ELECTRE METHODS (PART I)

E LECTRE M ETHODS J.R. Figueira 1. Introduction 1.1. References

E LECTRE M ETHODS (PART I)

1.2. Constructivism 1.3. Notation

2. Main features 2.1. Preference situations 2.2. Preference modeling 2.3. Concordance and Discordance

José Rui F IGUEIRA ([email protected]) Technical University of Lisbon

2.4. Illustrative example 2.5. Structure

10th MCDM Summer School, Paris, France

Contents E LECTRE M ETHODS J.R. Figueira

1

1. Introduction 1.1. References 1.2. Constructivism 1.3. Notation

2

2. Main features 2.1. Preference situations 2.2. Preference modeling 2.3. Concordance and Discordance 2.4. Illustrative example 2.5. Structure



E LECTRE M ETHODS

Main references for this talk:

J.R. Figueira

1

Figueira, J., B. Roy, and V. Mousseau (2005). E LECTRE methods. In J. Figueira, S. Greco, and M. Ehrgott (Eds.), Multiple Criteria Decision Analysis: State of the Art Surveys, pp. 133162. New York, U.S.A.: Springer Science + Business Media, Inc.

2

´ Figueira, J.R., S. Greco, B. Roy, and R. Słowinski, (2010). E LECTRE methods: Main features and recent developments. In C. Zopounidis and P. Pardalos (Eds.), Handbook of Multicriteria Analysis, Chapter 4, New York, USA: Springer.

3

´ Greco, S., R. Słowinski, J.R. Figueira, and V. Mousseau (2010). Robust ordinal regression. In M. Ehrgott, J.R. Figueira, and S. Greco (Eds.), Trends in Multiple Criteria Decision Analysis, pp. 273320. New York, U.S.A.: Springer Science + Business Media, Inc.



1. Introduction 1.1. E LECTRE methods were designed according to a constructivist conception of MCDA: A decision aiding situation (Roy, 2009). E LECTRE M ETHODS J.R. Figueira 1. Introduction 1.1. References

A decision aiding situation 1

Imagine that in a company or institution, a CEO is confronted with a certain decision aiding situation and has to make a decision.

2

The CEO needs the help of an analyst (an in-house operational service, a consultant, or a university research team).

3

Two key elements in a decision aiding situation are: The Analyst and the Decision Maker (DM). The latter is here represented by the CEO.



1. Introduction 1.1. E LECTRE methods were designed according to a constructivist conception of MCDA: The fundamental pillars (Roy, 2009). E LECTRE M ETHODS J.R. Figueira

The decision aiding activity is based on three fundamental pillars:

1. Introduction 1.1. References 1.2. Constructivism

1

The actions (formal definition of the possible actions or alternatives).

2

The consequences (aspects, attributes, characteristics, . . . of the actions that allow to compare them).

3

The modeling of a preference system (it consists of an implicit or explicit process, that for each pair of actions envisioned, assigns one and only one of the three possibilities: indifference, preference, or incomparability).

1.3. Notation


1. Introduction. 1.1. E LECTRE methods were designed according to a constructivist conception of MCDA (Roy, 2009). E LECTRE M ETHODS J.R. Figueira 1. Introduction 1.1. References 1.2. Constructivism 1.3. Notation


Based on the above three pillars: 1. The analyst should try to obtain a coherent structured set of results in order to guide the decision aiding process and facilitate the communications about the decisions. 2. The analyst must follow an approach that leads or aims to produce knowledge from a certain number working hypotheses defined a priori. 3. This approach should be based on models that are, at least co-constructed interactively with the DM.

1. Introduction 1.1. E LECTRE methods were designed according to a constructivist conception of MCDA (Roy, 2009). E LECTRE M ETHODS J.R. Figueira 1. Introduction

Based on the above three pillars:

1.1. References 1.2. Constructivism 1.3. Notation

2. Main features 2.1. Preference situations

4. During the co-construction process, that takes into account the values of the DM, contradictory judgements or ambiguities may occur.

2.2. Preference modeling 2.3. Concordance and Discordance 2.4. Illustrative example 2.5. Structure

5. The analyst must admit that the novelty of these questions can bring (the DM) or the person this questioned to revise certain pre-existing preferences momentarily and locally.

