outline soft computing in decision support lsp the different components of lsp suitability vs....
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Outline
Soft computing in decision support• LSP
The different components of LSP Suitability vs. affordability
• What can we learn from decision support?• Applications
The Project is co-financed by the European Union from resources of the European Social Fund
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
J.J. Dujmović“Preference Logic for System Evaluation”IEEE Transactions on Fuzzy Systems 15 6 (2007) 1082-1099.
Logic Scoring of Preferences
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of Preferences
mulitiple criteria decision making
cases
?
userpreferences
(multiple criteria)
select the best
score
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of Preferences
scoring: overall degree of suitability
the overall degree of suitability E is a soft computing logical function of n attributes of which it is assumed that its range is normalized
𝐸=𝐺 (𝑎1 ,…,𝑎𝑛)∈ [ 0,1 ]
the value 0 denotes an unsuitable case and the value 1 (or 100%) denotes the maximum level of suitability
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of Preferences
main steps of the LSP method
1. create the system attribute tree2. define an elementary criterion for each attribute3. for each competitive system, compute elementary degrees of
suitability of elementary criteria4. use logic aggregators developed to aggregate all elementary
degrees of suitability and compute the overall suitability (of all user requirements)
5. if the overall degree of suitability E corresponds to the overall cost C, perform a cost/suitability analysis to find the best value
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of Preferences
step 1: creation of the system attribute tree
array of elementary attributes
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of Preferences
step 2: definition of elementary criteria
array of elementary attributes
array of elementary criteria
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of Preferences
step 2: definition of elementary criteria (cont’d)
examples
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of Preferences
step 3: evaluation of elementary criteria
array of elementary suitability degrees
array of elementary criteria
𝑔𝑖 :𝑑𝑜𝑚𝑎𝑖→ [ 0,1 ]
𝑎𝑖 [𝐶 ]→𝑔𝑖 (𝑎𝑖 [𝐶 ] )
for case C, attribute
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of Preferences
step 3: evaluation of elementary criteria (cont’d)
examples
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of Preferences
step 4: aggregation of elementary degrees of suitability
construction of a hierarchic preference aggregation structure that reflects the semantics of the attribute tree
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of Preferences
step 4: aggregation of elementary degrees of suitability (cont’d)
building blocks
• simple aggregators• compound aggregators
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of Preferences
step 4: aggregation of elementary degrees of suitability (cont’d)
simple aggregators
• Based on superposition of the fundamental Generalized Conjunction/Disjunction (GCD) function (basic LSP aggregator)
• Continuous transition from conjunction to disjunction • Adjustable degrees of andness/orness (r)• Adjustable relative importance of inputs (wi)
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of Preferences
step 4: aggregation of elementary degrees of suitability (cont’d)
generalized conjunction/disjunction (GCD)
• GCD is implemented as a mean• frequently used implementations
– weighted power mean (WPM)– exponential mean– quasi-arithmetic mean– OWA
• WPM is used for practical purposes
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of Preferences
step 4: aggregation of elementary degrees of suitability (cont’d)
• given weights , such that , determine the relative importance of the input preferences
• the pre-computed exponent determines the logic properties of the WPM aggregator
weighted power mean (WPM)
𝐺𝐶𝐷 (𝑒1 ,…,𝑒𝑛 ,𝑤1 ,…,𝑤𝑛 ;𝑟 )={(𝑤1 ∙𝑒1𝑟+…+𝑤𝑛∙𝑒𝑛
𝑟 )1𝑟 , if 0<|𝑟|<+∞
𝑚𝑖𝑛 (𝑒1 ,…,𝑒𝑛) , if 𝑟=−∞𝑚𝑎𝑥 (𝑒1 ,…,𝑒𝑛) , if 𝑟=+∞
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of Preferences
step 4: aggregation of elementary degrees of suitability (cont’d)
• discrete levels of andness/orness associate aggregators with linguistic interpretations
