1 Sorting Problems and Electre Methods
-
Upload
hieu-tran-trung -
Category
Documents
-
view
232 -
download
0
Transcript of 1 Sorting Problems and Electre Methods
-
8/17/2019 1 Sorting Problems and Electre Methods
1/25
Sorting problem statementor ‘problematic’
A(t)
A referencemodel
A can be an evolutive set, A(t)
The actions are uncomparable and each action has to be consideredindipendently from the others and its intrinsic value has to be
defined
The DM needs more
guarantees on the quality of an
action.a absolute versus relative
judgement
Several possible issues
A(t)
-
8/17/2019 1 Sorting Problems and Electre Methods
2/25
ELECTRE and the problematic
Eight criteria, the evaluations of a1 on the criteria (profile of
a1 ), the evaluation profile of a positive reference action
(i.e. the acceptability condition) (- - - -)
Is a1 acceptable?
a1
ar
-
8/17/2019 1 Sorting Problems and Electre Methods
3/25
And is this action acceptable?
ELECTRE and the problematic
-
8/17/2019 1 Sorting Problems and Electre Methods
4/25
Bipolar reference
Absolute acceptability (ra) Absolute refutability (rr)
a1
-
8/17/2019 1 Sorting Problems and Electre Methods
5/25
Bipolar reference
a2
Absolute acceptability (ra) Absolute refutability (rr)
-
8/17/2019 1 Sorting Problems and Electre Methods
6/25
Bipolar reference
a3
Absolute acceptability (ra) Absolute refutability (rr)
-
8/17/2019 1 Sorting Problems and Electre Methods
7/25
Bipolar reference
ra
rr
a1
a1S rr a1S ra rr S a1 ra S a1
-
8/17/2019 1 Sorting Problems and Electre Methods
8/25
Processes and problem situations in which
actions have to be assigned to specific categories
Project selection, evaluation of applicants for loans
or grants, medical diagnosis, ...Risk assessment and management (in financial
ambits – e.g. business failure risk, in enterprise
risk management, in relation to the environmentand the territory problems, ...)
Management processes (maintenance problems,
supplier control, client management, monitoring,human resources, ... )
-
8/17/2019 1 Sorting Problems and Electre Methods
9/25
Structure of the methods ELECTRE
for the sorting ptoblems• Input: a finite set A or an evolutive one A(t), F, R = , p j
• Phase O: definition of the assignment rules (structure andcategory number, nature of R - the reference set -, rules toassign the candidates to the categories), preference
modeling, calibration of the parameters and R validation• Phase I: Outranking model (to compare (a,r) and (r,a))
• Phase II: application of the rules to assign the candidates to
the categories
• Result analysis
r
-
8/17/2019 1 Sorting Problems and Electre Methods
10/25
The trichotomic segmentation method with
a multi-profile intersecting reference set
• Input: A(t), F, R = , p j
• Phase O: preference and assignment rules modeling,
verification of the reference set consistency andcalibration of the parameters
• Phase I: Outranking model of ELECTRE II or I
• Phase II: application of the rules to assign thecandidates to the categories of Accetable or Refutable
• Result analysis
BUC
-
8/17/2019 1 Sorting Problems and Electre Methods
11/25
Bipolar reference
rarr
a1
a1S rr a1S ra rr S a1 ra S a1
-
8/17/2019 1 Sorting Problems and Electre Methods
12/25
Multiple not hierarchical references: a trichotomic
segmentation method with a multi-profile intersecting
reference set
(C)(B1 e B2)
an
Absolute acceptability Absolute refutability
-
8/17/2019 1 Sorting Problems and Electre Methods
13/25
Phase II: decision situations and rules for a
bipolar reference
a5
cb
a3
cb
a2
cba1
cb
cba4
ca6b
ca7b
ca8b
b ca11
ca9b
ca10b cba12
-
8/17/2019 1 Sorting Problems and Electre Methods
14/25
δ(a, a’) b1 b2 c1 c2 c3
b1 - 0,14 0,90 0,87 0,45
b2 0 - 0,81 0,70 1
c1 0 0,67 - 0,19 0,71
c2 0,46 0,66 0,42 - 0,70c3 0,58 0,54 0,67 0,41 -
c2
c1
c3
b1
b2
Thresholdδ*= 0.65
Verification of the reference set (R) consistency
-
8/17/2019 1 Sorting Problems and Electre Methods
15/25
Trichotomic segmentation method with a
multi-profile intersecting reference setPhase II: 4 situations
a1
c1b1
c2
c3
b2
a1c1b1
c2
c3
b2
a1c1
b1
c2
c3b2
a1c1
b1
c2
c3
b2
-
8/17/2019 1 Sorting Problems and Electre Methods
16/25
Phase II: applications of the
assignment rules
a1c1b1
c2
c3
b2
a1c1b1
c2
c3
b2
a1c1
b1
c2
c3
b2
a1c1
b1
c2
c3
b2
-
8/17/2019 1 Sorting Problems and Electre Methods
17/25
Multiple hierarchical reference
Categories of sequential assignment for the candidate actions(in terms of risk, urgency,adequacy,..........)
