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Fuzzy Set: 1965 … Fuzzy Logic: 1973 … Soft Decision: 1981 … BISC: 1990 … Human-Machine Perception: 2000 - …
Theory and the Applications of Natural Language Computing:Theory and the Applications of Natural Language Computing:Computation and Reasoning with Information Presented in Natural LanguagesComputation and Reasoning with Information Presented in Natural Languages
Masoud NikraveshBISC Program, EECS-UCB
&Informatics and Imaging- Life Sciences
Lawrence Berkeley National Laboratory (LBNL)
http://www-bisc.cs.berkeley.edu/Email: [email protected]
Tel: (510) 643-4522; Fax: (510) 642-5775
Acknowledgements: James S. Albus
Senior NIST FellowIntelligent Systems Division
Manufacturing Engineering LaboratoryNational Institute of Standards and Technology
Acknowledgements: Prof. Lotfi A. Zadeh
BISC ProgramEECS-UCB
ICMLA'05 The Fourth International Conference on Machine Learning and Applications
15-17 December 2005, Sheraton Gateway Hotel, Los Angeles, CA, USA
22
Outline
• BISC Program
• Introduction
• Natural Language Computing• CONCEPTS• ORIGIN• APPLICATIONS
• Neu-Search*• BISC-DSS
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TURING’s TESTTuring: A computer can be said to be intelligent if its Turing: A computer can be said to be intelligent if its
answers are indistinguishable from the answers of a answers are indistinguishable from the answers of a human beinghuman being
??
Computer
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Artificial Neural Network vs. Human Brain
Largest neural computer: 20,000 neurons
Worm’s brain: 1,000 neurons
But the worm’s brain outperforms neural computers
It’s the connections, not the neurons!Human brain: 100,000,000,000 neurons200,000,000,000,000 connections
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• Processing Speed: Milliseconds VS Nanoseconds.
• Processing Order: Massively parallel.VS serially.
• Abundance and Complexity: 1011 and 1014 of neurons operate in parallel in the brain at any given moment, each with between 103 and 104 abutting connections per neuron.
• Knowledge Storage: Adaptable VS New information destroys old information.
• Fault Tolerance: Knowledge is retained through the redundant, distributed encoding information VS the corruption of a conventional computer's memory is irretrievevable and leads to failure as well.
Brain vs. Computer Processing
Cesare Pianese
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Machine Intelligence – Human Intelligence Year is 2020
Computing Power == > Quadrillion/sec/$100 5-15 Quadrillion/sec (IBM’s Fastest computer =
100 Trillion) High Resolution Imaging (Brian and Neuroscience)
Human Brain, Reverse Engineering Dynamic Neuron Level Imaging/Scanning and Visualization
Searching, Logical Analysis Reasoning Searching for Next Google; Internet Protocol TV (IPTV)
Every viewer could potentially receive different advertisement based on its profile, search, and shows the viewer has been watched Family will not skip the ads, because it is targeted advertising
Technology goes Nano and Molecular Level Nanotechnology Nano Wireless Devices and OS
Tiny- blood-cell-size robots Virtual Reality through controlling Brain Cell Signals
Who should work and who should get paid? Human or Robots/Machines?
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Q
Q2
Q1
Q3Q3
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a1
a2
a2a2
a12 a2
2
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a23 a1
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aa1111
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aa1133
aa2233
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aa22
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**
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...
is F THEN is Aand is A
is F THEN is Aand is Aand is A
is F THEN is Aand is Aand is A
is F THEN is A
is F THEN is Aand is A
is F THEN is A is Aand is A
121
1321
1321
12
131
1321
221
12
232
21
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21
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132
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aaaIF
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Reasoning ?
Deduction ?
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Reasoning ?
Deduction ?
1010
Human-Machine-Perception-Based Reasoning
Machine Agent Intelligent Agent Phantoms Humanoid Human
Computer Mind
Machine based on Human Brain and Neuroscience
1111
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The Human Mind
Arguably the most important for humankind.
The next unexplored frontier of science
Mind is what distinguishes humans from the rest of creation
Your mind is who you are
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Recent Breakthroughs
Neurosciences – Focused on understanding the brain- chemistry, synaptic transmission, axonal connectivity, functional MRI
Cognitive Modeling – Focused on representation and useof knowledge in performing cognitive tasks
- mathematics, logic, language
Intelligent Control – Focused on making machines behave appropriately (i.e., achieve goals) in an uncertain environment
- manufacturing, autonomous vehicles, agriculture, mining
Depth Imaging – Enables geometrical modeling of 3-D world. Facilitates grouping and segmentation.Provides solution to symbol-grounding problem.
Computational Power – Enables processes that rival the brainin operations per second. At 1010 ops, heading for 1015 ops.
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EVOLUTION OF COMPUTATION
naturallanguage
arithmetic algebra
algebra
differentialequations
calculusdifferentialequations
numericalanalysis
symboliccomputation
computing with wordsprecisiated natural language
symboliccomputation
+ +
+ +
+ +
+
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Classical Logic is inadequate for ordinary life
Intuitionism
Non- Monotonic Logic
Second thoughts
Plausible reasoning
Quick, efficient response to problems when an exact solution is not necessary
COMMON SENSE
The World Of ObjectsThe Measure SpaceQualitative Reasoning
HeuristicsRules of thumbsGeorge Polya: “Heuretics"
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1919
EVOLUTION OF LOGIC
two-valued (Aristotelian): nothing is a matter of degree
multi-valued: truth is a matter of degree
fuzzy: everything is a matter of degree
2020
In bivalent logic, BL, truth is bivalent, implying that every proposition, p, is either true or false, with no degrees of truth allowed
In multivalent logic, ML, truth is a matter of degree
In fuzzy logic, FL: everything is, or is allowed to be, to be partial, i.e., a
matter of degree everything is, or is allowed to be, imprecise
(approximate) everything is, or is allowed to be, granular (linguistic) everything is, or is allowed to be, perception based
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EVOLUTION OF FUZZY LOGICA PERSONAL PERSPECTIVE (L.A. Zadeh)
generality
time1965 1973 1999
1965: crisp sets fuzzy sets1973: fuzzy sets granulated fuzzy sets (linguistic variable)1999: measurements perceptions
nl-generalization
f.g-generalization
f-generalization
classical bivalent
computing with words and perceptions (CWP)
2222
Natural Language Computing
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•it is 35 C°
•Eva is 28
•probability is 0.8
•
•
•It is very warm
•Eva is young
•probability is high
•it is cloudy
•traffic is heavy
•it is hard to find parking near the campus
INFORMATION
measurement-based numerical
perception-based linguistic
MEASUREMENT-BASED VS. PERCEPTION-BASED INFORMATION
• measurement-based information may be viewed as special case of perception-based information
2424
MEASUREMENT-BASED
a box contains 20 black a box contains 20 black and white ballsand white balls
over seventy percent over seventy percent are blackare black
there are three times as there are three times as many black balls as many black balls as white ballswhite balls
what is the number of what is the number of white balls?white balls?
