rather than numbers and with rules of thumb, or symbols rather than numbers and with rules of thumb, or heuristic, methods for processing information”. heuristic, methods for processing information”. heuristic, methods for processing information”. heuristic, methods for processing information”. Bruce G. Buchanan, Encyclopedia BritannicaBruce G. Buchanan, Encyclopedia Britannica
�� “ In simplified terms, artificial intelligence works with “ In simplified terms, artificial intelligence works with pattern matching methods which attempt to describe pattern matching methods which attempt to describe objects, events, or processes in terms of their qualitative objects, events, or processes in terms of their qualitative features and logical and computational relationships”. features and logical and computational relationships”. Brattle Research Corporation, Artificial Intelligence and Fifth Brattle Research Corporation, Artificial Intelligence and Fifth Generation Computer TechnologiesGeneration Computer Technologies
Goals of AIGoals of AI
�� Scientific ,Business and engineeringScientific ,Business and engineering•• Understanding of computational Understanding of computational mechanisms needed for intelligent mechanisms needed for intelligent behaviorbehavior
•• Intelligent connection of perception Intelligent connection of perception and actionand actionand actionand action
•• Replicate human intelligenceReplicate human intelligence•• Solve knowledgeSolve knowledge--intensive tasksintensive tasks•• Enhance humanEnhance human--human, humanhuman, human--computer and computercomputer and computer--computer computer interaction/communicationinteraction/communication
What Computers can do better than People
•Numerical Computation
•Information Storage•Information Storage
•Repetitive Operations
What people can do better than Computers
•Understand Information
•Common Sense
•Inference
•Pattern Matching
•Intuition
What problems the people are What problems the people are
facing in ICT age?facing in ICT age?�� A professor of psychology at Harvard University A professor of psychology at Harvard University
warned that by the year 2000 the limit of man’s mind warned that by the year 2000 the limit of man’s mind to absorb information may be reachedto absorb information may be reached
�� Most recently very complex and technologically Most recently very complex and technologically oriented society has created a situation in which more oriented society has created a situation in which more people an organizations have become concerned with people an organizations have become concerned with handling information and fewer with handling materialhandling information and fewer with handling materialpeople an organizations have become concerned with people an organizations have become concerned with handling information and fewer with handling materialhandling information and fewer with handling material
�� Information is an essential element in decision makingInformation is an essential element in decision making
�� One of the major problems in design of modern One of the major problems in design of modern information systems is automatic pattern recognition. information systems is automatic pattern recognition. Which forms the dominant part of Computer Science Which forms the dominant part of Computer Science and Information Technology.and Information Technology.
�� J. T. Tou, R.C. Gonzalez; Pattern recognition Principles J. T. Tou, R.C. Gonzalez; Pattern recognition Principles Addison Wesley Publishing Company, LondonAddison Wesley Publishing Company, London
Fields of AI
•Expert Systems
•Natural Language Processing
•Speech Recognition
•Computer Vision•Computer Vision
•Robotics
•Intelligent Computer Assisted Instruction
•Automatic Programming
•Planning and Decision Support
Artificial Life
Modeling Hu
man
Performance
ArtificialIntelligence
Machine
Learning &
Robotics
AI & Phil
osophy
Neural
Networks Parallel
Distribute processing
Automated
Reasoning
Natural
Language
Processing
Expert Systems Distributed AI
Playing Game
�� Computer ScienceComputer Science
�� CriminologyCriminology�� Cognitive ScienceCognitive Science
Kinesiology & Health SciencesKinesiology & Health Sciences
�� Information TechnologyInformation Technology
�� Mathematics Mathematics
�� Religious StudiesReligious Studies
�� PsychologyPsychology
�� Professional WritingProfessional Writing
�� WomenWomen’’s Studiess Studies
�� Environmental ManagementEnvironmental Management