1. Introduction 1.2. Notation: Basic data. E LECTRE M ETHODS

Basic data

J.R. Figueira

1

A = {a1 , a2 , . . . , ai , . . . , am } is the set of m potential actions. This set can be partially known a priori (it is frequent in sorting problems).

2

F = {g1 , g2 , . . . , gj , . . . , gn } is a coherent family of criteria, with n > 3.

3

gj (ai ) is the performance of action ai on criterion gj , for all ai ∈ A and gj ∈ F . A performance matrix M can thus be built.

4

Assume w.l.g. that the higher the performance gj (a) is, the better for the DM (increasing direction of preference).



2. Main features 2.1. Preferences situations. E LECTRE M ETHODS J.R. Figueira 1. Introduction

Four main comprehensive preference situations


1

I (Indifference)

2

P (strict preference)

3

Q (hesitation : weak preference)

4

R (incomparability).


(For more details see Figueira et al., 2010)

2. Main features 2.2. Preference modeling through outranking relations: The concept of pseudo-criterion (Roy, 1996). E LECTRE M ETHODS J.R. Figueira 1. Introduction 1.1. References 1.2. Constructivism

Pseudo-criterion

1.3. Notation


A pseudo-criterion is a function gj associated with two threshold functions, qj (·) and pj (·), satisfying the following condition: for all ordered pairs of actions (a, a′ ) ∈ A × A such that gj (a) > gj (a′ ), gj (a) + pj (gj (a′ )) and gj (a) + qj (gj (a′ )) are non-decreasing monotone functions of gj (a′ ), such that pj (gj (a′ )) > qj (gj (a′ )) > 0, for all a ∈ A.

2. Main features 2.2. Preference modeling through outranking relations: Partial binary relations. E LECTRE M ETHODS J.R. Figueira 1. Introduction 1.1. References 1.2. Constructivism 1.3. Notation

Partial binary relations (1)


1

gj (a) − gj (a′ ) > pj (gj (a′ )) ⇔ aPj a′ ,

2

qj (gj (a′ )) < gj (a) − gj (a′ ) 6 pj (gj (a′ )) ⇔ aQj a′ ,

3

−qj (gj (a)) 6 gj (a) − gj (a′ ) 6 qj (gj (a′ )) ⇔ aIj a′ .


2. Main features 2.2. Preference modeling through outranking relations: Partial binary relations. E LECTRE M ETHODS J.R. Figueira 1. Introduction

Partial binary relations (2)


1


2

2.2. Preference modeling

Sj = Pj ∪ Qj ∪ Ij aSj a′ means that “a is at least as good as a′ ” on criterion gj .

2.3. Concordance and Discordance 2.4. Illustrative example 2.5. Structure

3

When aSj a′ the voting power of criterion gj , denoted by wj is taken in total (assume w.l.g. that w1 + w2 + . . . + wn = 1).

2. Main features 2.2. Preference modeling through outranking relations: Comprehensive outranking. E LECTRE M ETHODS J.R. Figueira 1. Introduction 1.1. References 1.2. Constructivism 1.3. Notation

Let S = P ∪ Q ∪ I, whose meaning “is at least as good as”. Comprehensive outranking Consider two actions, a and a′ and the relation ≻= P ∪ Q. Four situations may occur:


1

2.2. Preference modeling 2.3. Concordance and Discordance 2.4. Illustrative example

2

2.5. Structure

3 4

aSa′ and not(a′ Sa), i.e., a ≻ a′ (a is preferred in a broader sense to a′ ). a′ Sa and not(aSa′ ), i.e., a′ ≻ a (a′ is preferred in a broader sense to a). aSa′ and a′ Sa, i.e., aIa′ (a is indifferent to a′ ). not(aSa′) and not(a′ Sa), i.e., aRa′ (a is incomparable to a′ ).

2. Main features 2.3. Concordance and Discordance: Concordance. E LECTRE M ETHODS

Concordance

J.R. Figueira

1 1. Introduction 1.1. References

Concordance. To validate aSa′ , a sufficient majority of criteria in favor of this assertion must occur.