what is the probability what is the probability that a ball picked at that a ball picked at random is white?random is white?
a box contains about 20 a box contains about 20 black and white balls black and white balls
most are blackmost are black there are several times there are several times
as many black balls as as many black balls as white ballswhite balls
what is the number of what is the number of white ballswhite balls
what is the probability what is the probability that a ball drawn at that a ball drawn at random is white?random is white?
PERCEPTION-BASED
version 2version 1
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COMPUTATION (version 2)
measurement-basedmeasurement-based
X = number of black X = number of black ballsballs
YY22 number of white number of white
ballsballs
X X 0.7 0.7 • 20 = 14• 20 = 14
X + Y = 20X + Y = 20
X = 3YX = 3Y
X = 15X = 15; Y = 5; Y = 5
p =5/20 = .25p =5/20 = .25
perception-basedperception-based
X = number of black X = number of black ballsballs
Y = number of white Y = number of white ballsballs
X = most X = most × 20*× 20*
X = several *YX = several *Y
X + Y = 20*X + Y = 20*
P = Y/NP = Y/N
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BASIC POINT
Conventional methods of systems analysis are Conventional methods of systems analysis are oriented toward numerical attributes and oriented toward numerical attributes and measurement-based information. They lack the measurement-based information. They lack the capability to deal with linguistic attributes and capability to deal with linguistic attributes and perception-based informationperception-based information
Computing with words is aimed at adding to Computing with words is aimed at adding to methods of systems analysis and decision analysis methods of systems analysis and decision analysis an important high-level capability—the capability to an important high-level capability—the capability to deal computationally and logically with linguistic deal computationally and logically with linguistic attributes and perception-based informationattributes and perception-based information
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Natural Language Computing
Computation?
•Traditional Sense: Manipulation of Numbers
• Human: Uses Word for Computation and Reasoning
Words are less precise than numbers!
Computing Word <== Natural Language
2929
Natural Language Computing?
Human: Uses Natural LanguagesHuman: Uses Word for ComputationHuman: Uses Reasoning
LogicWords are less precise than numbers!Reality vs. Being Certain
Fuzzy Set and Fuzzy Logic as basis for Natural Language Computing
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Inspired by human’s remarkable capability to perform a wide variety of physical and mental tasks without any measurements and computations and dissatisfied with classical logic as a tool for modeling human reasoning in an imprecise environment, Lotfi A. Zadeh developed the theory and foundation of fuzzy logic with his 1965 paper “Fuzzy Sets” [1] and extended his work with his 2005 paper “Toward a Generalized Theory of Uncertainty (GTU)—An Outline”
Theory of Natural Language Computing ORIGIN, CONCEPTS, AND TRENDS
Fuzzy Set and Fuzzy Logic as basis for Natural Language Computing
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WHAT IS FUZZY LOGIC?
fuzzy logic (FL) is aimed at a formalization of modes of reasoning which are approximate rather than exact
examples:
exact all men are mortal
Socrates is a man
Socrates is mortal
approximate most Swedes are tall
Magnus is a Swede
it is likely that Magnus is tall
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““Fuzzy logic” is not fuzzy logicFuzzy logic” is not fuzzy logic Fuzzy logic is a Fuzzy logic is a preciseprecise logic of logic of
approximate reasoning and approximate approximate reasoning and approximate computationcomputation
The principal distinguishing features of fuzzy The principal distinguishing features of fuzzy logic are:logic are:
a)a) In fuzzy logic everything is, or is allowed to In fuzzy logic everything is, or is allowed to be graduated, that is, be a matter of degreebe graduated, that is, be a matter of degree
b)b) In fuzzy logic everything is allowed to be In fuzzy logic everything is allowed to be granulatedgranulated
FUZZY LOGIC—KEY POINTS
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When do we use Fuzzy Logic?
To exploit the tolerance for imprecision, uncertainty and partial truth to achieve tractability, robustness, low solution cost and better rapport with reality
Crisp, fine grained information is not available Economic systems, everyday decision-making
Precise information is costly Diagnosis systems, quality control, decision analysis
Fine-grained information is not necessary Cooking, balancing, parking a car
Coarse-grained information reduces cost Camera, consumer products
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Natural Language Computing?