C1
C2
C3
C4
C5
am
-
8/17/2019 1 Sorting Problems and Electre Methods
18/25
Category but also strategy of action which is associated to the category, inrelation to a specific activity (of monitoring and control, design, activation of
new processes,....)
C1
C2
C3
C4
C5
ELECTRE TRI: a sorting method with a multiple
hierarchical reference set
Reference profiles (i.e. combinations of values on the family of
criteria) which represent the theoretical limits between the categories
C j
-
8/17/2019 1 Sorting Problems and Electre Methods
19/25
ELECTRE Tri: a sorting method with a multiple
hierarchical reference set
• Input: A(t), F, R = , p j
• Phase O: preference and assignment rules modeling,
calibration of the parameters (ELECTRE TriAssistant)
• Phase I: Outranking model of ELECTRE III
• Phase II: the pessimistic (or conjunctive) assignment procedure and the optimistic (or disjunctive) one toassign the candidates to the sequential categories
• Result analysis
r
-
8/17/2019 1 Sorting Problems and Electre Methods
20/25
Ordered categories defined by limit profiles
b b b b b
C C C
g
g
. . .
1
g2
n
0 1 2 k-1 k
1 2 k
g3
-
8/17/2019 1 Sorting Problems and Electre Methods
21/25
Imprecision, uncertainty and ill determination of the data
require discrimination thresholds that identify the limitsbetween situations of indifference and strict preference
b b b b b
C C C
g
g
. . .
1
g2
n
0 1 2 k-1 k
1 2 k
g3
-
8/17/2019 1 Sorting Problems and Electre Methods
22/25
Partial concordance index c j(a,b)
1
g(b) (b)(b) (b) (b)p q
c
g g
g
j j
- j
- j j
j
j
(a, b)
(a)
Direction of preference
-
8/17/2019 1 Sorting Problems and Electre Methods
23/25
1
g(b)(b) (b)(b)(b) pq
c
ggg
j j
+ j
+ j j
j
j
(b, a)
(a)
Direction of preference
-
8/17/2019 1 Sorting Problems and Electre Methods
24/25
1
g(b)(b) (b)(b) (b) pg gg
j j j j j
j
j(a)
Senso di preferenza(a, b)D
- v -
1
g(b) (b) (b) (b)(b) pg g g j j j j j
j
j(a)
Senso di preferenza
D (b, a)
+ v+
-
8/17/2019 1 Sorting Problems and Electre Methods
25/25
Phase II: example
Degrees of credibility of the outranking relation
σs(ai,b1) σs(b1,ai) σs(ai,b2) σs(b2,ai) σs(ai,b3) σs(b3,ai)
a1 0.70 0.50 0.56 0.75 0.21 0.81
a2 0.95 0.32 0.65 0.70 0.29 0.98
bmin b1 b2 b3 bmax|-----------|--------|--------|----------|
C1
C2
C3
C4
Cuting level λ = 0.60
a1 - pessimistic procedure
a1 /Sb3 (a1 does not outrank b3)
a1 /Sb2a1Sb1Then a1∈C2
a1 - optimistic procedure
b1 / a1 (b1 is not preferred to a1)b2 a1Then a1 C2