Perception-based Intelligent Decision Systems

8/2/2019 Perception-based Intelligent Decision Systems

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PERCEPTION-BASED INTELLIGENT DECISION SYSTEMS

Lotfi A. Zadeh and Masoud Nikravesh

Computer Science Division Department of EECS

UC Berkeley

URL: http://www-bisc.cs.berkeley.edu

URL: http://zadeh.cs.berkeley.edu/

Email: [email protected] and [email protected]

ONR Summer 2002 Program Review UCLA, July 30-August 1

LAZ 7-31-02
http://www-bisc.cs.berkeley.edu/http://zadeh.cs.berkeley.edu/mailto:[email protected]:[email protected]:[email protected]:[email protected]://zadeh.cs.berkeley.edu/http://www-bisc.cs.berkeley.edu/http://www-bisc.cs.berkeley.edu/http://www-bisc.cs.berkeley.edu/


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BASIC GOAL

CONCEPTION, DESIGN AND IMPLEMENTATION OF INTELLIGENT

DECISION SYSTEMS

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BASIC STRUCTURE

acquisition of information

communication of information

processing of information (extracting decision-relevant information)

decision

execution

assessment

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INTELLIGENT DECISION SYSTEM

INFORMATION-ON-DEMAND MODULE

INFORMATION PROFFERAL MODULE

INFORMATION ALERT MODULE

INFORMATION-ON-DEMAND MODULE=Q/A SYSTEM

Q/A SYSTEM=SEARCH ENGINE + DEDUCTION MODULE

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primary goal secondary goal

BASIC GOAL

development of new tools for solving existing and

new problems

use of new tools for solving existing and new

problems


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CONTENTION coordinated management of multi-agent

decision systems is beyond the capabilities of measurement-based methods

the problem is analogous to driving a car in heavy city traffic

humans can do this without any measurements and any computations, using perceptions of distance, speed, position intent and other decision-relevant variables and parameters

automation of driving in heavy city traffic is beyond the capabilities of existing

measurement-based systems LAZ 7-22-02


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TRANSFORMATION OF VISIONS INTO REALITY

needed: addition to the existing,

measurement-based, methods of the capability to operate and base decisions on perception-based information

it is this essential capability that humans have and machines have not

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THE TRIP-PLANNING PROBLEM

I have to fly from A to D, and would like to get there as soon as possible I have two choices: (a) fly to D with a connection in B; or

(b) fly to D with a connection in C

if I choose (a), I will arrive in D at time t 1 if I choose (b), I will arrive in D at time t 2 t 1 is earlier than t 2

therefore, I should choose (a) ?

A

C

B

D

(a)

(b)

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CONTINUTED now, let us take a closer look at the problem the connection time, c B , in B is short should I miss the connecting flight from B to D, the next flight will bring me to D at t 3 t 3 is later than t 2

what should I do?

decision = f ( t 1 , t 2 , t 3 ,c B ,c C )

existing methods of decision analysis do not have the capability to compute f

reason: nominal values of decision variables

observed values of decision variables LAZ 7-30-02


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CONTINUED

the problem is that we need information about the probabilities of missing connections in B and C.

I do not have, and nobody has, measurement-based information about this probabilities

whatever information I have is perception-based

with this information, I can compute perception-based granular probability distributions of arrival times in D for (a) and (b)

the problem is reduced to ranking of granular probability distributions

Note: subjective probability = perception of likelihood


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PERCEPTION-BASED GRANULAR PROBABILITY DISTRIBUTION

A1 A2 A3

P 1

P 2 P 3

arrival time (AT)

probability

P(AT) = P 1\A1 + P 2 \A2 + P 3 \A3

Prob {AT is A i } is P i

0

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NEW TOOLS

CN

IA GrC PNL

CW + + +

computing

with numbers

computing with intervals

computing with granules

precisiated natural language

computing

with words

PTp CTP: computational theory of perceptions

PTp: perception-based probability theory

THD: theory of hierarchical definability

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CTP THD a granule is defined by a generalized constraint