Fuzzy Set and Fuzzy Logic as basis for
Natural Language Computing
+
NEW TOOLSComputing with words and perceptions (CWP) & Precisiated Natural Language (PNL)
3535
Fuzzy Sets (Zadeh 1965)
(Info. And Control, 8, 338-353 (1965) A fuzzy set is a class of objects with a
continuum of grades of membership
Each Set is characterized by membership function which assigns to each object a grade of membership
The notion of a fuzzy set is completely non statistical
3636
PRECISIATION OF “approximately a,” *a
x
x
x
a
a
a0
1
0
0
1
p
fuzzy graph
probability distribution
interval
x 0
a
possibility distribution
x a0
1
s-precisiation singleton
g-precisiation
cg-precisiation
3737
CONTINUED
x
p
0
bimodal distribution
GCL-based (maximal generality)GCL-based (maximal generality)
g-precisiation X isr R
GC-form
*a
g-precisiation
3838
Fuzzy Concept(Zadeh, 1971)
If x is a term, then its meaning, M(x), is a concept
Level 1 concept: K : a set of objects Concepts (labels for concepts); “white”, “yellow”, “green”, … “redder than”, “darker than” are level 1 concept, since
If y1 and y2 are objects (y1,y2), we can calculate µ(y1,y2) such as “darker than”
Level 2 Concept Example : “color”
This concept is a collection of the concepts M(white), M(green), …, M(black), …
Level 3 Concept Example : “visual attribute”
This concept is a collection of the concepts such as “color”, “shape”, “size”, … Concept at higher level than 1 is much harder to define by exemplification than concepts
at level 1.
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Fuzzy Concept
Natural language for teaching a kid or machine
Exemplification a set of primitive concepts at level 1 (vocabulary)
Build up on this vocabulary by defining other level 1 concepts in term of the already defined
Build up on this vocabulary by defining other higher level concepts in term of the already defined level 1 (or lower level concepts)
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Language as fuzzy relation iscloser to the Linguistic than formal languages
Each Word x in a natural language L may be viewed as a summarized description of a fuzzy subset M(x) of universe of discourse U, with M(x) representing the meaning of x
Language is a fuzzy correspondence between the element of T and U, where T is a set of terms
Let x be a term in T. Then the meaning of x, denoted by M(x) is a fuzzy subset of U characterized by a membership function µ (x l y).
T: white, gray, green, blue, yellow, red, black, …T: young, old, middle-aged, not old, not young, ….
Computing with Words and Perception
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Computation of Meaning by the use ofQuantitative Semantics
Meaning:Simple terms (young, old, very, not, and, or)Composite terms (not very young and not very old)
Quantitative Semantics is a procedure for computing the meaning, M(x), of a composite x in T from the knowledge of the meanings of the simple terms x1 x2 … xn
Computing with Words and PerceptionPrecisation of Variables
4242
Fuzzy Grammar for Computation of Meaning for composite terms
not very young not very young and not very old young and not old old or not old old or not very very young young and (old or not young)
S A C O S S or A C YA B O very OA A and B Y very YB not C O oldC (S) Y youngB C
4343
Fuzzy Grammar for Computation of Meaning for composite terms
)y(old,)y(young,)y(x,
oldvery not and very young not :
)(young)(Y youngY
)(old)(O oldO
)(S)(C (S)C
)(Y)(C Y C
)(O)(C OC
)(Y)(Y Y Y
)(O)(O O O
)(C)(B C notB
)(B)(A)(A B andA A
)(A)(S)(S A or SS
)(A)(S CB
)(B)(A BA
)(A)(S A S
L
L
RL
RL
RL
RL
RL
RL
RRL
RRL
RL
RL
RL
42
2
2
11
1
LLL μμμ
termcomposite
μμ
μμ
μμ
μμ
μμ
μμvery
μμvery
μμ
μμμ
μμμ
μμ
μμ
μμ
4444
Fuzzy Grammar for Computation of Meaning for composite terms
)y(old,1)y(young,1)y(x,
oldnot very and youngnot very : 42LLL
termcomposite
S1
A2
A3 B8
B4C9
C5 O10
O11
O12
Y6
Y7
oldyoung
very
very
very
not
not
and
4545
Fuzzy Grammar for Computation of Meaning for composite terms
)y(old,)y(young,)y(x,
oldvery not and very young not :
)(A)(S)y(x,
)(B)(A)(A
)(C)(B
)(O)(C
)(O)(O
) y(old,)(O
)(B)(A
)(C)(B
)(Y)(C
)(Y)(Y
) y(young,)(Y
21
832
9
9
10
12
3
54
5
76
7
42
10
112
4
6
2
11
18
1
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L
L
L
μμμ
termcomposite
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μμ
μμ
4646
Fuzzy Logic(Outline of New Approach to the Analysis of Complex Systems and Decision Process, IEEE
Trans. On system, man and cybernetics, Vol. SMC-3, No. 1, Jan 1973, 28-44)
The use of Linguistic variables Simple relations between variables by fuzzy
conditional statementComplex relations by fuzzy Algorithms
IF x is small and x is not large THEN y is very largeIF x is not very small THEN y is very largeIF x is not small and not large THEN y is not very large
4747
The use of Linguistic variablesMeaning
Information Summarization
Humans: Ability to summarize information finds its most pronounce manifestation in the use of Natural Languages
Linguistic Variables: Each word x in a natural language L may be viewed as a summarized description of a fuzzy subset M(x) of universe of discourse U, with M(x) representing the meaning of x.
4848
The use of Linguistic variables
Object: red Meaning: M(Red)Object: flower Meaning: M(flower)Object: red flower Meaning: M (red) ∩ M (flower) ∩ : Intersection or Min. Operator
Object: Variable: Color of the object Values: red, blue, yellow, green Values for the Object: Labels of fuzzy sets
Attribute: Color Fuzzy VariableValues: red, blue, …, Labels of the fuzzy sets Attributes: HeightValues: tall, not tall, somewhat tall, very tall, …
Sentences: Label (tall, red,….), Negation (not), Connective (and, but, or), and hedges (very, somewhat, quite, more or less, …)
4949
Simple relations between variables by fuzzy conditional statement
IF x is small THEN y is very largeIF x is not very small THEN y is very largeIF x is not small and not large THEN y is not
very large
5050
Complex relations by fuzzy Algorithms
Fuzzy Algorithm is an ordered sequences of instructions
Reduce x slightly if y is largeIncrease x very slightly if y is not very large
and not very smallIf x is small then stop; otherwise increase x
by 2.