• the use of linguistic labels (weak, medium, strong, etc.) simplifies the process of selecting the most appropriate aggregator
• LSP basically uses a system with 17 discrete levels
in practice: discrete levels of andness/orness
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of Preferences17 discrete levels and their symbols
C
C
C
C
Strongest
Strong
CA
C
C
C
Medium
Weak
D
D
D
DA
Weak
MediumD
D
D
D
Strong
Strongest
StrongVery
Strong Medium
WeakMedium
Very Weak
ty Simultanei
ANeutralityVery weak
WeakMedium
Strong Medium
StrongVery
lity Replaceabi
PCD
GCD
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of PreferencesGCD implemented as a weighted power mean
mandatory (all inputs must be satisfied)
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of Preferences
step 4: aggregation of elementary degrees of suitability (cont’d)
compound aggregators
• combining a mandatory with a desired input– conjunctive partial absorption
• combining a sufficient with a desired input– disjunctive partial absorption
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of Preferences
step 4: aggregation of elementary degrees of suitability (cont’d)
conjunctive partial absorption
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of Preferences
step 4: aggregation of elementary degrees of suitability (cont’d)
conjunctive partial absorption ()
HPFddC+D+
C+A
annihilator 0 for mandatory input
P(enalty); R(eward)
P(enalty); R(eward)
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of Preferences
step 4: aggregation of elementary degrees of suitability (cont’d)
conjunctive partial absorption ()
𝑥⊵𝑦=𝑤2∙𝑥 ∆́ (1−𝑤2 )∙ (𝑤1 ∙ 𝑥~𝛻 (1−𝑤1 ) ∙ 𝑦 )
where and
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of Preferences
step 4: aggregation of elementary degrees of suitability (cont’d)
conjunctive partial absorption ()
𝑥⊵𝑦=((1−𝑤2) ∙ (𝑤1 ∙ 𝑥𝑞+ (1−𝑤1 ) ∙ 𝑦𝑞)
𝑟𝑞+𝑤2∙𝑥
𝑟 )1𝑟
where• is determined by and is determined by • and are computed from P and R
in practice
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of Preferences
step 4: aggregation of elementary degrees of suitability (cont’d)
disjunctive partial absorption ()
D+C+
D+A
annihilator 0 for mandatory input
P(enalty); R(eward)
P(enalty); R(eward)
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of Preferences
step 4: aggregation of elementary degrees of suitability (cont’d)
disjunctive partial absorption ()
𝑥⊳ 𝑦=𝑤2∙𝑥 �́� (1−𝑤2 ) ∙(𝑤1 ∙𝑥~∆ (1−𝑤1 ) ∙ 𝑦 )
where and
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of Preferences
step 4: aggregation of elementary degrees of suitability (cont’d)
example
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of Preferences
step 4: aggregation of elementary degrees of suitability (cont’d)
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of Preferences
step 5: perform a cost/suitability analysis to find the best value
suitability and affordability are orthogonal concepts
• both have a hierarchic structure• but aggregation is different as values are
different– suitability: logical aggregation (and, or, not, etc.)– cost: arithmetic aggregation (add, multiply, etc.)
• decision makers usually need a tradeoff between both
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of Preferences
step 5: perform a cost/suitability analysis to find the best value
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of Preferences
step 5: perform a cost/suitability analysis to find the best value
overall suitability E vs. global cost C
global quality Q
𝑄=𝐸𝐶 best suitability-cost tradeoff
minimal suitability and maximal cost
reject if or
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of Preferences
step 5: perform a cost/suitability analysis to find the best value
𝑄=𝑝 ∙ 𝐸𝐸𝑚𝑎𝑥 + (1−𝑝) ∙𝐶
𝑚𝑖𝑛
𝐶,0<𝑝<1
where denotes the relative significance of is the suitability of the best suitable caseis the cost of the cheapest case
Soft computing indecision support
LSP
The Project is co-financed by the European Union from resources of the European Social Fund
Logic Scoring of Preferences
step 5: perform a cost/suitability analysis to find the best value
𝑄=𝑝 ∙𝐸+ (1−𝑝 ) ∙(𝐶𝑚𝑎𝑥−𝐶 )𝐶𝑚𝑎𝑥 ,0<𝑝<1
where denotes the relative significance of is the cost of the most expensive case
Soft computing indecision support
What can we learn from decision support?
The Project is co-financed by the European Union from resources of the European Social Fund
what can we learn from decision support?
Soft computing indecision support
What can we learn from decision support?