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COMPUTING WITH WORDS


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CW AND PNL a concept which plays a central role in CW is that

of PNL (Precisiated Natural Language) basically, a natural language, NL, is a system for

describing perceptions

perceptions are intrinsically imprecise imprecision of natural languages is a reflection of

the imprecision of perceptions the primary function of PNL is that of serving as a

part of NL which admits precisiation PNL has a much higher expressive power than

any language that is based on bivalent logic

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COMPUTING WITH WORDS (CW) in computing with words, the objects of

computation are words and propositions in a natural language example: a box contains N balls of various sizes

a few are small

most are medium a few are large how many are neither small nor large

example: A is near B B is near C how far is A from C

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KEY POINTS words are less precise than numbers

computing with words (CW) is less precise than computing with numbers (CN)

CW serves two major purposes a) provides a machinery for dealing with

problems in which precise information is not available

b) provides a machinery for dealing with problems in which precise information is

available, but there is a tolerance for imprecision which can be exploited to achieve tractability, robustness, simplicity and low solution cost

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PRECISIATED NATURAL LANGUAGE


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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)

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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.


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PRECISIATED NATURAL LANGUAGE (PNL)

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NLGCL

generalized constraint form of type r

p X isr R translation

generalized constraint form of type r (GC(p))

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p translation

precisiation language (GCL)

precisiation explicitation

GC-form CSNL

precisiable propositions

in NL

p*


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DICTIONARIES A:

most Swedes are tall Count (tall.Swedes/Swedes) is most

p p* (GC-form)

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proposition in NL precisiation

B:

Count (tall.Swedes/Swedes) is most

p* (GC-form)

protoform precisiation PF(p*)

Q As are Bs


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PNL AND THE COMPUTATIONALTHEORY 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

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EXAMPLE I am driving to the airport. How long will it

take me to get there? Hotel clerks perception -based answer:

about 20-25 minutes about 20 - 25 minutes cannot be defined

in the language of bivalent logic and probability theory

To define about 20 - 25 minutes what isneeded is PNL

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DEFINITION OF p: ABOUT 20-25 MINUTES

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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


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EXAMPLE PNL definition of about 20 to 25 minutes

Prob {getting to the airport in less than about 20 min} is unlikely Prob {getting to the airport in about 20 to 25 min} is likely Prob {getting to the airport in more than 25 min} is unlikely

granular probability distribution

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P

likely

unlikely

Time 20 25


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COMPUTATIONAL THEORY OF PERCEPTIONS


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COMPUTATIONAL THEORY OF PERCEPTIONS (CTP) PREAMBLE

It is a deep-seated tradition in science to equate scientific progress to progression from perceptions to measurements

But, what humans have and machines have not is a remarkable capability to perform a wide variety of physical and mental tasks without any measurements and any computations. A canonical example of this capability is driving in heavy city traffic. Another example is summarizing a book

To endow machines with this capability it is necessary to

progress, countertraditionally, from measurements to perceptions

This is the objective of the computational theory of perceptions (CTP) a theory in which perceptions are objects of computation

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FROM MEASUREMENTS TO PERCEPTIONS

WINE EXPERT assessment sample

chemical analysis

NN excellent

perception

fuzzy measurements neural network

crisp input

wine excellent

perception

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NN is a neurofuzzy neural network

with crisp input and fuzzy output


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COMPUTATIONAL THEORY OF PERCEPTIONS

the point of departure in the computational theory of perceptions is the assumption that perceptions are described by propositions expressed in a natural language

examples economy is improving Robert is very honest it is not likely to rain tomorrow

it is very warm traffic is heavy

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in general, perceptions are summaries perceptions are intrinsically imprecise


