Introduction
Context & History
Pursued approaches
Avenues of thought
Computing with words: towards an end-to-end use of linguistic terms in the reasoning process Habilitation `a diriger des recherches
Isis Truck Universit´ e Paris 8
Sep. ,
Conclusions
Introduction
Context & History
Pursued approaches
Avenues of thought
Outline
1
Introduction
4
Avenues of thought
2
Context & History
5
Conclusions
3
Pursued approaches
Conclusions
Introduction
Context & History
Pursued approaches
Avenues of thought
Outline
1
Introduction
4
Avenues of thought
2
Context & History
5
Conclusions
3
Pursued approaches
Conclusions
Introduction
Context & History
Pursued approaches
Avenues of thought
Digitization
Affect numbers to entities → non-trivial problem implies a linguistic processing implies to deal with uncertainties ⇒ Computing with Words [Zadeh,71; Zadeh,96] ⇒ Knowledge representation, modeling, combination in imprecise context (fuzzy subset & multiset theories)
Conclusions
Introduction
Context & History
Pursued approaches
Avenues of thought
Outline
1
Introduction
4
Avenues of thought
2
Context & History Frameworks GSM SWM
5
Conclusions
3
Pursued approaches
Conclusions
Introduction
Context & History
Pursued approaches
Avenues of thought
Context
Zadeh’s vs. De Glas’ framework ⇒ membership may be partial: x ∈α A ⇒ “x is A” is τα -true A: multiset α: linguistic term or adverbial expression τα : truth degree 2nd dimension in data representation degrees on a scale ⇒ total order relation ≤
Conclusions
Introduction
Context & History
Pursued approaches
Avenues of thought
Conclusions
Context
Zadeh’s vs. De Glas’ framework ⇒ membership may be partial: x ∈α A ⇒ “x is A” is τα -true A: multiset α: linguistic term or adverbial expression τα : truth degree 2nd dimension in data representation ⇒ keep only abscissa axis degrees on a scale ⇒ total order relation ≤
Introduction
Context & History
Pursued approaches
Avenues of thought
Outline
1
Introduction
4
Avenues of thought
2
Context & History Frameworks GSM SWM
5
Conclusions
3
Pursued approaches
Conclusions
Introduction
Context & History
Pursued approaches
Avenues of thought
Conclusions
GSM Generalized Symbolic Modifier m mρ : LM τi
ER0 (ρ)
→ LM 0 7→ τi 0
CR(ρ)
ER(ρ)
several families: ER(ρ), DR(ρ). . . in a lattice composition ◦ of GSMs
DR(ρ)
EC0 (ρ)
Original
DC0 (ρ)
EC(ρ)
DC(ρ)
EW(ρ)
DW(ρ)
CW(ρ)
DW0 (ρ)
[Truck,02], [Truck & Akdag,06]
Introduction
Context & History
Pursued approaches
Avenues of thought
Learning of modifications (1/2) ⇒ use of an adjunction operator q composed of composition of qualifiers composition of modifiers: operator ◦ Definition of operator q q : (M × Q)2 → M × Q h(m1 , q1 ), (m2 , q2 )i 7→ (m10 , q10 )
Example: “much darker(2) ” ← “much darker(1) ” q “a little less drab”
Conclusions
Introduction
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Conclusions
Learning of modifications (2/2) Composition of modifiers needs ◦ and operators is the inverse function of ◦: ∀ mi , mj , mj (mi ◦ mj ) = mi Definition of operator ◦ ◦ : N×N → N (I (m1 ), I (m2 )) 7→ I (m1 ◦ m2 ) with I (m1 ◦ m2 ) = ±I (m1 ) ± I (m2 ) ± I (m0 ), according to the I (m1 ) and I (m2 ) values. I (m) is the intensity of m, depending on ρ and on the family of m m0 is a neutral modifier [Truck & Akdag,03]
Introduction
Context & History
Pursued approaches
Avenues of thought
Outline
1
Introduction
4
Avenues of thought
2
Context & History Frameworks GSM SWM
5
Conclusions
3
Pursued approaches
Conclusions
Introduction
Context & History
Pursued approaches
Avenues of thought
Conclusions
SWM Symbolic Weighted Median M uses operator ◦ gives a linguistic aggregation uses only the linguistic terms from the initial set Definition of M
haw0
0,b−1
M : B Lb → L b 0 wb−1 w0 , aw1 , . . . , awb−1 i) , . . . , ab−1,b−1 i 7→ M(ha0,b−1 b−1,b−1 1,b−1 1,b−1 = m(aj,b−1 )
, a w1
[Truck & Akdag,03], [Truck & Akdag,09]
Introduction
Context & History
Pursued approaches
Avenues of thought
Conclusions
General scheme An end-to-end linguistic approach? ⇒ a process that would only deal with linguistic terms
FM
taxonomy of the fuzzy modifiers, including compatibility and comparability
fuzzification numerical data
Symbolic modifiers (GSM)
SA
Symbolic aggregation (SWM)
Processing
& partitioning
result
(reasoning, aggregation,
adjustment, linguistic data
SM
comparison, ...)