2

The comprehensive concordance index c(a, a′ ) for each pair of actions (a, a′ ) ∈ A × A, for all gj ∈ F is fundamental to all the E LECTRE methods in order to compute a concordance matrix C. X X c(a, a′ ) = wj + wj ϕj {j | gj ∈C(a{P,Q,I}a′ })

where ϕj =

{j | gj ∈C(a′ Qa)}

gj (a) − gj (a′ ) + pj pj − qj

2. Main features 2.3. Concordance and Discordance: Voting power. E LECTRE M ETHODS J.R. Figueira 1. Introduction 1.1. References 1.2. Constructivism

Voting power

1.3. Notation


This index comprises the summation of the voting power of the criteria that clearly are in favor of the assertion aSa′ , plus the summation of the fraction, ϕj , of the voting power for those criteria included in the hesitation group.

2. Main features. 2.3. Concordance and Discordance: Graphical representation. E LECTRE M ETHODS J.R. Figueira

ϕj


2. Main features

1

2.1. Preference situations 2.2. Preference modeling 2.3. Concordance and Discordance 2.4. Illustrative example 2.5. Structure

0 gj (a′ ) − pj (gj (a))

gj (a′ ) ′

gj (a ) − qj (gj (a))

gj (a′ ) + pj (gj (a′ )) ′

′

gj (a ) + qj (gj (a ))

Figure: Variation of ϕj for a given gj (a′ ) and variable gj (a)

gj (a)

2. Main features 2.3.Concordance and Discordance: Discordance (1) E LECTRE M ETHODS

Discordance

J.R. Figueira

1 1. Introduction 1.1. References

Discordance. The assertion aSa′ cannot be validated if a minority of criteria is strongly against this assertions.


2. Main features

2

The concept of veto threshold, vj , gives the possibility to the criterion gj to impose its veto power. It means that gj (a′ ) is so much better than gj (a), that is not possible to allow that aSa′

3

The computation of the partial discordance indices leads to the construction of a discordance matrix, D.

4

The application of both types of indices is related to a specific E LECTRE method. For example, in E LECTRE T RI they are “combined” with c(a, a′ ) to define a degree of credibility of the assertion aSa′ (fuzzy relation).

2.1. Preference situations 2.2. Preference modeling 2.3. Concordance and Discordance 2.4. Illustrative example 2.5. Structure

2. Main features 2.3. Concordance and Discordance: Discordance (2) E LECTRE M ETHODS J.R. Figueira 1. Introduction 1.1. References 1.2. Constructivism 1.3. Notation

Partial discordance index


′

dj (a, a ) =

8 > < 1

if gj (a) − gj (a′ ) < −vj (gj (a)),

gj (a)−gj (a′ )+pj (gj (a)) pj (gj (a)) − vj (gj (a))

if −vj (gj (a)) 6 gj (a) − gj (a′ ) < −pj (gj (a)),

0

if gj (a) − gj (a′ ) > −pj (gj (a)).

> :

2. Main features 2.4. Reminder and additional notation E LECTRE M ETHODS J.R. Figueira 1. Introduction 1.1. References

Reminder and additional notation 1

1.2. Constructivism

- C(aSa′ ) is the coalition of criteria in favor of the assertion aSa′ . X - W {C(aSa′ }) = wj is the weight or power of

1.3. Notation

2. Main features 2.1. Preference situations 2.2. Preference modeling

{j : gj ∈C(aSa′ )} ′

the coalition C(aSa ).


We use kj as the non-normalized weights for each criterion)

2

qj (·) is the indifference threshold of criterion gj .

3

pj (·) is the preference threshold of criterion gj .

4

vj (·) is a veto threshold of criterion gj .

2. Main features 2.4. Location of a new hotel (Figueira et al., 2009) (1) E LECTRE M ETHODS

Location of a new hotel

J.R. Figueira

1

Matrix below presents the performances of the five sites - a, b, c, d, and e - according to the five criteria.

2

The performances of criterion g1 (investment costs) are expressed in thousands of e, designated Ke.

