Outline Soft computing in decision support LSP The different components of LSP Suitability vs....

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


J.J. Dujmović“Preference Logic for System Evaluation”IEEE Transactions on Fuzzy Systems 15 6 (2007) 1082-1099.

Logic Scoring of Preferences


LSP



mulitiple criteria decision making

cases

?

userpreferences

(multiple criteria)

select the best

score


LSP



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


LSP



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


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step 1: creation of the system attribute tree

array of elementary attributes


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step 2: definition of elementary criteria

array of elementary attributes

array of elementary criteria


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step 2: definition of elementary criteria (cont’d)

examples


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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


LSP



step 3: evaluation of elementary criteria (cont’d)

examples


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step 4: aggregation of elementary degrees of suitability

construction of a hierarchic preference aggregation structure that reflects the semantics of the attribute tree


LSP



step 4: aggregation of elementary degrees of suitability (cont’d)

building blocks

• simple aggregators• compound aggregators


LSP




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)


LSP




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


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• 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=+∞


LSP




• 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


LSP


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


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Logic Scoring of PreferencesGCD implemented as a weighted power mean

mandatory (all inputs must be satisfied)


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compound aggregators

• combining a mandatory with a desired input– conjunctive partial absorption

• combining a sufficient with a desired input– disjunctive partial absorption


LSP




conjunctive partial absorption


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conjunctive partial absorption ()

HPFddC+D+

C+A

annihilator 0 for mandatory input

P(enalty); R(eward)

P(enalty); R(eward)


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𝑥⊵𝑦=𝑤2∙𝑥 ∆́ (1−𝑤2 )∙ (𝑤1 ∙ 𝑥~𝛻 (1−𝑤1 ) ∙ 𝑦 )

where and


LSP





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


LSP




disjunctive partial absorption ()

D+C+

D+A

annihilator 0 for mandatory input

P(enalty); R(eward)

P(enalty); R(eward)


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disjunctive partial absorption ()

𝑥⊳ 𝑦=𝑤2∙𝑥 �́� (1−𝑤2 ) ∙(𝑤1 ∙𝑥~∆ (1−𝑤1 ) ∙ 𝑦 )

where and


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example


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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


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LSP




overall suitability E vs. global cost C

global quality Q

𝑄=𝐸𝐶 best suitability-cost tradeoff

minimal suitability and maximal cost

reject if or


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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


LSP




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


What can we learn from decision support?


what can we learn from decision support?




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.




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




there is a need for querying facilities tohandle mandatory and optional criteria




current querying facilities do not efficiently support complex data searches




query expressivity

• need for grouping and structuring preferences• need for generalizing and specializing preferences

criterion trees




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




query expressivity

aggregators GeneralisedConjunction

Disjunction(GCD)Ordered

Weighted

Average

(OWA)Yager

Dujmović

C DHPC HPDSPC SPD A




query expressivity

no more need for weight propagation!(because internal nodes have associated weights)

weighted aggregators




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




query expressivity

example

…




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)




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 )


Applications


some applications


Applications


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


Applications


LSP suitability mapsregular approach


Applications


LSP suitability mapsbipolar approach


Applications


the TILES projectTransnational and Integrated Long-term Marine

Exploitation Strategies


Applications


the TILES project


Applications


ear identification

Disaster Victim Identification• identification of human bodies• large scale disasters


Applications


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


Applications


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


Applications


ear identificationdata

=?

• victim: post mortem (PM) 3D ear picture• missing person: ante mortem (AM) 2D pictures


Applications


ear identificationchallenge

cope with poor picture quality of AM pictures


Applications


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


Applications



… …

AM ear

normalized 3D ear

ear detection

ear normalisation and enhancement


Applications



ear normalisationand enhancement

PM ear

normalized 3D ear

3D camera / 3D scanner


Applications



featureextraction

selecting n representative

points

LA=[p1A,…,pn

A]


Applications



earrecognition

comparing feature sets om 3D AM and

PM ear models

LA=[p1A,…,pn

A]

AM ear PM ear

LP=[p1P,…,pn

P]


Applications



earrecognition

comparing feature sets om 3D AM and

PM ear models

match

+ coping with imperfect data


Applications


ear identificationhesitation spheres


Applications


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 )


Applications


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)


Applications


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


Applications


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


Applications



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


Warsaw, June 22-26 2015


Outline Soft computing in decision support LSP The different components of LSP Suitability vs....

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