formatting SM
SA
FM
numerical data
naming
FM
linguistic data
Introduction
Context & History
Pursued approaches
Avenues of thought
Outline
1
Introduction
4
Avenues of thought
2
Context & History
5
Conclusions
3
Pursued approaches CW for visual perception CW for performing arts CW for the programmer intention capture
Conclusions
Introduction
Context & History
Pursued approaches
Avenues of thought
Colorimetric profile of an image (1/2)
Ft : membership of image I to color t Fet,q : membership of image I to color t and qualifier q
Definition of Fet,q P ˜ p∈P fq (lp , sp ) × gt (hp ) Fet,q (I ) = , ∀(t, q) ∈ T × Q |P| 1 if ft (hp ) 6= 0 with gt (hp ) = 0 otherwise
Conclusions
Introduction
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Avenues of thought
Conclusions
Colorimetric profile of an image (2/2)
But how to take into account the perception of colors? [A¨ıt Younes et al.,07]
Introduction
Context & History
Pursued approaches
Avenues of thought
Classifying images by perceived colors (1/3)
Compute zones Take into account the position and the quantity contrast [Itten,61]: yellow is three times more luminous than violet orange is twice more luminous than blue red is as much luminous as green
Recompute Ft (I ) and Fet,q (I ) ⇒ Another improvement: towards a learning of the color perceptions
Conclusions
Introduction
Context & History
Pursued approaches
Avenues of thought
Conclusions
Classifying images by perceived colors (2/3)
Measure a bias in the user request and correct it Construction of user profiles Modify the membership functions of the colors according to the user Recompute Ft (I ) and Fet ,q (I ), simulating the variations new
inew
j
Definition of Fetinew ,qj P ∀(ti , qj ) ∈ T × Q, Fetinew ,qj (I ) =
ti ∈Γ(tinew ) Φ(tinew , ti )
× Feti ,qj (I )
#Γ(tinew ) + 1
Introduction
Context & History
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Avenues of thought
Conclusions
Classifying images by perceived colors (3/3) Modified definitions, as perceived by the user
Standard definitions
f
f
red orange yellow
green
cyan
blue
purple magenta pink
red
red orange yellow
1
green
cyan
blue
purple magenta pink
red
1
0
21
43
85
128
170
191
213
234
255 H
0
21
43
r se 85
U
128
170
191
213
234
255 H
e il of pr
Fuzzy modifiers Profile of image I
Fred (I ) = ... e F red,somber (I ) = ... ... Fblack (I ) = ...
Modified profile of image I
Fred (I ) = ... e F red,somber (I ) = ... ... Fblack (I ) = ...
[El-Zakhem et al.,07]
Introduction
Context & History
Pursued approaches
Avenues of thought
Outline
1
Introduction
4
Avenues of thought
2
Context & History
5
Conclusions
3
Pursued approaches CW for visual perception CW for performing arts CW for the programmer intention capture
Conclusions
Introduction
Context & History
Pursued approaches
A virtual assistant for performers (1/2)
An original study of a performance
use of movement descriptors write fuzzy rules: how to partition?