3

The indifference and the preference thresholds assigned to this criterion are q1 (g1 (x )) = 500 + 0.03g1 (x ) Ke and p1 (g1 (x )) = 1000 + 0.05g1 (x ) Ke, respectively, where x is the worst of the two actions.

4

The performances of criterion g2 (annual costs) are also expressed in Ke; the thresholds assigned to this criterion are q2 (g1 (x )) = 50 + 0.05g1 (x ) Ke and p2 (g1 (x )) = 100 + 0.07g1 (x ) Ke, respectively.



2. Main features 2.4. Location of a new hotel (Figueira et al., 2009) (2) E LECTRE M ETHODS

Location of a new hotel

J.R. Figueira

1

The performances of criteria g3 (recruitment), g4 (image), and g5 (access) are expressed on the following seven-level qualitative scale: very bad (1), bad (2), rather bad (3), average (5), rather good (5), good (6), and very good (7). The values between parenthesis can be used in E LECTRE methods to code the different verbal statements.

2

Other ways of coding the verbal scale through the use of numerical values could be used by adjusting the thresholds values (see Martel and Roy, 2006).

3

The indifference threshold for each criterion has been set at one on the seven-level scale and the preference threshold at two levels.

4

In this example there is no veto.



2. Main features 2.4. Performances matrix (Figueira et al., 2009) E LECTRE M ETHODS

Performances matrix

J.R. Figueira 1. Introduction

1

Quantitative criteria: g1 (investment costs) and g2 (annual costs)

2

Qualitative criteria: g3 (recruitment), g4 (image), and g5 (access)



a b c d e kj

g1 [min] 13 000 Ke 15 000 Ke 10 900 Ke 15 500 Ke 15 000 Ke 5

g2 [min] 3 000 Ke 2 500 Ke 3 400 Ke 3 500 Ke 2 600 Ke 4

g3 [max] Average Good Good Good Good 3

g4 [max] Average Bad Good Good Very Bad 3

g5 [max] Average Very Good Very Bad Good Bad 3

2. Main features 2.4. Pairwise comparison E LECTRE M ETHODS J.R. Figueira

Pairwise comparison 1. Introduction 1.1. References 1.2. Constructivism 1.3. Notation

1

Does a outrank d , aSd ? For the moment we cannot answer this question.

2

The coalition of criteria in favor of aSd : C(aSd ) = {g1 , g2 }

3

The power of this coalition: W {C(aSd )} = (normalized)

4

What about dSa?


4+5 18

= 0.5

2. Main features. 2.5. The structure of E LECTRE methods. E LECTRE M ETHODS

Each E LECTRE method comprises two main procedures:

J.R. Figueira

Two procedures 1. Introduction 1.1. References 1.2. Constructivism 1.3. Notation

1

The first procedure is a Multiple Criteria Aggregation Procedure (MCAP) that builds one or possibly several outranking relations aim to compare, in a comprehensive way, each ordered pair of actions.

2

The second procedure, called Exploitation Procedure (EP) is used to obtain adequate results from which recommendations can be derived.

3

The nature of the results depends of the specific problematique.


2. Main features. 2.5. Example: MCAP of E LECTRE III E LECTRE M ETHODS J.R. Figueira 1. Introduction 1.1. References 1.2. Constructivism 1.3. Notation


MCAP of E LECTRE III It is modeled through a credibility index i.e. a fuzzy measure denoted by σ(a, a′ ) ∈ [0, 1], which combines c(a, a′ ) and dj (a, a′ ):


σ(a, a′ ) = c(a, a′ )

Y j∈J (a,a′ )

1 − dj (a, a′ ) , 1 − c(a, a′ )

where j ∈ J (a, a′ ) if and only if dj (a, a′ ) > c(a, a′ ).

2. Main features 2.5. The nature of the results: Choosing (Mousseau, 1993; Roy, 2002). E LECTRE M ETHODS J.R. Figueira 1. Introduction 1.1. References 1.2. Constructivism 1.3. Notation


Choosing: Selecting a restricted number as small as possible of potential actions, which justify to eliminating others.

2. Main features 2.5. The nature of the results: Choosing (Mousseau, 1993; Roy, 2002). E LECTRE M ETHODS J.R. Figueira 1. Introduction 1.1. References 1.2. Constructivism 1.3. Notation


Choosing: Selecting a restricted number as small as possible of potential actions, which justify to eliminating all others.