�� MusicMusic
MusicMusic
�� Film & VideoFilm & Video
�� BiologyBiology �� LatinLatin
�� Creative WritingCreative Writing
�� Kinesiology & Health SciencesKinesiology & Health Sciences
�� Political SciencePolitical Science
�� Communication StudiesCommunication Studies
�� Theatre Theatre
�� MusicMusic
�� Translation Translation
�� Physics & Astronomy Physics & Astronomy
�� Law & SocietyLaw & Society
�� International StudiesInternational Studies
�� EconomicsEconomics �� European StudiesEuropean Studies
�� Health & SocietyHealth & Society
�� Classical StudiesClassical Studies
�� Computer Science/ICTComputer Science/ICT
�� CriminologyCriminology�� Cognitive ScienceCognitive Science
Kinesiology & Health SciencesKinesiology & Health Sciences
�� Information TechnologyInformation Technology
�� Mathematics Mathematics
�� Religious StudiesReligious Studies
�� PsychologyPsychology
�� Professional WritingProfessional Writing
�� WomenWomen’’s Studiess Studies
�� Environmental ManagementEnvironmental Management
�� MusicMusic
MusicMusic
�� Film & VideoFilm & Video
�� BiologyBiology �� LatinLatin
�� Creative WritingCreative Writing
�� Kinesiology & Health SciencesKinesiology & Health Sciences
�� Political SciencePolitical Science
�� Communication StudiesCommunication Studies
�� Theatre Theatre
�� MusicMusic
�� Translation Translation
�� Physics & Astronomy Physics & Astronomy
�� Law & SocietyLaw & Society
�� International StudiesInternational Studies
�� EconomicsEconomics �� European StudiesEuropean Studies
�� Health & SocietyHealth & Society
�� Classical StudiesClassical Studies
Life and IntelligenceLife and Intelligence
�� Self organization and perpetuation Self organization and perpetuation leads to Intelligence and Intelligence leads to Intelligence and Intelligence created in noncreated in non--biological Systems is biological Systems is Artificial Intelligence.Artificial Intelligence.Artificial Intelligence.Artificial Intelligence.
Modeling Human Performance
Human intelligence is reference point in AI. The
understanding of human intelligence is essential and
open scientific challenge.
• AI engineers usually not committed to • AI engineers usually not committed to
“making their programs act like humans.
•AI engineer seldom ignore the humans solution.
The discipline that uses AI tools to explore the nature
of human intelligence is called Cognitive Science.
Automated Reasoning
• Logic lends itself to automation.
• A variety of problems can be attacked by
representing the problem description and representing the problem description and
relevant background information as logical
axioms and treating problem instances as
theorems to be proved.
Logic and ReasoningLogic and Reasoning
Logical Reasoning
Reasoning Subjective
Probabilistic Reasoning
Bayesian Networks
�� Using given knowledge and truth Using given knowledge and truth value help us to solve, understand value help us to solve, understand real life problems.real life problems.
EXAMPLEEXAMPLE
•• p: All mathematicians wear glassesp: All mathematicians wear glasses
•• q: Anyone who wears glasses is an q: Anyone who wears glasses is an algebraistalgebraist
•• r: All mathematicians are algebraistr: All mathematicians are algebraist•• r: All mathematicians are algebraistr: All mathematicians are algebraist
pp∧∧q q →→ r r ≡≡ ( ( ∼∼( p( p∧∧q) q) ∨∨ r)r)
TRUTH TABLE
Truth Table for the formulae built with the Logical Operators
p q r pΛΛΛΛq ~(pΛΛΛΛq) ~(pΛΛΛΛq)Vr
T T T T F T
T T F T F F
T F T F T TT F T F T T
T F F F T T
F T T F T T
F T F F T T
F F T F T T
F F F F T T
�� If r is the conclusion, and we know If r is the conclusion, and we know that p and q are true simultaneously that p and q are true simultaneously then r is valid statement.then r is valid statement.
�� In real life, the statements are true In real life, the statements are true or false, here statement means an or false, here statement means an or false, here statement means an or false, here statement means an atomic statement, thus statements atomic statement, thus statements may be simple (atomic) or may be simple (atomic) or component. If p, q and r are component. If p, q and r are independent statements, then we independent statements, then we
need to prove: need to prove: pp∧∧q q →→ r r
CommitmentCommitment
Ontological CommitmentOntological Commitment: : PPTPPT
What exists in the world: Language of What exists in the world: Language of reasoning (Formal).reasoning (Formal).