5151
VARIABLES AND LINGUISTIC VARIABLES
one of the most basic concepts in science is that of a variable
variable -numerical (X=5; X=(3, 2); …)
-linguistic (X is small; (X, Y) is much larger)
a linguistic variable is a variable whose values are words or sentences in a natural or synthetic language (Zadeh 1973)
the concept of a linguistic variable plays a central role in fuzzy logic and underlies most of its applications
5252
Fuzzy sets, logics and reasoningExamples
(Zadeh 1973)Set: U
U = 1 + 2 + 3 + 4 + 5
small = 1/1 + .8/2 + .6/3 + .4/4 + .2/5
(degree/set)
very x := x2
very small = 1/1 + 0.64/2 + 0.36/3 + 0.16/4 + 0.04 /5
very very small = very (very x) = very (x2 )= x4
very very small = 1/1 + 0.4/2 + 0.1/3
5353
Computation of the Meaning of Values of Linguistic Variables
not very small = not (very small)= ¬ (very small) = ¬ (small2)
very small = 1/1 + 0.64/2 + 0.36/3 + 0.16/4 + 0.04 /5
not very small = 0/1 + 0.36/2 + 0.64/3 + 0.84/4 + 0.96/5
5454
Computation of the Meaning of Values of Linguistic Variables
very very large = very (very large)= very (large2) large4
not very very large = ¬ large4
X= not very small and not very very large:
¬ (small2) ∩ ¬ (large4 ) = Min. (¬ (small2), ¬ (large4 )
5555
Fuzzy Conditional Statement and Compositional Rule of Inference
In general : IF A THEN B ; A x B ; A B
Min (A,B) ; x : Intersection or ∩
A = 1/1 + 0.8/2
B = 0.6/1 + 0.9/2 + 1/3
808060
19060
2
1
...
..
3 2 1
BA
IF (x is) large THEN (y is) smallIF (the road) slippery THEN (driving is) dangerous
R : Fuzzy Relation
5656
Fuzzy Conditional Statement and Compositional Rule of Inference
IF A1 THEN B1 ELSE IF A2 THEN B2 ELSE IF An THEN Bn ELSE
= A1 x B1 + A1 x B1 + . . .+ An x Bn
IF A THEN (IF B THEN C ELSE D) ELSE E
= A x B x C + A x ¬B x D + ¬A x E
IF A THEN B ELSE C : A x B + (¬A x C) + : union or U
5757
Fuzzy Conditional Statement and Compositional Rule of Inference
IF (x is) very small THEN (y is) large ELSE (y is) not very large A x B + (¬A x C)A: small B: large C: not very largex : Min. or ∩ or intersection + : Max. or U or union Operation to calculate: Min Max operator
small = 1/1 + 0.8/2 + 0.6/3 + 0.4/4 + 0.2/5large = 0.2/1 + 0.4/2 + 0.3/3 + 0.8/4 + 1/5
R : Fuzzy Relation = A x B + (¬A x C)
5858
Fuzzy Conditional Statement and Compositional Rule of Inference
203606408080
4040606060
6060604040
8080604020
180604020
.....
.....
.....
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....
)( CABAR
R : Fuzzy Relation
IF (x is) very small THEN (y is) large ELSE (y is) not very large
x = very small (x2)x o R = y =[0.36 0.4 0.6 0.8 1]
5959
Fuzzy Conditional Statement and Compositional Rule of Inference
203606408080
4040606060
6060604040
8080604020
180604020
.....
.....
.....
.....
....
)( CABAR
R : Fuzzy Relation
IF (x is) very small THEN (y is) large ELSE (y is) not very large
x : very small = (small2) = [ 1 0.64 0.36 0.16 0.04] x o R = y =[0.36 0.4 0.6 0.8 1] ≈ not very small
6060
Fuzzy Conditional Statement and Compositional Rule of Inference
Given Inferred
A B x y
small large not small not very large
medium medium very large very very large
large very small very very small very very large
not very large small or medium
6161
Joint Probability
P: if X is small then p is smallIf X is medium then p is largeIf X is large then p is small
Q: if Y is small then q is largeIf Y is medium then q is smallIf Y is large then q is large
6262
Joint Probability
P
X psmall small
medium large
large small
Q
Y qsmall large
medium small
large small
P: small x small + medium x large + large x small
Q: small x large + medium x small + large x small
(P,Q)= small x small (small* large) +
+ small x medium x (small *small) + …
Large x large x (small * large)
* : the arithmetic product in fuzzy arithmetic
6363
Possibilistic Relational Universal Fuzzy
6464
PRUF – A meaning Representation Language for Natural Languages (Zadeh, 1977)
Possibilistic Relational Universal Fuzzy
Assumption: imprecision is possibilistic rather than probabilistic in nature
The Logic: Fuzzy logic, rather than two-valued or multivalued- logic
The quantifiers in PRUF are allowed to be linguistic, “most”, “many”, “some”, “few”
6565
PRUF – A meaning Representation Language for Natural Languages (Zadeh, 1977)
The concept of Semantic Equivalence and Semantic Entailment in PRUF provide a basis for Question-Answering (Q&A) and Inference from fuzzy premises
Foundation for Approximate Reasoning
Language for representation of imprecise knowledge and as a means of precisiation of fuzzy propositions expressed in a natural language.
Precisiated Natural LanguagePrecisation of Meaning
6666
PRUF – A meaning Representation Language for Natural Languages (Zadeh, 1977)
Translation rules in PRUF:
Type I: pertaining to modification Type II: pertaining to composition Type III: pertaining to quantification Type IV: pertaining to qualification
6767
PRUF Type I: pertaining to modification
X is very small
X is much larger than Y
Eleanor was very upset
The Man with the blond hair is very tall
PRUF Type II: pertaining to composition
X is small and Y is large (conjunctive composition)
X is small or Y is large (disjunctive composition)
If X is small then Y is large (conditional and conjunctive composition)
If X is small the Y is large else Y is very large (conditional and conjunctiv composition)
6868
PRUF – Type III: pertaining to quantification
Most Swedes are tall
Many men are much taller than most men
Most tall men are very intelligent
PRUF – Type IV: pertaining to qualification
Abe is young is not very true (truth qualification) Abe is young is quite probable (probability
qualification Abe is young is almost impossible (possibility
qualification)
6969
Proposition p
p : N is F
Modified proposition p+
p+ = N is mF
m: not, very, more or less, quite, extremely, etc.