Avenues of thought
Conclusions
Introduction
Context & History
Pursued approaches
Avenues of thought
Conclusions
A virtual assistant for performers (2/2) ⇒ use of real data for an ad hoc partitioning ⇒ compute their min, max and mean Example: L
A
x1
x0 (min)
µ
x2 (max)
(mean)
L
VL
H
A
H
VH
1
x0
x0,1 x0,2
x1
x1,1
x1,2
x2
Ai
[Bonardi et al.,06]
Introduction
Context & History
Pursued approaches
Avenues of thought
A fuzzy library for Max/MSP (1/2) What about sound processing? Max/MSP: an environment for music real time processing (1D-signal) improve Max/MSP to manage linguistic data implementation of Max/MSP objects
Conclusions
Introduction
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Avenues of thought
Conclusions
A fuzzy library for Max/MSP (2/2) user can enter his own vocabulary artists can specify interactions in their shows CW inputs −−→ outputs Example (Gesture recognition): semantic overview of the gesture
[Bonardi & Truck,09]
Introduction
Context & History
Pursued approaches
Avenues of thought
Outline
1
Introduction
4
Avenues of thought
2
Context & History
5
Conclusions
3
Pursued approaches CW for visual perception CW for performing arts CW for the programmer intention capture
Conclusions
Introduction
Context & History
Pursued approaches
Avenues of thought
Conditional preference modeling
Framework: autonomic computing Problem of service selection Match the non-functional constraints with the customer request Linguistic approach: preference expression (in a precise or imprecise way) ⇒ Proposition: Linguistic Conditional Preference networks (LCP-nets) inspired by CP-nets [Brafman et al.,04]
Conclusions
Introduction
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Conclusions
LCP-nets (1/2)
Deal with clauses such as “I tend to prefer the more or less V1 value for property X over exactly V2 if properties Y equals approximately VY and Z equals a bit more than VZ ” Example (Choice of a dress): woman has to attend a formal evening prefers a long dress if she can find shoes going with it always prefers to optimize the length (L) over the color (C ) of her dress preference about the color of her shoes (S) and about the height of heel (H) is conditioned by the color of the dress
Introduction
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Avenues of thought
Conclusions
LCP-nets (2/2) Ls vh
Lm med
Ll low
89:; ?>=< L H
Cd Cm Cl
Hnone vl low vh
HM med med med
Cd Cm high med ?>=< 89:; C? ?? ?? ?? ?? ?? ?? ?? ? L GFED @ABC 89:; ?>=< H S HH Sd vh Cd vh high Cm high vl Cl vl H .Ls S H .Lm S S .Ll H
Cl low
Sm high med m
Sl vl low vh
[Chˆatel et al.,10]
Introduction
Context & History
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Avenues of thought
Conclusions
Request & offer modeling for an ad hoc policy definition (1/2) Framework: Cloud computing Dynamic adaptation of the resource Need of a decision making process and ad hoc policies Express the experts’ knowledge and compute with it: CW Allocate the necessary and sufficient resource Virtual Machines (VM)
SLA ⇒ SLO
customer
provider
Introduction
Context & History
Pursued approaches
Avenues of thought
Conclusions
Request & offer modeling for an ad hoc policy definition (1/2) Framework: Cloud computing Dynamic adaptation of the resource Need of a decision making process and ad hoc policies Express the experts’ knowledge and compute with it: CW Allocate the necessary and sufficient resource Virtual Machines (VM)
SLA ⇒ SLO
customer
provider
Introduction
Context & History
Pursued approaches
Avenues of thought
Conclusions
Request & offer modeling for an ad hoc policy definition (2/2) Resource (VM) 2 dimensions in the scalability: horizontal and vertical ⇒ diagonal what about fuzzy VMs? ⇒ linguistic variables to define “very fast machine”, “reliable machine”, “gold machine”, “silver machine”, etc. definition of a fuzzy model of contract (SLA) through linguistic variables
[Dutreilh et al.,10]
Introduction
Context & History
Pursued approaches
Avenues of thought
Conclusions
Modeling the needs for self-adaptation
Framework: very large distributed systems Produce an architecture able to scale up to very big systems Automate the setting of the system parameters CW to elicit system configuration rules ⇒ fuzzy sets? linguistic 2-tuples [Herrera & Mart´ınez,01]?
[Melekhova et al.,10]
Introduction
Context & History
Pursued approaches
Avenues of thought
Conclusions
Outline
1
Introduction
2
Context & History
3
Pursued approaches
4
Avenues of thought On the CW in autonomic computing On the unification of linguistic models?
5
Conclusions
Introduction
Context & History
Pursued approaches
Avenues of thought
Conclusions
On a formalization of the LCP-nets
valid LCP-nets? towards an algebra of LCP-nets? optimization queries: not an abduction problem?
[Truck & Malenfant,11]
Introduction
Context & History
Pursued approaches
Avenues of thought
Conclusions
On an end-to-end linguistic processing
Never use a numeric-symbolic encoding of the linguistic terms? Another partitioning for unbalanced 2-tuples? An ad hoc inference for (unbalanced) 2-tuples? ⇒ may speed up the computations?