Epistemological CommitmentEpistemological CommitmentEpistemological CommitmentEpistemological Commitment
What an intelligent entity believes What an intelligent entity believes about the fact.about the fact.
Believe System: True, False, Believe System: True, False, Unknown, degree of believe, degree Unknown, degree of believe, degree believe with ranks (known values)believe with ranks (known values)
NUMBERS ARE RESPECTEDNUMBERS ARE RESPECTED——WORDS ARE NOTWORDS ARE NOT
�� “In science and engineering there is a deep“In science and engineering there is a deep--seated tradition of according much more seated tradition of according much more respect to numbers than to words. The respect to numbers than to words. The essence of this tradition was stated essence of this tradition was stated succinctly by Lord Kelvin in 1883.”succinctly by Lord Kelvin in 1883.”succinctly by Lord Kelvin in 1883.”succinctly by Lord Kelvin in 1883.”
Zadeh Zadeh -- 20042004
�� But now imprecise knowledge But now imprecise knowledge in words is also of immense in words is also of immense importance in developing importance in developing logical systems.logical systems.
FormalFormal
LanguageLanguage
OntologyOntology
What exists)What exists)
EpistemologyEpistemology
PropositionPropositional Logical Logic
factsfacts True/False True/False /Unknown/Unknown
Predicate Predicate LogicLogic
Facts, objects, Facts, objects, relationsrelations
True/False True/False /Unknown/UnknownLogicLogic relationsrelations /Unknown/Unknown
Probability Probability TheoryTheory
Facts with Facts with changechange
Degree of Degree of believe on [0,1]believe on [0,1]
Temporal Temporal LogicLogic
Facts, objects, Facts, objects, relation and relation and timetime
True/False True/False /Unknown/Unknown
Fuzzy LogicFuzzy Logic(Lectures of Dr. (Lectures of Dr. Burney)Burney)
Facts with Facts with degree of degree of believebelieve
Known Known interval interval valuevalue
ANNANN--FLFL
(NFL (NFL Example)Example)
Facts with Facts with degree of degree of believe with believe with
Known Known interval interval values with values with Example)Example) believe with believe with
learninglearningvalues with values with improvement improvement in believein believe
Spatial LogicSpatial Logic Facts, Facts, objects, objects, relation, time relation, time & Space& Space
True/False True/False /Unknown/Unknown
Application of Fuzzy LogicApplication of Fuzzy Logic
�� An Example of Traffic Light Controller An Example of Traffic Light Controller SystemSystem
Evolution of NeuroEvolution of Neuro--Fuzzy LogicFuzzy Logic
Neural
Approximate Reasoning
Fuzzy Logic
Functional Approximation/
Randomized Search
Neuro-FuzzySystems
NeuralNetworks
Fuzzy Logic
Production systems
A production system provides pattern-solving process
and consists of a set of
• Production rule• Production rule
• A working Memory
• A recognize-act control cycle
Example of a production system
Problem statement:
Sort (re-arrange the alphabets in) a string
composed of only three alphabets a, b and c. for
Example the string cbaca should be sorted to
give out aabcc.give out aabcc.
Solution
To understand how this can be solved consider
the following three points
1. Production rules
To solve this problem we need production rules.
A Production rule is a structure used to
represent a variety of knowledge types. Such
rules are often described in an if … thenrules are often described in an if … thenfromat.
For this problem the Production set(i.e. set of rules to solve the problem)is given below
.ba → ab
.ca → ac.ca → ac
.cb → bc
Rules say that whenever the pattern“ba” is found replace it with “ab”, andso on.
The recognize act cycle
The current state of the problem solving
process is maintained as a set of
patterns in working memory. Working
memory is initialized with the beginning
problem description. Production rules areproblem description. Production rules are
then applied to current state of the
pattern. All the rules which match the
current pattern are noted and then
conflict resolution is performed. This
process is repeated until the set of
conflicting rules is null
Conflict resolution
The patterns in a working memory are matched against the conditions of the production rules; this produces a subset of the productions, called conflict set. Whose conditions match the patterns in working memory. The productions in the conflict set are said to be enabled. One of the are said to be enabled. One of the productions in the conflict set is then selected and a production rule is fired. That is the action of the rule is performed. Conflict resolution strategies may be as simple as selecting the first rule or may also be complex.