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CONTINUED imprecision of perceptions is a manifestation of

the bounded ability of sensory organs and,ultimately, the brain, to resolve detail and store information

perceptions are f-granular in the sense that (a) the boundaries of perceived classes are fuzzy; and (b) the values of perceived attributes are granular, with a granule being a clump of values drawn together by indistinguishability, similarity,proximity or functionality

it is not possible to construct a computational theory of perceptions within the conceptual

structure of bivalent logic and probability theory LAZ 7-22-02


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it is 35 C Eva is 28 Tandy is three years

older than Dana

It is very warm Eva is young Tandy is a few

years older than Dana it is cloudy traffic is heavy Robert is very honest

INFORMATION

measurement-based numerical

perception-based linguistic

MEASUREMENT-BASED VS. PERCEPTION-BASED INFORMATION

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CONTINUED

with probability 0.9

Robert returns from work between 5:45pm and 6:15pm.

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usually Robert returns from work at about 6 pm

the mathematics of perception-based information has a higher level of generality than the mathematics of measurement-based information

a proposition is a perception if it contains fuzzy quantifiers: many, most, few, ; fuzzy qualifiers: usually,

probably, possibly, typically, generally, ; fuzzy modifiers: very, more or less; extremely, ; and/or fuzzy nouns, adjective or adverbs,


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PERCEPTION OF A FUNCTION

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if X is small then Y is small if X is medium then Y is large if X is large then Y is small 0

X

0

Y

f f* : perception

Y

f* (fuzzy graph)

medium x large

f

0

S M L

LM S

granule


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DEDUCTION (COMPUTING) WITH PERCEPTIONS

deduction

example

p 1

p 2

p n

P n+1

Dana is young Tandy is a few years older than Dana

Tandy is (young+few)

deduction with perceptions involves the use of protoformal rules of generalized constraint propagation

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PROTOFORM LANGUAGE


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THE CONCEPT OF PROTOFORM protoform=abbreviation of prototypical form

syntactic parse

semantic parse

syntax tree

logical form

semantic network

conceptual graph

canonical form

p parsing

semantic parse protoform 1 protoform 2 abstraction abstraction

protoform 3

protoform=abstracted summary

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THE CONCEPT OF PROTOFORM a protoform is an abstracted prototype of a class of

propositions

examples: most Swedes are tall

many Americans are foreign-born

overeating causes obesity Q As are Bs

obesity is caused by overeating Q Bs are As

Q As are Bs

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P-abstraction

P-abstraction

P-abstraction


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WHAT IS A PROTOFORM p=proposition in a natural language if p has a logical form, LF(p), then a protoform of p, PF(p),

is an abstraction of LF(p)

all men are mortal x(man(x) mortal(x)) x(A(x) B(x))

abstraction=deinstantiation

all men are mortal all men are A

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abstraction deinstantiation

p LF(p) PF(p)


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CONTINUED if p does not have a logical form but is in PNL,

then a protoform of p is an abstraction (deinstantiation) of the generalized constraint form of p, GC(p)

most Swedes are tall Count(tall.Swedes/Swedes) is most

p GC(p)

QAs are Bs

PF(p)

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abstraction


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EXAMPLES

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N L LOGICAL FORM PROTOFORM

all men are mortal

most Swedes are tall

usually Robert

returns from work at about 6pm

Vx(man(x) mortal(x)) Vx(A(x) B(x))

Q As are Bs

Prob (A) is B

fuzzy event

fuzzy probability


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ORGANIZATION OF KNOWLEDGE

much of human knowledge is perception-based examples of factual knowledge

height of Eiffel Tower is 324 m (with antenna) (measurement-based)

Berkeley is near San Francisco (perception-based) icy roads are slippery (perception-based) if Marina is a student then it is likely that Marina is young

(perception-based) LAZ 7-22-02

FDB DDB

factual database deduction database fact rule

measurement-based perception-based

knowledge


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PROTOFORM AND PF-EQUIVALENCE