PRUF Type I: pertaining to modificationRules of Type I: Basis is the Modifier
);()(
friends are Pat and Vera:p* p eApproximat
friends close are Pat and Vera:
),,(
very young is Lisa
),,(
2
YOUNG
Age(Lisa)
YOUNG
2
PatNameVeraNameFRINDSμFRIENDSπ
p
Sμ
YOUNG
Sμ
21
4535251
4535251
2
2
2
7070
PRUF Type II: pertaining to composition Rules of Type II: operation of composition
difference arithmetic -
sum, arithmetic ,min:
)()(),(
)()(),(
F
V F G F G is N then F is M If
or
GF G is N then F is M if
GF : G is N or F is M
G F GF : G is N and F is M
G is N : r
F is M : q
r * q p
GF
''
'
'
'
vμuμvuμ
vμuμvuμ
GUG
VF
GF
GFGF
11
7171
PRUF Type II: pertaining to composition Rules of Type II: operation of composition
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606010
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.//./.::
/././::
:,:
,
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LARGEG
SMALLF
YNXM
VU
Example
909090
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:large is Y or small is
Y)(X,
Y)(X,
Y)(X,
Xif
Xif
X
7272
PRUF Type II: pertaining to composition Rules of Type II: operation of composition
H is N then F not is M If
and G is N then F is M If
H is N else G is N then F is M If
'
H is N else G is N then F is M If
),...,,,...,(
or
HFGFnm YYXX
1
7373
PRUF Type II: pertaining to composition Rules of Type II: operation of composition
mnm11n11
mn2m22m11
2n2222211
1n2122111
FFFF R
F is X ... and F is X and F is X
OR F is X ... and F is X and F is X
OR F is X ... and F is X and F is X R
R X1 X2 … X1n
F11 F12 … F1n
… … … …
Fm1 … … Fmn
7474
Compactification Algorithm InterpretationA Simple Algorithm for Qualitative Analysis
Rule Extraction and Building Decision Tree
Dr. Nikravesh and Prof. Zadeh (2005)(Zadeh, 1976)
7575
Compactification Algorithm Interpretation
AA11 AA22 oo AAnn FF11
aa1111
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oo
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oo
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Test Attribute Set
7676
Table 1 (intermediate results)
Group 1(initial)
Pass (1)
Pass (2)
Pass (3)
AA11 AA22 AA33 FF11
aa1111
aa1111
aa2211
aa3311
aa3311
aa1111
aa2211
aa3311
aa1122
aa2222
aa2222
aa2222
aa1122
aa2222
aa2222
aa2222
aa1133
aa1133
aa1133
aa1133
aa2233
aa2233
aa2233
aa2233
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aa11
aa11
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aa1133
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aa2211
aa3311
**
aa2222
aa2222
aa2222
aa2222
**
**
**
**
aa11
aa11
aa11
aa11
7777
MAXIMALLY COMPACT REPRESENTATIONQ
Q2
Q1
Q3Q3
a1
a1
a2
a2a2
a12 a2
2
a31
a21a1
1
a13
a23 a1
3 a23
aa22
aa22
aa22
aa11
aa11
aa11
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aa1133
aa2233
**
aa1122
aa1122
aa1122
aa3311
aa1111
aa2211
aa1133
aa2233
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aa1111
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aa22
aa22
aa22
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aa11
aa11
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aa1133
aa2233
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aa1122
aa1122
aa3311
aa1111
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aa1111
aa3311
**
AA33AA22AA11
...
is F THEN is Aand is A
is F THEN is Aand is Aand is A
is F THEN is Aand is Aand is A
is F THEN is A
is F THEN is Aand is A
is F THEN is A is Aand is A
121
1321
1321
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221
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232
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7878
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7979
PRUF Type II: pertaining to composition Rules of Type II: operation of composition
X Ysmall
very small
not small
Large
not very large
very small
small SMALLlarge LARGE very small SMALL2
not small SMALL’not very large (LARGE2)’
R SMALL x LARGE + (SMALL2) x (LARGE2)’ + SMALL’ x SMALL2
8080
Type III: pertaining to quantificationRules of Type III: p: Q N are F
less or more : m if )(
very : m if )(
not : m if )'(
F
F is N
tall are Swedes Most
almost some, few, many, most, :quantifier
quantifierfuzzy :Q
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8181
Type III: pertaining to quantificationRules of Type III: p: Q N are F
F are N Q) (not F) are N (Q not
F are N Q) (m F) are N (Q m
G less or more is N
and F less or more is M ) G is N and F is M ( less of more
Gvery is N
and Fvery is M ) G is N and F is M (very
G not is N
or F not is M
G)' (F is Y)(X, ) G is N and F is M ( not
G) (F m is Y)(X, ) G is N and F is M ( m
F less of more is N ) F is N ( less of more
Fvery is N ) F is N (very
F not is N ) F is N ( not
mF is N )F is N (
m
8282
PRUF – Type IV: pertaining to qualificationRules of Type IV: q: p is ү
F is N true-u is F is N
[0,1]v )(
true-u If
))(()(
F is F is N Then
F F is N
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value-truthliguistic a is
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X
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1510512 uSSuπ
μ
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τ
8383
PRUF – Type IV: pertaining to qualificationRules of Type IV: q: p is ү
)( )(
)( )(
is F is N is Fvery is N
true ant : false
antonym :ant
ant is F is N is F not is N
less or more is F is N ) is F is N ( less or ore
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ατα
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8484
PRUF – Type IV: pertaining to qualificationRules of Type IV: q: p is ү
true".very not" is " ? rich Barbara Is "
true"very not is rich is Barbara"
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25 1
8585
8686
PT
BL
FL
+
bivalent logic
probability theoryTheory of Generalized-Constraint-Based Reasoning
CW
PT: standard bivalent-logic-based probability theoryCTPM : Computational Theory of Precisiation of MeaningPNL: Precisiated Natural LanguageCW: Computing with WordsGTU: Generalized Theory of UncertaintyGCR: Theory of Generalized-Constraint-Based Reasoning
CTPM GTU PNL
GC
Tools in current use New Tools
GCR
Generalized Constraint
fuzzy logic
NEED FOR NEW TOOLS
8787
PRECISIATED NATURAL LANGUAGE
8888
WHAT IS PRECISIATED NATURAL LANGUAGE (PNL)?