The Project is co-financed by the European Union from resources of the European Social Fund
Bipolarity in ‘fuzzy’ querying
‘and if possible’ is a special case of Conjunctive Partial Absorption
𝑐 and if possible𝑤=𝑚𝑖𝑛 (𝑐 ,𝑘 ∙𝑐+(1−𝑘 ) ⋅𝑤 ) ,𝑘∈¿0,1¿
𝑥⊵𝑦=𝑤2 ∙𝑥 ∆́ (1−𝑤2 )∙ (𝑤1 ∙ 𝑥~𝛻 (1−𝑤1 ) ∙ 𝑦 )
where and
J.J. Dujmović“Partial Absorption Function”Journal of the University of Belgrade 659 (1979) 156-163.
Soft computing indecision support
What can we learn from decision support?
The Project is co-financed by the European Union from resources of the European Social Fund
Bipolarity in ‘fuzzy’ querying
𝑐 or else𝑤=𝑚𝑎𝑥 (𝑐 ,𝑘 ∙𝑐+(1−𝑘 ) ⋅𝑤 ) ,𝑘∈¿0,1¿
‘or else’ is a special case ofDisjunctive Partial Absorption
J.J. Dujmović“Partial Absorption Function”Journal of the University of Belgrade 659 (1979) 156-163.
𝑥⊳ 𝑦=𝑤2∙𝑥 �́� (1−𝑤2 ) ∙(𝑤1 ∙𝑥~∆ (1−𝑤1 ) ∙ 𝑦 )
where and
Soft computing indecision support
What can we learn from decision support?
The Project is co-financed by the European Union from resources of the European Social Fund
there is a need for querying facilities tohandle mandatory and optional criteria
Soft computing indecision support
What can we learn from decision support?
The Project is co-financed by the European Union from resources of the European Social Fund
current querying facilities do not efficiently support complex data searches
Soft computing indecision support
What can we learn from decision support?
The Project is co-financed by the European Union from resources of the European Social Fund
query expressivity
• need for grouping and structuring preferences• need for generalizing and specializing preferences
criterion trees
Soft computing indecision support
What can we learn from decision support?
The Project is co-financed by the European Union from resources of the European Social Fund
query expressivity
tree structure• leaf node: elementary criterion ci on a single attribute ai
• internal node: specification of an aggregation operator A• edge: relative weight (importance) of the criterion
A
c1 c2 ck…
w1 w2 wk
∑𝑖=1
𝑘
𝑤 𝑖=1
Soft computing indecision support
What can we learn from decision support?
The Project is co-financed by the European Union from resources of the European Social Fund
query expressivity
aggregators GeneralisedConjunction
Disjunction(GCD)Ordered
Weighted
Average
(OWA)Yager
Dujmović
C DHPC HPDSPC SPD A
Soft computing indecision support
What can we learn from decision support?
The Project is co-financed by the European Union from resources of the European Social Fund
query expressivity
no more need for weight propagation!(because internal nodes have associated weights)
weighted aggregators
Soft computing indecision support
What can we learn from decision support?
The Project is co-financed by the European Union from resources of the European Social Fund
query expressivity
evaluation• leaf node: evaluation of elementary criterion ci
• internal node: aggregation of evaluation results of all leaf nodes• criterion tree: evaluation of the root node
Soft computing indecision support
What can we learn from decision support?
The Project is co-financed by the European Union from resources of the European Social Fund
query expressivity
example
…
Soft computing indecision support
What can we learn from decision support?
The Project is co-financed by the European Union from resources of the European Social Fund
query expressivity
advanced GCD aggregation for BSDs
𝐺𝐶𝐷 ((𝑠1 ,𝑑1 ) ,…, (𝑠𝑛 ,𝑑𝑛) ,𝑤1 ,…,𝑤𝑛 ;𝑟 )=¿
, if 0<|r|<+
, if r= -, if r= +
{ ((∑𝑖=1
𝑛
𝑤𝑖𝑠𝑖𝑟)
1 /𝑟
,(∑𝑖=1
𝑛
𝑤 𝑖𝑑𝑖𝑟)
1 /𝑟
)(𝑚𝑖𝑛 (𝑠1,…, 𝑠𝑛) ,𝑚𝑎𝑥 (𝑑1 ,…,𝑑𝑛 ))(𝑚𝑎𝑥 (𝑠1 ,… ,𝑠𝑛 ) ,𝑚𝑖𝑛 (𝑑1 ,…,𝑑𝑛 ))
where r models the logical counterpart of the operator modelled by r (e.g., if r models HPC, then r models HPD)
Soft computing indecision support
What can we learn from decision support?