P is the class of PF-equivalent propositions P does not have a prototype P has an abstracted prototype: Q As are Bs P is the set of all propositions whose protoform is: Q As are Bs

knowledge base (KB)

PF-equivalence class (P)

P q

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protoform (p): Q As are Bsmost Swedes are tall

few professors are rich


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PROTOFORMAL CONSTRAINT PROPAGATION

Dana is young Age (Dana) is young X is A

p GC(p) PF(p)

Tandy is a few years older than Dana

Age (Tandy) is (Age (Dana)) Y is (X+B)

X is AY is (X+B) Y is A+B

Age (Tandy) is (young+few)

)-()((sup)( uvuv B Au B A

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+few

REASONING WITH PERCEPTIONS


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REASONING WITH PERCEPTIONS: DEDUCTION MODULE

GC-form GC(p)

perceptions p

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GC-forms GC(p)

terminal data set

terminal protoform

set

initial protoform

set

protoforms PF(p)

translation explicitation precisiation

IDS IGCS

initial data set initial generalized

constraint set

IGCS IPS

TPS TDS IPS

abstraction deinstantiation

goal-directed deduction

deinstantiation

initial protoform set

DEDUCTION MODULE


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DEDUCTION MODULE rules of deduction are rules governing

generalized constraint propagation

rules of deduction are protoformal examples generalized modus ponens

X is A

if X is B then Y is C Y is A o (B C) )),()(sup()( vuuv C B A y

Prob (A) is B

Prob (C) is D

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)))()(((sup)( duu guvU

A B g D

subject to duu guv

U

C )()(


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EXAMPLE OF DEDUCTION

most Swedes are tall ? R Swedes are very tall

most Swedes are tall Q As are Bs s/a-transformation

Q As are Bs

Q 1/2 As are 2 Bs

most 1/2 Swedes are very tall r 1

1

0 0.25 0.5

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most 1/2

most

CONTINUED


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CONTINUED

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not(QAs are Bs) (not Q) As are Bs

Q 1 As are Bs Q 2 (A&B)s are Cs

Q 1 Q 2 As are (B&C)s

Q 1 As are Bs Q 2 As are Cs

(Q 1 + Q 2 - 1) As are (B&C)s


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INFORMAL PROTOFORM-BASED REASONING

most As are BsX is Ait is likely that X is B

QAs are Bs X is A

Prob(X is B) is Q

tacit assumptions: X is picked at random from As LAZ 7-22-02

COUNT AND MEASURE RELATED RULES


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COUNT- AND MEASURE-RELATED RULES

Q As are Bs

ant (Q) As are not Bs r 0

1

1

ant (Q)

Q

Q As are Bs

Q 1/2 As are 2 Bs r 0

1

1

Q

Q 1/2

most Swedes are tall ave (tall |Swedes) is ?h

Q As are Bsave (B|A) is ?C

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))(1

(sup)( i BiQaave a N v

)(1

iia

N v

),...,( 1 N aaa,

crisp


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THE ROBERT EXAMPLE


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THE ROBERT EXAMPLE

the Robert example relates to everyday commonsense reasoning a kind of reasoning which is preponderantly perception-based

the Robert example is intended to serve as a test of the deductive capability of a

reasoning system to operate on perception-based information

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THE ROBERT EXAMPLE

Version 1.My perception is that Robert usually returns from work at about 6:00pm

q 1 : What is the probability that Robert is home at about t pm?

q 2 : What is the earliest time at which the probability that Robert is home is high?

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THE ROBERT EXAMPLE (VERSION 3)

IDS: Robert leaves office between 5:15pm and 5:45pm. When the time of departure is about 5:20pm, the travel time is usually about 20min; when the time of departure is about 5:30pm, the travel time is usually about 30min; when the time

of departure is about 5:40pm, the travel time is about 20min

usually Robert leaves office at about 5:30pm

What is the probability that Robert is home at about t pm?