For this problem we choose “apply
rule with smallest rule number” asrule with smallest rule number” as
conflict resolution strategy.
Trace of the above production system.
Iteration # Working memory Conflict set Rule fired
0 “cbaca” 1, 2, 3 1
1 “cabca” 2 2
2 “acbca” 3, 2 22 “acbca” 3, 2 2
3 “acbac” 1, 3 1
4 “acabc” 2 2
5 “aacbc” 3 3
6 “aabcc” Null Halt
AI and Philosophy:
As human intelligence is reference As human intelligence is reference point to AI and HI evolves in point to AI and HI evolves in philosophical, mathematical, social philosophical, mathematical, social environment and have roots in environment and have roots in environment and have roots in environment and have roots in societies.societies.
ContributesContributes
HI AIHI AI
A design is made concrete in a program and the
program is run as experiment, then redesign,
rerun and testing and validity is done to conform
over representations and algorithms are sufficient
model of required intelligent behavior.
Software Development ModelsTuring Test
The necessary and sufficient condition for a
physical system to exhibit intelligence is that it
should be physical symbol system.
The Turing Test:
The Turing Test has been called the pinnacle of AI. In
the simplest case, a human judge sits in front of a
terminal. At the other end of the communication link
sits another human or a computer running AI
software. After an on-line chat, the judge decidessoftware. After an on-line chat, the judge decides
whether he or she has been communicating with a
computer or a human. If the judge can’t guess
correctly 70% of the time, the program passes the
Turing Test.
THE INTERROGATOR
Human Response
Machine Response
TURING TEST
Expert Systems:
An expert system is knowledge based program
that provides “expert quality solutions to problems
in a specific domain”.
Converting the knowledge of an expert in to a Converting the knowledge of an expert in to a
software usually give rise to an expert system--an
intelligent entity replaces an expert
In Simple
Human Experts in any field are frequently in great
Computer programs that embody human expertise
Human Experts in any field are frequently in great
demand and are, therefore, usually in short supply.
Limitation: Unfortunately in most fields there are
more problems than experts.
Components of an Expert System (SE)
Knowledge BaseKnowledge Base
Inference Engine
User
Interface
User
Communication
Knowledge Base
The component of ES that contains the systems
knowledge is called its knowledge base as meree
emulation of the human reasoning process is not
sufficient.
Declarative Knowledge (object Oriented)
facts about objects, events and situations
KB
Procedural Knowledge
(Information about possible courses of actions)
Knowledge Representation Techniques Knowledge Representation Techniques
Logic: For declarative Knowledge (DK)
Semantic Network: Graphical representation of DK
Production Systems: Procedural Knowledge is represented as production rules
about actions to be taken.
Rule-based expert Systems
Rule-based Systems
Expert systems development tools are needed to avoid expanses and delays and to improve efficiency of the development process.
ART TM (Automated Reasoning Tool TM )
useful for commercial expert systems for useful for commercial expert systems for
Resource scheduling, Manufacturing, Planning
Financial planning, command & control
• HES (Human Edge Software) Product
Expert Ease TM
• KEE TM (Knowledge Engineering Environment)
• KES (Knowledge Engineering SYSTEM)
• Expert Rule etc.
Natural Language Processing (NLP)
NLP Language that is typed, printed or displayed
rather than being spoken
Speech Recognition (SR)
SR Getting Computers to understand spoken
language is the focus of related AI technologies called
Speech Recognition.
Neural Network
Computing or information processing has been dominated
by the concept of “Programmed Computing” in which
i) Algorithms are designed
ii) Algorithms are implemented using currently
dominant architecture.
Computing in biological systems is much different from Computing in biological systems is much different from
above mentioned paradigm in that
i) The computation is massively distributed and parallel
ii) Learning replaces a prior program development
Artificial neural networks (ANN) are developed using
paradigm of computing in biological system such as
computation in brain.