The Project is co-financed by the European Union from resources of the European Social Fund
query expressivity
advanced OWA aggregation for BSDs
• Dynamically assigned weights, for which • Based on ranking– is the ith largest BSD of – depends on the ranking function used! (e.g., )
𝑂𝑊𝐴 ( (𝑠1 ,𝑑1 ) ,…, (𝑠𝑛 ,𝑑𝑛) ,𝑤1 ,…,𝑤𝑛)=(∑𝑖=1
𝑛
𝑤𝑖 ∙𝑠 ′ 𝑖
∑𝑖=1
𝑛
𝑤𝑖
,∑𝑖=1
𝑛
𝑤 𝑖∙𝑑 ′𝑖
∑𝑖=1
𝑛
𝑤𝑖 )
Soft computing indecision support
Applications
The Project is co-financed by the European Union from resources of the European Social Fund
some applications
Soft computing indecision support
Applications
The Project is co-financed by the European Union from resources of the European Social Fund
LSP suitability maps
• logically aggregated geographical suitability maps (S-maps) • provide specialized maps of the suitability degree of a
selected geographic region for a specific purpose– construction of industrial objects, airports, entertainment centers,
shopping malls, sport facilities– land/sea exploitation– agriculture– etc.
• for the purpose of evaluating and comparing locations, areas or regions
• suitability degrees are computed using the LSP method
Soft computing indecision support
Applications
The Project is co-financed by the European Union from resources of the European Social Fund
LSP suitability mapsregular approach
Soft computing indecision support
Applications
The Project is co-financed by the European Union from resources of the European Social Fund
LSP suitability mapsbipolar approach
Soft computing indecision support
Applications
The Project is co-financed by the European Union from resources of the European Social Fund
the TILES projectTransnational and Integrated Long-term Marine
Exploitation Strategies
Soft computing indecision support
Applications
The Project is co-financed by the European Union from resources of the European Social Fund
the TILES project
Soft computing indecision support
Applications
The Project is co-financed by the European Union from resources of the European Social Fund
ear identification
Disaster Victim Identification• identification of human bodies• large scale disasters
Soft computing indecision support
Applications
The Project is co-financed by the European Union from resources of the European Social Fund
ear identification
• collect as many data as possible about:– victims– missing persons
• data examples– biometrical (DNA, dental records, ear photographs...)– general data (gender, name...)– descriptive data (clothes, tattoo’s, piercings...)
strategy
Soft computing indecision support
Applications
The Project is co-financed by the European Union from resources of the European Social Fund
ear identificationissues
• fast data collection• intelligent combination of all information• final decision by a committee of experts• uncertainty in early stage• charitable approach is preferred
Soft computing indecision support
Applications
The Project is co-financed by the European Union from resources of the European Social Fund
ear identificationdata
=?