2. Main features 2.5. The nature of the results: Choosing (Mousseau, 1993; Roy, 2002). E LECTRE M ETHODS J.R. Figueira 1. Introduction

Choosing: Selecting a restricted number as small as possible of potential actions, which justify to eliminating all others. Choice set



Actions rejected

2. Main features 2.5. The nature of the results: Ranking (Mousseau, 1993; Roy, 2002). E LECTRE M ETHODS J.R. Figueira 1. Introduction 1.1. References 1.2. Constructivism 1.3. Notation


Ranking: Ranking of actions from the best to the worst, with the of ties (ex aequo) and incomparabilities.

E LECTRE M ETHODS J.R. Figueira 1. Introduction 1.1. References 1.2. Constructivism 1.3. Notation


Ranking: Ranking of actions from the best to the worst, with the of ties (ex aequo) and incomparabilities.

2. Main features 2.5. The nature of the results: Sorting (Mousseau, 1993; Roy, 2002). E LECTRE M ETHODS J.R. Figueira 1. Introduction 1.1. References 1.2. Constructivism 1.3. Notation


Ordinal classification or sorting: Assigning each potential action to one of the categories among those of a family previously defined; the categories are ordered, in general, from the worst to the best one.

2. Main features 2.5. The nature of the results: Sorting (Mousseau, 1993; Roy, 2002). E LECTRE M ETHODS J.R. Figueira 1. Introduction 1.1. References



2. Main features

Category 1

2.1. Preference situations 2.2. Preference modeling 2.3. Concordance and Discordance 2.4. Illustrative example

Category 2

2.5. Structure

.. .

Category k

2. Main features 2.5. The nature of the results: Sorting (Mousseau, 1993; Roy, 2002). E LECTRE M ETHODS J.R. Figueira 1. Introduction 1.1. References



2. Main features

Cat. 1

2.1. Preference situations 2.2. Preference modeling 2.3. Concordance and Discordance

Cat. 2


.. .

Cat. k

2. Main features 2.5. The nature of the results: Absolute versus relative evaluation (Roy, 1996). E LECTRE M ETHODS J.R. Figueira 1. Introduction 1.1. References 1.2. Constructivism 1.3. Notation

2. Main features 2.1. Preference situations 2.2. Preference modeling

In sorting problems there is an absolute evaluation: the assignment of an action only takes into account the intrinsic evaluation of this action on all the criteria and does not depend on nor influence the category to which another action should be assigned.


As for the remaining problematiques the actions are compared against each other and thus there exists a relative evaluation instead of an absolute evaluation as for the previous case.

2. Main features. 2.6. Software (Figueira et al., 2005). E LECTRE M ETHODS J.R. Figueira 1. Introduction 1.1. References 1.2. Constructivism 1.3. Notation


Choosing: E LECTRE I, E LECTRE I V, and E LECTRE IS. Ranking: E LECTRE II, E LECTRE III, and E LECTRE IV.

2.2. Preference modeling 2.3. Concordance and Discordance

Ordinal classification or sorting: E LECTRE T RI.


New software (see later on).

E LECTRE M ETHODS J.R. Figueira 2. Main features

E LECTRE M ETHODS (PART II)

2.6. Strong features 2.7. Weaknesses

José Rui F IGUEIRA ([email protected]) Technical University of Lisbon 10th MCDM Summer School, Paris, France

Contents E LECTRE M ETHODS J.R. Figueira 2. Main features 2.6. Strong features 2.7. Weaknesses

1

2. Main features 2.6. Strong features 2.7. Weaknesses

2. Main features Introduction E LECTRE M ETHODS J.R. Figueira 2. Main features

Summary


1

The qualitative nature of some criteria

2

The heterogeneity of scales

3

The non-relevance of compensatory effects

4

The imperfect knowledge and arbitrariness

5

The reasons for and reasons against and outranking

2. Main features 2.6. Some strong features of E LECTRE methods E LECTRE M ETHODS

Strong features

J.R. Figueira 2. Main features 2.6. Strong features 2.7. Weaknesses

1. They have the possibility of taking into account the qualitative nature of some criteria. They allow thus to consider the original data. 2. They can deal with very heterogeneous scales to model noisy, delay, aesthetics, cost, . . . Whatever the nature of scales, every procedure can run by preserving the original performances of the actions. 3. The compensatory effects are not pertinent. This is due to the fact that the weights cannot be interpreted as substitution rates. Contrarily to other methods there is no need in E LECTRE methods to use, from the starting point of their application, identical and commensurable scales.