PRELIMINARIES
• a proposition, p, in a natural language,
NL, is precisiable if it translatable into
a precisiation language
• in the case of PNL, the precisiation
language is the Generalized Constraint
Language, GCL
• precisiation of p, p*, is an element of
GCL (GC-form)
8989
WHAT IS PNL?
PNL is a sublanguage of precisiable propositions in NL which is equipped with two dictionaries: (A) NL to GCL; (B) GCL to PFL (Protoform Language); and (C) a collection of rules of deduction (rules of generalized constrained propagation) expressed in PFL.
9090
PRECISIATED NATURAL LANGUAGE (PNL)
NLGCL
generalized constraint form of type r
p X isr Rtranslation
generalized constraint form of type r (GC(p))
p translation
precisiation language (GCL)
precisiation explicitation
GC-form CSNL
precisiablepropositions
in NL
p*
9191
PNL AND THE COMPUTATIONAL THEORY OF PERCEPTIONS
in the computational theory of perceptions (CTP), perceptions are dealt with through their descriptions in a natural language
perception = descriptor(s) of perception
• a proposition, p, in NL qualifies to be an object of computation in CTP if p is in PNL
9292
DEFINITION OF p: ABOUT 20-25 MINUTES
time
time
time
time
20 25
20 25
20 25
A
P
B
6
0
1
0
0
1
1c-definition:
f-definition:
f.g-definition:
PNL-definition: Prob (Time is A) is B
9393
PRECISIATION OF “approximately a,” *a
x
x
x
a
a
20 250
1
0
0
1
p
fuzzy graph
probability distribution
interval
x 0
a
possibility distribution
x a0
1
s-precisiation singleton
g-precisiation
cg-precisiation
9494
CONTINUED
x
p
0
bimodal distribution
GCL-based (maximal generality)GCL-based (maximal generality)
g-precisiation X isr R
GC-form
*a
g-precisiation
9595
9696
THE CENTERPIECE OF PNL IS THE CONCEPT OF A GENERALIZED
CONSTRAINT (ZADEH 1986)
9797
THE BASICS OF PNL
The point of departure in PNL is the key idea:A proposition, p, drawn from a natural
language, NL, is precisiated by expressing its meaning as a generalized constraint
In general, X, R, r are implicit in p
p X isr R
constraining relation
Identifier of modality (type of constraint)
constrained (focal) variable
The concept of a generalized constraint serves as a bridge from natural languages to mathematics
9898
GENERALIZED CONSTRAINT (Zadeh 1986)
• Bivalent constraint (hard, inelastic, categorical:)
X Cconstraining bivalent relation
X isr R
constraining non-bivalent (fuzzy) relation
index of modality (defines semantics)
constrained variable
Generalized constraint:
r: | = | | | | … | blank | p | v | u | rs | fg | ps |…
bivalent non-bivalent (fuzzy)
9999
CONTINUED
• constrained variable
• X is an n-ary variable, X= (X1, …, Xn)• X is a proposition, e.g., Leslie is tall• X is a function of another variable: X=f(Y)• X is conditioned on another variable, X/Y• X has a structure, e.g., X= Location
(Residence(Carol))• X is a generalized constraint, X: Y isr R• X is a group variable. In this case, there is a
group, G[A]: (Name1, …, Namen), with each member of the group, Namei, i =1, …, n, associated with an attribute-value, Ai. Ai may be vector-valued. Symbolically
G[A]: (Name1/A1+…+Namen/An)
Basically, X is a relation
100100
SIMPLE EXAMPLES
“Check-out time is 1 pm,” is an instance of a generalized constraint on check-out time
“Speed limit is 100km/h” is an instance of a generalized constraint on speed
“Vera is a divorcee with two young children,” is an instance of a generalized constraint on Vera’s age
101101
GENERALIZED CONSTRAINT—MODALITY r
X isr R
r: = equality constraint: X=R is abbreviation of X is=Rr: ≤ inequality constraint: X ≤ Rr: subsethood constraint: X Rr: blank possibilistic constraint; X is R; R is the possibility
distribution of Xr: v veristic constraint; X isv R; R is the verity
distribution of Xr: p probabilistic constraint; X isp R; R is the
probability distribution of X
102102
CONTINUED
r: rs random set constraint; X isrs R; R is the set-valued probability distribution of X
r: fg fuzzy graph constraint; X isfg R; X is a function and R is its fuzzy graph
r: u usuality constraint; X isu R means usually (X is R)
r: g group constraint; X isg R means that R constrains the attribute-values of the group
• Primary constraints: possibilistic, probabilisitic and veristic
• Standard constraints: bivalent possibilistic, probabilistic and bivalent veristic
103103
104104
BASIC PROBLEM
•identification of query-relevant information
•relevance-ranking of query-relevant information
question-answering system
search engine
•deduction from query-relevant information
meta-deduction
+
105105
DECISION ?