• victim: post mortem (PM) 3D ear picture• missing person: ante mortem (AM) 2D pictures
Soft computing indecision support
Applications
The Project is co-financed by the European Union from resources of the European Social Fund
ear identificationchallenge
cope with poor picture quality of AM pictures
Soft computing indecision support
Applications
The Project is co-financed by the European Union from resources of the European Social Fund
ear identificationapproach
1. Ear detectionPositioning and extraction
2. Ear normalisation and enhancementTransform to a 3D ear model using geometrical and photometric corrections
3. Feature extraction4. Ear recognition
Compare feature sets and compute matching score
5. Decision
Soft computing indecision support
Applications
The Project is co-financed by the European Union from resources of the European Social Fund
ear identificationapproach
… …
AM ear
normalized 3D ear
ear detection
ear normalisation and enhancement
Soft computing indecision support
Applications
The Project is co-financed by the European Union from resources of the European Social Fund
ear identificationapproach
ear normalisationand enhancement
PM ear
normalized 3D ear
3D camera / 3D scanner
Soft computing indecision support
Applications
The Project is co-financed by the European Union from resources of the European Social Fund
ear identificationapproach
featureextraction
selecting n representative
points
LA=[p1A,…,pn
A]
Soft computing indecision support
Applications
The Project is co-financed by the European Union from resources of the European Social Fund
ear identificationapproach
earrecognition
comparing feature sets om 3D AM and
PM ear models
LA=[p1A,…,pn
A]
AM ear PM ear
LP=[p1P,…,pn
P]
Soft computing indecision support
Applications
The Project is co-financed by the European Union from resources of the European Social Fund
ear identificationapproach
earrecognition
comparing feature sets om 3D AM and
PM ear models
match
+ coping with imperfect data
Soft computing indecision support
Applications
The Project is co-financed by the European Union from resources of the European Social Fund
ear identificationhesitation spheres
Soft computing indecision support
Applications
The Project is co-financed by the European Union from resources of the European Social Fund
ear identificationhesitation spheres
• handle unreliable parts• manually assigned by forensic experts• overall hesitation of point p covered by
multiple hesitation spheres
h (𝑝 )=𝑚𝑎𝑥𝑘h𝐻𝑘(𝑝 )
Soft computing indecision support
Applications
The Project is co-financed by the European Union from resources of the European Social Fund
ear identificationtraditional approach
pA
1. distance d(pA,pP)
𝑑 (𝑝𝐴 ,𝑝𝑃 )=√(𝑝𝑥𝐴−𝑝𝑥
𝑃 )2+(𝑝 𝑦𝐴−𝑝 𝑦
𝑃 )2+(𝑝𝑧𝐴−𝑝𝑧
𝑃 )22. similarity fsim(pA,pP)
Soft computing indecision support
Applications
The Project is co-financed by the European Union from resources of the European Social Fund
ear identificationbipolar approach
pA
local similarity fBsim(pA,pP)
𝑠=(1−𝑚𝑎𝑥 (h (𝑝𝐴 ) , h (𝑝𝑃 ))) .𝜇𝑠𝑖𝑚 (𝑑 (𝑝𝐴 ,𝑝𝑃 ) )𝑑=(1−𝑚𝑎𝑥 (h (𝑝𝐴 ) , h (𝑝𝑃 ))) . (1−𝜇𝑠𝑖𝑚 (𝑑 (𝑝𝐴 ,𝑝𝑃 ) ))
h=1−𝑠−𝑑=𝑚𝑎𝑥 (h (𝑝𝐴 ) , h (𝑝𝑃 ))
match
Soft computing indecision support
Applications
The Project is co-financed by the European Union from resources of the European Social Fund
ear identificationbipolar approach
overall similarity
𝑠=(1−∑𝑖=1
𝑛
𝑚𝑎𝑥 (h (𝑝𝑖𝐴 ) , h (𝑝𝑖𝑃 ) )
𝑛 )∙∑𝑖=1
𝑛
𝜇𝑠𝑖𝑚 (𝑑 (𝑝𝑖𝐴 ,𝑝𝑖
𝑃 ) )𝑛
𝑑=(1−∑𝑖=1
𝑛
𝑚𝑎𝑥 (h(𝑝𝑖𝐴 ) , h (𝑝𝑖
𝑃 ) )𝑛 )∙ (1−∑
𝑖=1
𝑛
𝜇𝑠𝑖𝑚(𝑑 (𝑝𝑖𝐴 ,𝑝𝑖𝑃 ))
𝑛 )h=1−𝑠−𝑑=
∑𝑖=1
𝑛
𝑚𝑎𝑥 (h (𝑝𝑖𝐴 ) , h (𝑝𝑖
𝑃 ))𝑛
Soft computing indecision support
Applications
The Project is co-financed by the European Union from resources of the European Social Fund
ear identificationapproach
interpretationof results
each comparison i : (si,di)
satisfaction about matchingdissatisfaction about matching
hi = 1-si-di : overall hesitation about matching
ranking of the results:
top-k matching results
Questions?
Warsaw, June 22-26 2015
The Project is co-financed by the European Union from resources of the European Social Fund
Warsaw, June 22-26 2015
The Project is co-financed by the European Union from resources of the European Social Fund