�� Primary motor: voluntary movementPrimary motor: voluntary movement�� Primary somatosensory: tactile, pain, Primary somatosensory: tactile, pain,
pressure, position, temp., mvt.pressure, position, temp., mvt.�� Motor association: coordination of Motor association: coordination of
complex movementscomplex movements�� Sensory association: processing of Sensory association: processing of
multisensorial informationmultisensorial information�� Prefrontal: planning, emotion, judgementPrefrontal: planning, emotion, judgement�� Speech center (Broca’s area): speech Speech center (Broca’s area): speech
production and articulationproduction and articulation
Major Functional Areas
production and articulationproduction and articulation�� Wernicke’s area: comprehension of Wernicke’s area: comprehension of
speechspeech�� Auditory: hearingAuditory: hearing�� Auditory association: complex auditory Auditory association: complex auditory
processingprocessing�� Visual: lowVisual: low--level visionlevel vision�� Visual association: higherVisual association: higher--level visionlevel vision
Modeling of Brain Modeling of Brain
Functions: Functions:
InterconnectInterconnect
Structure of a NeuronStructure of a Neuron
Electron Micrograph of a Real Electron Micrograph of a Real
NeuronNeuron
Remember? Neurons & Synapses Remember? Neurons & Synapses
Key terms:Key terms:
�� AxonAxon
�� DendritesDendrites
�� SynapsesSynapses
�� Soma Soma (cell (cell (cell (cell body)body)
Engineering Applications: Engineering Applications: ClassificationClassification
•• Machinery defect diagnosis Machinery defect diagnosis
•• Signal processing Signal processing
•• Character recognition Character recognition
•• Process supervision Process supervision
•• Process fault analysis Process fault analysis •• Process fault analysis Process fault analysis
•• Speech recognition Speech recognition
•• Machine vision Machine vision
•• Speech recognition Speech recognition
•• Radar signal classificationRadar signal classification
Engineering Applications: Engineering Applications: ModellingModelling
•• Transducer linearization Transducer linearization
•• Color discrimination Color discrimination
•• Robot control and navigation Robot control and navigation
•• Process control Process control
•• Aircraft landing control Aircraft landing control •• Aircraft landing control Aircraft landing control
•• Car active suspension control Car active suspension control
•• Printed Circuit auto routing Printed Circuit auto routing
•• Integrated circuit layout Integrated circuit layout
•• Image compression Image compression
A MachineA Machine--gun Equipped Robotic gun Equipped Robotic Sentry.Sentry.
�� The sentry robot is equipped The sentry robot is equipped with two cameras, one for with two cameras, one for dayday--time and one for infrared time and one for infrared night vision, zooming night vision, zooming capabilities, a speaker for capabilities, a speaker for notifying the intruder of notifying the intruder of inpending death,.inpending death,.
�� Sophisticated pattern Sophisticated pattern recognition to detect the recognition to detect the
�� Sophisticated pattern Sophisticated pattern recognition to detect the recognition to detect the difference between humans difference between humans and trees, and a 5.5mm and trees, and a 5.5mm machinemachine--gun.gun.
�� http://www.gorobotics.net/Thhttp://www.gorobotics.net/Thee--News/Military/SouthNews/Military/South--KoreaKorea--DevelopsDevelops--Machine%11GunMachine%11Gun--SentrySentry--Robot/Robot/
Example: face recognitionExample: face recognition
�� Here using the 2Here using the 2--stage approach:stage approach:
TrainingTraining
�� http://www.nhttp://www.neci.nec.com/eci.nec.com/homepages/lhomepages/lawrence/papawrence/papers/faceers/face--ers/faceers/face--tr96/latex.httr96/latex.htmlml
AI AI –– Few AchievementsFew Achievements
�� Robots make cars in all advanced countries.Robots make cars in all advanced countries.�� Reasonable machine translation is available for a Reasonable machine translation is available for a
large range of foreign web pages.large range of foreign web pages.�� Computers land 200 ton jumbo jets unaided Computers land 200 ton jumbo jets unaided
every few minutes.every few minutes.�� Search systems like Google are not perfect but Search systems like Google are not perfect but �� Search systems like Google are not perfect but Search systems like Google are not perfect but
provide very effective information retrievalprovide very effective information retrieval�� Robots cut slots for hip joints better than Robots cut slots for hip joints better than
surgeons.surgeons.�� Deep blue beat Kasparov in 1997 and the current Deep blue beat Kasparov in 1997 and the current
world Go champion is a computer.world Go champion is a computer.�� Medical expert systems can outperform doctors in Medical expert systems can outperform doctors in
many areas of diagnosis.many areas of diagnosis.