DECISION-RELEVANTINFORMATION
QUERY-RELEVANTINFORMATION
SEARCH ENGINE
SYNTHESIS
INFORMATION
Q/A SYSTEM
DEDUCTION ENGINE
DECISION
INFORMATION COMMAND
106106
CFS
Unit
USER
Spiders-Crawlers
Indexed WebPages Search Index
User Query
Retrieval
Web
SVM
Un-Supervised
Clustering
DB
CFS
UnitWeb
Analyzer
Terms
InLink
OutLink
tf.idf
Eqv. tf.idf
Eqv. tf.idf
Aggregation
SOM
Community Builder
DataMiner
Visualization
Image Analyzer
Image Analyzer and Annotation
Image Query
and Retrieval
Image Annotation
Image Extraction
Summarization
Deduction
Q/A System
Summarization Deduction Q/A System
Structured Information
Semantic Web
Intelligent System Analyzer
i.e. Diagnosis-Prognosis
Experts Knowledge
Model Representation Including Linguistic Formulation
• Functional Requirements• Constraints• Goals and Objectives• Linguistic Variables Requirement
Input From Decision Makers
Model Management • Query• Aggregation• Ranking• Fitness Evaluation
Evolutionary KernelGenetic Algorithm, Genetic Programming, and DNA
• Selection• Cross Over• Mutation
Model and
Data Visualization
Data Management
Un-Structured Information
User
User InterfaceDialog Function
Knowledge Base Editor
Inference Engine
Recommendation, Advice, and Explanation
KnowledgeRefinement
DataIF … THEN
Rule
Knowledge of Engineer
Knowledge Base
users ask for advice or provide preferences
inferences & conclusion
advises the user andexplains the logic
expertise is transferred and
it is stored
Data Sources and Warehouse
(databases)
Knowledge Representation, Data Visualization and
Visual Interactive Decision Making
Knowledge Discovery
and Data Mining
Generate Knowledge
Organize Knowledge Bases
Expert Knowledge
CFS
Unit
USER
Spiders-Crawlers
Indexed WebPages Search Index
User Query
Retrieval
Web
SVM
Un-Supervised
Clustering
DB
CFS
UnitWeb
Analyzer
Terms
InLink
OutLink
tf.idf
Eqv. tf.idf
Eqv. tf.idf
Aggregation
SOM
Community Builder
DataMiner
Visualization
Image Analyzer
Image Analyzer and Annotation
Image Query
and Retrieval
Image Annotation
Image Extraction
Summarization
Deduction
Q/A System
Summarization Deduction Q/A System
Structured Information
Semantic Web
Intelligent System Analyzer
i.e. Diagnosis-Prognosis
Experts Knowledge
Model Representation Including Linguistic Formulation
• Functional Requirements• Constraints• Goals and Objectives• Linguistic Variables Requirement
Input From Decision Makers
Model Management • Query• Aggregation• Ranking• Fitness Evaluation
Evolutionary KernelGenetic Algorithm, Genetic Programming, and DNA
• Selection• Cross Over• Mutation
Model and
Data Visualization
Data Management
Un-Structured Information
User
User InterfaceDialog Function
Knowledge Base Editor
Inference Engine
Recommendation, Advice, and Explanation
KnowledgeRefinement
DataIF … THEN
Rule
Knowledge of Engineer
Knowledge Base
users ask for advice or provide preferences
inferences & conclusion
advises the user andexplains the logic
expertise is transferred and
it is stored
Data Sources and Warehouse
(databases)
Knowledge Representation, Data Visualization and
Visual Interactive Decision Making
Knowledge Discovery
and Data Mining
Generate Knowledge
Organize Knowledge Bases
Expert Knowledge
Concept-Based Intelligent Decision Analysis
BISC-DSS
Deductive Web Engine
Beyond the Semantic Web
NeuFCSearch
107107
[ 0, 1]
[ tf-idf]
[set]
Term-Document Matrix
The use of Fuzzy Set Theory
The use of statistical-Probabilistic TheoryThe use of bivalent-logic Theory
The use of Fuzzy Set-Object-Based Theory
Specialization
Imprecise Search
Lycos, etc.
GA-GP Context-Based tf-idf; Ranked tf-idf
Topic, Title,
Summarization
Concept-Based Indexing
Keyword search; classical techniques; Google, Teoma, etc.
Use Graph Theory and Semantic Net. NLP with GA-GP Based NLP; Possibly AskJeeves.