2. Main features 2.6. Some strong features of E LECTRE methods E LECTRE M ETHODS J.R. Figueira 2. Main features 2.6. Strong features 2.7. Weaknesses

Strong features Consider the following example with 4 criteria and only 2 actions (scales:P [0,10]). The weighted-sum model was chosen, i.e, n V (a) = j=1 wj gj (a). In the considered example, the weights, wj , are equal for all criteria: g1 g2 g3 g4 a1 9.5 9.5 8.1 5.4 a2 8.3 8.3 7.3 8.5 V (a1 ) = 8.125 > V (a2 ) = 8.100. This example shows, in an obvious way, the possibility that a big preference difference not favorable to a1 on one of the criteria (g4 ) can be compensated by 3 differences of weak amplitude on the remaining criteria, in such a way that a1 becomes finally preferred to a2 . In E LECTRE methods this effect does not occurs in a systematic way.

2. Main features 2.6. Some strong features of E LECTRE methods E LECTRE M ETHODS J.R. Figueira 2. Main features 2.6. Strong features 2.7. Weaknesses

Strong features 4. They are adequate to take the imperfect knowledge of the data and the arbitrariness related to the construction of the criteria. This is modeled through the indifference and preference thresholds. Consider the same example with the following (constant) discrimination thresholds:

a1 a2 qj pj

g1 9.5 8.3 1 2

g2 9.5 8.3 1 2

g3 8.1 7.3 1 2

g4 5.4 8.5 1 2


Strong features


If on criterion g3 we change the performance from 7.3 to 7.1, the score moves from 8.100 to 8.050 (V (a1 ) − V (a2 ) = 0.050). Consequently there is a reinforcement of the preference in favor of a1 . On the other hand, with E LECTRE c(a1 , a2 ) and c(a2 , a1 ) remain unchanged. Now, if we consider 7.5 instead of 7.3, then V (a2 ) = 8.150, and consequently a2 Pa1 . Again this small variation is too small. When adding the discrimination thresholds and using E LECTRE methods, c(a1 , a2 ) = 0.25 + 0.25 + 0.25 = 0.75 and c(a2 , a1 ) = 0.2 + 0.2 + 0.25 + 0.25 = 0.8. Thus, a2 Pa1 .


Strong features


5. They are based in a certain sense in the reasons for and the reasons against of an outranking between two actions (concordance and discordance). Consider the same example and that a veto threshold should vj = 3, for all j = 1, . . . , 4. g1 g2 g3 g4 a1 9.5 9.5 8.1 5.4 a2 8.3 8.3 7.3 8.5 qj 1 1 1 1 pj 2 2 2 2 vj 3 3 3 3 If s = 0.8 then a2 Sa1 and not(a2 Sa1 ). But, if s = 0.7, a1 Ia2 . Since d4 (a2 , a1 ) = 1, g4 imposes a veto, for whatever the chosen s. We get allays not(a2 Sa1 ).

2.7. Weaknesses Introduction E LECTRE M ETHODS J.R. Figueira 2. Main features

Summary


1

Scoring actions

2

The quantitative nature of family of criteria

3

The independence with respect to irrelevant alternatives

4

The intransitivities

2. Main features 2.7. Some weaknesses of E LECTRE methods E LECTRE M ETHODS J.R. Figueira 2. Main features 2.6. Strong features 2.7. Weaknesses

Some weaknesses 1. Scoring the actions. In certain contexts it is required to assign a score to each action. When the decision makers require each action should appear associated with a score, the E LECTRE methods are not adequate for such a purpose and the scoring based methods should be applied instead. The decision makers should be, however, aware that they cannot provide information that leads, for example, to intransitivities or to incomparabilities between certain pairs of actions. Indeed, this score is very fragile.