Experts of Artificial Intelligence?Experts of Artificial Intelligence?
�� One of major divisions in AI (and you can see it One of major divisions in AI (and you can see it in the definitions on the previous slide) is in the definitions on the previous slide) is betweenbetween
�� Those who think AI is the only serious way of Those who think AI is the only serious way of finding finding out how out how wewe work (since opening heads does not work (since opening heads does not yet yet out how out how wewe work (since opening heads does not work (since opening heads does not yet yet give much insight into this) andgive much insight into this) and
�� Those who want computers to do very smart Those who want computers to do very smart things, things, independentlyindependently of how we work.of how we work.
�� This is the important distinction betweenThis is the important distinction betweenCognitive ScientistsCognitive Scientists vs. vs. EngineersEngineers..
AI AI –– A CommentA Comment
�� Despite all these achievements, one of the Despite all these achievements, one of the major philosophers of Cognitive Science major philosophers of Cognitive Science wrote recently:wrote recently:
“… the failure of artificial intelligence to “… the failure of artificial intelligence to produce successful simulation of routine produce successful simulation of routine produce successful simulation of routine produce successful simulation of routine commonsense cognitive competences is commonsense cognitive competences is notorious, not to say scandalous. We still notorious, not to say scandalous. We still don't have the fabled machine that can don't have the fabled machine that can make breakfast without burning down the make breakfast without burning down the house; or the one that can translate house; or the one that can translate everyday English into everyday Italian, or everyday English into everyday Italian, or the one that can summarize texts..” the one that can summarize texts..” (Jerry Fodor, The Mind doesn’t Work (Jerry Fodor, The Mind doesn’t Work that Way, 2000, p.37).that Way, 2000, p.37).
“ The whole of science is nothingmore than a refinement of everydaythinking”.
- Albert Einstein- Albert Einstein
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�� 72. S.M.Aqil Burney; Tahseen A. Jilani Supervised Artificial Neural Network for 72. S.M.Aqil Burney; Tahseen A. Jilani Supervised Artificial Neural Network for Karachi Stock Exchange Share Rates Forecasting” Accepted at Artificial Intelligence Karachi Stock Exchange Share Rates Forecasting” Accepted at Artificial Intelligence and Neural Network Conference .Department of Computer Engineering Canakkle and Neural Network Conference .Department of Computer Engineering Canakkle University ,TurkeyJuly2University ,TurkeyJuly2--4,20034,2003
�� TAINNTAINN--2003.2003.�� TAINNTAINN--2003.2003.
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Time Series Forecasting for Car Road Accidents”, International Journal of Computational Time Series Forecasting for Car Road Accidents”, International Journal of Computational Intelligence, 4(1), pp 15Intelligence, 4(1), pp 15--20, ISSN 130420, ISSN 1304--2386.2386.
�� 88. Aqil Burney S. M. and Jilani T. A. (2007), M88. Aqil Burney S. M. and Jilani T. A. (2007), M--Factor High Order Fuzzy Time Series Factor High Order Fuzzy Time Series Forecasting for Road Accident Data, Accepted in IEEEForecasting for Road Accident Data, Accepted in IEEE--IFSA, 18IFSA, 18--21 June, Cancun21 June, Cancun--Mexico. Published in Analysis and Design of Intelligent Systems Using Fuzzy Logic and Mexico. Published in Analysis and Design of Intelligent Systems Using Fuzzy Logic and Soft Computing, Advances in Soft Computing, 41, SpringerSoft Computing, Advances in Soft Computing, 41, Springer--Verlag.Verlag.