NeuFCS
RBF
PRBF
GRRBF
ANFIS
RBFNN (BP, GA-GP, SVM)
Probability
Bayesian
Fuzzy
NNnet(BP, GA-GP, SVM)
LSI
FCS Based on Neuroscience Approach
Classical Search
NeuSearch: Neuroscience ApproachSearch Engine Based on Conceptual Semantic Indexing
),( jiw
),( jiw
Neuro-Fuzzy Conceptual Search (NeuFCS)
108108
109109
)(),(),,(),( kpjpkjpfkjw
Documents Space or
Concept and Context Space
Based on SOM or PCA
Word Space
Concept-Context Dependent Word Space
)(),(),,(),( jpipjipfjiw
W(i, j) is calculated based on Fuzzy-LSI or Probabilistic LSI
(In general form, it can be Calculated based on PNL)
i: neuron in word layer
j: neuron in document or Concept-Context layer
j: neuron in document or Concept-Context layer
k: neuron in word layer
Document
(Corpus)
Neu-FCS
110110
111111
ORGANIZATION OF WORLD KNOWLEDGEEPISTEMIC (KNOWLEDGE-DIRECTED) LEXICON (EL)
(ONTOLOGY-RELATED)
i (lexine): object, construct, concept (e.g., car, Ph.D. i (lexine): object, construct, concept (e.g., car, Ph.D. degree)degree)
K(i): world knowledge about i (mostly perception-based)K(i): world knowledge about i (mostly perception-based) K(i) is organized into n(i) relations K(i) is organized into n(i) relations RRiiii, …, R, …, Rinin
entries in Rentries in Rijij are bimodal-distribution-valued attributes of i are bimodal-distribution-valued attributes of i values of attributes are, in general, granular and context-values of attributes are, in general, granular and context-
dependentdependent
network of nodes and links
wij= granular strength of association between i and j
i
jrij
K(i)lexine
wij
112112
EPISTEMIC LEXICON
lexinei
lexinej
rij: i is an instance of j (is or isu)i is a subset of j (is or isu)i is a superset of j (is or isu)j is an attribute of ii causes j (or usually)i and j are related
rij
113113
GENERALIZED CONSTRAINT
•standard constraint: X C•generalized constraint: X isr R
X isr R
copula
GC-form (generalized constraint form of type r)
type identifier
constraining relation
constrained variable
•X= (X1 , …, Xn )•X may have a structure: X=Location (Residence(Carol))•X may be a function of another variable: X=f(Y)•X may be conditioned: (X/Y)• ...//////////...//: psfgrsupvblank≤r ⊃⊂=
114114
CONTINUED
r: rs random set constraint; X isrs R; R is the set-valued probability distribution of X
r: fg fuzzy graph constraint; X isfg R; X is a function and R is its fuzzy graph
r: u usuality constraint; X isu R means usually (X is R)
r: ps Pawlak set constraint: X isps ( X, X) means that X is a set and X and X are the lower and upper approximations to X
115115
116116
Where wi,j is granular strength of association between i and j, ri,j
is epistemic lexicon, wi,j <== ri,j, and ri,j is defined as follows: rij: i is an instance of j (is or isu) i is a subset of j (is or isu) i is a superset of j (is or isu) j is an attribute of i i causes j (or usually) i and j are related
Wi,j
i j ri,j
Based on PNL approach, w(i,j) is defined based on ri,j as follows:
117117
Original keywords Extended keyword
Concept-Context Nodes (RBF Nodes)
Wi,j Wj,k
Original Documents Extended Documents
Concept-Context Nodes (RBF Nodes)
W’i,j W’j,k
NeuSearch Model
118118
...
x1
x2
x3
Nx
X
...
)(1X
)(3X
)(1X
m
)(2X
Increased dimension: N->m1 functionlinear non :)(X
i
3w
1mw
1w
2w
Output
y
More likely to be linearly separated
im
i
iiXwy
1
)(
Radial Basis Function is used to extract Concept
119119
...
x1
x2
x3
Nx
X
...
)(1 X
)(3 X
)(1Xm
)(2 X
Increased dimension:N->m1 functionlinear non :)(Xi
3w
1mw
1w
2w
Output
y
More likely to be linearly separated
im
iii Xwy
1
)(
...
x1
x2
x3
Nx
X
...
)(1 X
)(3 X
)(1Xm
)(2 X
Increased dimension:N->m1 functionlinear non :)(Xi
3w
1mw
1w
2w
Output
y
More likely to be linearly separated
im
iii Xwy
1
)(
SOM are used to make 2-D plot of Concepts
120120
...
x1
x2
x3
Nx
X
...
)(1 X
)(3 X
)(1Xm
)(2 X
Increased dimension:N->m1 functionlinear non :)(Xi
3w
1mw
1w
2w
Output
y
More likely to be linearly separated
im
iii Xwy
1
)(
...
x1
x2
x3
Nx
X
...
)(1 X
)(3 X
)(1Xm
)(2 X
Increased dimension:N->m1 functionlinear non :)(Xi
3w
1mw
1w
2w
Output
y
More likely to be linearly separated
im
iii Xwy
1
)(
Concept 1
...
x1
x2
x3
Nx
X
...
)(1 X
)(3 X
)(1Xm
)(2 X
Increased dimension:N->m1 functionlinear non :)(Xi
3w
1mw
1w
2w
Output
y
More likely to be linearly separated
im
iii Xwy
1
)(
...
x1
x2
x3
Nx
X
...
)(1 X
)(3 X
)(1Xm
)(2 X
Increased dimension:N->m1 functionlinear non :)(Xi
3w
1mw
1w
2w
Output
y
More likely to be linearly separated
im
iii Xwy
1
)(
Concept 2
...
x1
x2
x3
Nx
X
...
)(1 X
)(3 X
)(1Xm
)(2 X
Increased dimension:N->m1 functionlinear non :)(Xi
3w
1mw
1w
2w
Output
y
More likely to be linearly separated
im
iii Xwy
1
)(
...
x1
x2
x3
Nx
X
...
)(1 X
)(3 X
)(1Xm
)(2 X
Increased dimension:N->m1 functionlinear non :)(Xi
3w
1mw
1w
2w
Output
y
More likely to be linearly separated
im
iii Xwy
1
)(
Concept n
N Concepts are Extracted based on SOM and RBFs
SOM/LVQ are used to make 2-D plot of ConceptsSupervised and Unsupervised
121121
PNL-Based Conceptual Fuzzy Sets Using Neuroscience
Interconnection based on
Mutual Information
i: neuron in document layer
j: neuron in word layer
rij: i is an instance of j (is or isu)i is a subset of j (is or isu)i is a superset of j (is or isu)j is an attribute of ii causes j (or usually)i and j are related
ijrjiw ),(
Word Space
Concept-Context Dependent Word Space
i: neuron in word layer
j: neuron in document or Concept-Context layer
j: neuron in document or Concept-Context layer
k: neuron in word layerDocument
(Corpus) )(),(),,(),( jpipjipfjiw
)(),(),,(),( kpjpkjpfkjw
122122
Word Space
Input: Word
Neu-FCS
Activated Document or
Concept-Context
Output: Concept-Context Dependent Word
123123
Activated Document or
Concept-Context
Word Space
Input: Word
Neu-FCSOutput: Concept-Context Dependent Word
Document
(Corpus)
124124
FC-DNA as a basis for Common Sense Knowledge, Human Reasoning and
Deduction
125125
FC-DNA as a basis for Next Generation of Concept-Based Search Engine
126126
Masoud Nikravesh and Germano Resconi