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THE ROBERT EXAMPLE

Version 4 Usually Robert returns from work at about 6 pm

Usually Ann returns from work about half-an-hour later What is the probability that both Robert and Ann are home at about t pm?

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1

0 6:00 t time

Robert Ann P

THE ROBERT EXAMPLE


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THE ROBERT EXAMPLE

event equivalence

Robert is home at about t pm= Robert returns from work before about t pm

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1

0 T t time

time of return

before t*

t* (about t pm)

Before about t pm= o about t pm


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THE ROBERT EXAMPLE

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backtracking from query to query-relevant information

query (q) : what is the probability,P, that Robert is home at about t pm (t*)?

query (q) : what is the earliest time at which the probability that Robert is home is high?

Version 1

query-relevant information (q 1 ): probability distribution of time, T, at which Robert returns from work

relevant fact (f(q -1 ): usually Robert returns from work at about 6pm

CONTINUED (VERSION 1)


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CONTINUED (VERSION 1) Q: what is the probability that Robert is home at t*?

CF(q): duu gu t )()(12

0*

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is ?P

PF(q): Prob(C) is ? D

0

1

6 pm t time

* t

t*

KB


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CONTINUED

Prob (C) is D

Prob (A) is B

KB FDB DDB

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Q -1

P(C) is ?D P(A) is ?B

q

protoformal rule in DDB

Prob (C is D)

Prob (A is B) Prob (C is D) Prob (Robert returns from

work at about t) is usually instantiation

duuqut )()(12

0

* is usually

PROBABILISTIC CONSTRAINT PROPAGATION RULE


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PROBABILISTIC CONSTRAINT PROPAGATION RULE (a special version of the generalized extension principle)

duuu g AU )()( is R

duuu g BU )()( is ?S

)))()(((sup)( duuugv AU RgS

subject to

1)(

)()(

duu g

duuu gv

U

BU

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CONTINUATION


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CONTINUATION P : membership function of P

generalized extension principle

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(u)du))g(u) ((max=(v) *612

0usuallygP

subject to: g(u)du(u)=v *t

12

0

1=g(u)du12

0

THE BALLS IN BOX EXAMPLE


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THE BALLS-IN-BOX EXAMPLE a box contains N balls of various sizes

my perceptions are:

a few are small most are medium a few are large

a ball is drawn at random

what is the probability that the ball is neither small nor large

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IDS (initial data set)

PERCEPTION BASED ANALYSIS


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PERCEPTION-BASED ANALYSIS

a few are small Count(small) is few Q 1 As are B 1s

most are medium

a few are large

Count(medium) is most Q 2 As are B 2 s

Count(large) is few Q 3 As are B 3 s

} u ,...,{u = A n1

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; u i =size of i th ball; u= ( u 1, , u n )

: ) u ,...,(u n11 possibility distribution function of (u 1, , u n ) induced by the protoform Q 1 As are Bs

))(u (-)u,...,(u1111 i BiQn

1

N 1

N 1

N

1N

CONTINUED


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CONTINUED : ) u ,...,(u n1 possibility distribution function induced by IDS

) u ,...,(u ) u ,...,(u ) u ,...,(u ) u ,...,(u n 1312111

query: (proportion of balls which are neither large nor small) is? Q 4

)) ( (1 ) (u ((1 = Q irgmall -4

protoformal deduction rule (extension principle)

(u)) (u) (u) ( sup = (v) 3214

subject to

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))) (u (1 )) ( ((1 = V i- 311N

1N


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CONCLUSION

the goal of realization of an intelligent multi- agent decision system is beyond the capabilities of measurement-based systems

to achieve the goal, it is necessary to employ systems which have the capability to operate on perception-based information

CW, PNL and CTP are necessary tools for adding this capability to measurement-based systems

Documents

Perception-based Intelligent Decision Systems