[Abchir & Truck,11]
Introduction
Context & History
Pursued approaches
Avenues of thought
Conclusions
Outline
1
Introduction
2
Context & History
3
Pursued approaches
4
Avenues of thought On the CW in autonomic computing On the unification of linguistic models?
5
Conclusions
Introduction
Context & History
Pursued approaches
Avenues of thought
Conclusions
A common characteristics 2-tuples everywhere! [Herrera & Mart´ınez,01]
[Wang & Hao,06] li
si
[Truck & Akdag,03]
li+1
0
α
1
2
3
1−α
− αi → u
0
→ − v0
→ − v0 − → − vi + αi → u
6
O
− → v− i+1 → − vg − → α→ vi + β − v− i+1
4 5 6
8
10
12
2nd 2-tuple: p(a0 ) = 5, b 0 = 13
g
0 → − vi
→ − vg O
0 1 2
2-tuple: (αli , (1 − α)li+1 )
g
→ − vi
5
DW(6)
αi 2-tuple: (si , αi )
4
1st 2-tuple: p(a) = 5, b = 7
− −.5→ u 1 2 3 4 5 6 → − v1 → − → − v2 v3 → − → − v0 v6 → − − v3 − .5→ u O
0
[Truck & Malenfant,10]
Introduction
Context & History
Pursued approaches
Avenues of thought
Outline
1
Introduction
4
Avenues of thought
2
Context & History
5
Conclusions
3
Pursued approaches
Conclusions
Introduction
Context & History
Pursued approaches
Avenues of thought
Conclusions (1/2)
CW in practice colorimetrics performing arts autonomic computing
CW in theory ad hoc partitioning LCP-nets towards a unification of linguistic models
Conclusions
Introduction
Context & History
Pursued approaches
Avenues of thought
Conclusions
Conclusions (2/2)
FP
ad hoc fuzzy partitioning
FM taxonomy of the fuzzy modifiers, including compatibility and comparability
P2t partitioning method for 2-tuples M2t modus ponens for 2-tuples
FP numerical data
L
LCP-nets
U
unification of the linguistic models
formatting, elicitation
Symbolic modifiers (GSM)
SA
Symbolic aggregation (SWM)
Processing
P2t
fuzzification & partitioning
(reasoning, unification of the models U
adjustment
aggregation, comparison, ...)
linguistic data numerical data
adjustment, linguistic data
SM
L
M2t
SM
SA
FM
L
SM result naming
FM
linguistic data
Introduction
Context & History
Pursued approaches
Avenues of thought
Conclusions
Conclusions (2/2)
FP
ad hoc fuzzy partitioning
FM taxonomy of the fuzzy modifiers, including compatibility and comparability
P2t partitioning method for 2-tuples M2t modus ponens for 2-tuples
FP numerical data
L
LCP-nets
U
unification of the linguistic models
formatting, elicitation
Symbolic modifiers (GSM)
SA
Symbolic aggregation (SWM)
Processing
P2t
fuzzification & partitioning
(reasoning, unification of the models U
adjustment
aggregation, comparison, ...)
linguistic data numerical data
adjustment, linguistic data
SM
L
M2t
SM
SA
FM
L
SM result naming
FM
linguistic data
Introduction
Context & History
Pursued approaches
Avenues of thought
Conclusions
Future works
Linguistic approaches in decision making: integrate criteria, objectives and behavior in decision policies ⇒ give a first approximation system observation ⇒ refine the approximation formalize the LCP-nets ⇒ make elicitation of the knowledge easier & tools easy to handle measure the quality of the decision process extend the CW to the whole process ⇒ provide more tools and operators
Introduction
Context & History
Pursued approaches
Avenues of thought
Conclusions
Report
publications (since 2003): 6 int. journals 2 int. book chapters 19 int. conf. 4 nat. conf.
projects and contracts: 1 research contract 2 “CIFRE” contracts 1 “ANR” contract
advisorship: co-supervision of 4 Ph.D students (3 in progress and 1 is Doctor)
Computing with words: towards an end-to-end use of linguistic terms in the reasoning process Habilitation `a diriger des recherches
Isis Truck Universit´ e Paris 8
Sep. ,
Computing with words: towards an end-to-end use of linguistic terms in the reasoning process Habilitation `a diriger des recherches
Isis Truck Universit´ e Paris 8
Sep. ,
Le pot a lieu en salle A 2278 (bˆatiment A, 2e ´etage, salle du Conseil scientifique)