�� 89. Aqil Burney S. M. and Jilani T. A. and (2007), New Method of Learning and 89. Aqil Burney S. M. and Jilani T. A. and (2007), New Method of Learning and Knowledge Management in TypeKnowledge Management in Type--I Fuzzy Neural Networks, Accepted in IEEEI Fuzzy Neural Networks, Accepted in IEEE--IFSA, 18IFSA, 18--21 21 June, World Congress, CancunJune, World Congress, Cancun-- Mexico. Published in Theoretical Advances and Mexico. Published in Theoretical Advances and Applications of Fuzzy Logic and Soft Computing; Advances in Soft Computing, 42, Applications of Fuzzy Logic and Soft Computing; Advances in Soft Computing, 42, SpringerSpringer--Verlag.Verlag.
�� 90. Aqil Burney S. M. and Jilani T. A. (2007), Multivariate Stochastic Fuzzy Forecasting 90. Aqil Burney S. M. and Jilani T. A. (2007), Multivariate Stochastic Fuzzy Forecasting Models, In Expert Systems with Applications, ESWA, to apppear in 37(2) in late 2008 or Models, In Expert Systems with Applications, ESWA, to apppear in 37(2) in late 2008 or 2009.2009.
�� 91. Aqil Burney S. M., Jilani T. A. and Ardil C. (2007), Fuzzy Metric approach for Fuzzy 91. Aqil Burney S. M., Jilani T. A. and Ardil C. (2007), Fuzzy Metric approach for Fuzzy time Series Forecasting Based on Frequency Density Based Partitioning, Proceedings of time Series Forecasting Based on Frequency Density Based Partitioning, Proceedings of World Academy of Science, Engineering and Technology vol. 23, August, ISSN 1307World Academy of Science, Engineering and Technology vol. 23, August, ISSN 1307--68846884
�� 92. S. M. Aqil Burney , Akhtar Raza (2007), Monte Carlo Simulation and Prediction of 92. S. M. Aqil Burney , Akhtar Raza (2007), Monte Carlo Simulation and Prediction of internet load using conditional mean and conditional variance model. Proceedings of The internet load using conditional mean and conditional variance model. Proceedings of The 9th Islamic Countries Conference on Statistical Sciences (ICCS9th Islamic Countries Conference on Statistical Sciences (ICCS--IX) 12IX) 12--14 December 14 December 20072007
�� 20082008�� 93. Aqil Burney S. M. and Jilani T. A. (2008), A Refined Fuzzy 93. Aqil Burney S. M. and Jilani T. A. (2008), A Refined Fuzzy
Time Series Model for Stock Market Forecasting. PHYSICA A: Time Series Model for Stock Market Forecasting. PHYSICA A: Statistical Mechanics with Applications(Econophysics and Models) Statistical Mechanics with Applications(Econophysics and Models) Volume 387, Issue 12, 1 May 2008, Pages 2857Volume 387, Issue 12, 1 May 2008, Pages 2857--2862, Elsevier 2862, Elsevier Publishers.Publishers.
�� 94. Aqil Burney S. M. and Jilani T. A. (2008), Multivariate 94. Aqil Burney S. M. and Jilani T. A. (2008), Multivariate �� 94. Aqil Burney S. M. and Jilani T. A. (2008), Multivariate 94. Aqil Burney S. M. and Jilani T. A. (2008), Multivariate Stochastic Fuzzy Forecasting Models. Expert Systems with Stochastic Fuzzy Forecasting Models. Expert Systems with Applications: An International Journal, Volume 35, Issue 3 Applications: An International Journal, Volume 35, Issue 3 (October 2008) Pages 691(October 2008) Pages 691--700. ISSN:0957700. ISSN:0957--41744174
�� 95. Tahseen Ahmed Jilani, Syed Muhammad Aqil Burney, C. Ardil 95. Tahseen Ahmed Jilani, Syed Muhammad Aqil Burney, C. Ardil (2008), Fuzzy Metric Approach for Fuzzy Time Series Forecasting (2008), Fuzzy Metric Approach for Fuzzy Time Series Forecasting based on Frequency Density Based Partitioning. International based on Frequency Density Based Partitioning. International Journal of Computation (Internet), World Academy of Science, Journal of Computation (Internet), World Academy of Science, Engineering and Technology (Volume 4 Number 2 Spring 2008) Engineering and Technology (Volume 4 Number 2 Spring 2008) Pages 112Pages 112--117 www.waset.org 117 www.waset.org