2. Main features 2.7. Some weaknesses of E LECTRE methods E LECTRE M ETHODS J.R. Figueira 2. Main features

Some weaknesses


2. The quantitative nature of the family of criteria. When all the criteria are quantitative it is “better” to use other methods. But, if we want to take into account a completely or even a partial noncompensatory method, the reasons for and against, or the imperfect character of at least one criterion, even under such conditions, we can use the E LECTRE methods.

2. Main features 2.7. Some weaknesses of E LECTRE methods E LECTRE M ETHODS

Some weaknesses


3. The independence with respect to irrelevant alternatives. Except E LECTRE T RI -B, T RI -C, the remaining E LECTRE methods does not fulfill the independence w.r.t. irrelevant alternatives (Roy, 1973). In 1973, B. Roy shows that rank reversal may occur and consequently the property of independence with respect to irrelevant alternatives can be violated when dealing with outranking relations. Notice that rank reversal may occur only when the set of potential actions is subject to evolve, which is quite a natural assumption, but one that is not present in many hard decision-aiding processes where the number of alternatives is rather small and easily identified.

2. Main features 2.7. Some weaknesses of E LECTRE methods E LECTRE M ETHODS J.R. Figueira 2. Main features

Some weaknesses


4. Intransitivities may also occur in E LECTRE methods (Roy, 1973). It is also well-known that methods using outranking relations (not only the E LECTRE methods) do not need to fulfill the transitivity property. This aspect represents only a weakness if we impose a priori that preferences should be transitive. There are, however, some raisons that lead us to do not impose transitivity.

E LECTRE M ETHODS J.R. Figueira 3. Some recent developments (>2000)

E LECTRE M ETHODS (PART III)

3.1. Methodological 3.2. New approaches 3.3. Axiomatic and meaningfulness analysis

José Rui F IGUEIRA ([email protected])

3.4. Other aspects

4. Applications 4.1. Some applications areas 4.2. Real-world applications

5. Concluding remarks

Technical University of Lisbon 10th MCDM Summer School, Paris, France

Contents E LECTRE M ETHODS J.R. Figueira

1

3. Some recent developments (>2000) 3.1. Methodological 3.2. New approaches 3.3. Axiomatic and meaningfulness analysis 3.4. Other aspects

2


3


3. Some recent developments (>2000) 3.1. Methodological 3.2. New approaches 3.3. Axiomatic and meaningfulness analysis 3.4. Other aspects



3. Some recent developments (>2000) 3.1. Methodological (1) E LECTRE M ETHODS

Recent developments

J.R. Figueira 3. Some recent developments (>2000)

1 Pure inference based approaches after the work by ´ Mousseau and Słowinski (1998) (Software: E LECTRE T RI-Assistant):

3.1. Methodological 3.2. New approaches 3.3. Axiomatic and meaningfulness analysis 3.4. Other aspects



inferring only the weights (Mousseau et al, 2001); inferring veto (Mousseau and Dias, 2006); and, inferring category bounds (Ngo The and Mousseau, 2002). Some manageable disaggregation procedures for valued outranking relations (Mouuseau and Dias, 2006); Inconsistent judgements (Mousseau et al., 2006a; Mousseau et al., 2006b) or an inadequate preference model (Figueira, 2009).

3. Some recent developments (>2000) 3.1. Methodological (2) E LECTRE M ETHODS J.R. Figueira 3. Some recent developments (>2000) 3.1. Methodological 3.2. New approaches 3.3. Axiomatic and meaningfulness analysis 3.4. Other aspects



Recent developments 2 The inference-robustness based approach for inferring weights and derive robust conclusions in sorting problems (Dias et al., 2002). Software: IRIS. 3 The pseudo-robustness based approach dealing with simulation methods mainly for ranking and sorting problems (Tervonen et al., 2008, 2009). Software: SMAA-III, SMAA-TRI. 4 New robustness analysis concepts (Aissi and Roy, 2009; Roy, 2009). These papers are more general, but some techniques can be applied to E LECTRE methods.

3. Some recent developments (>2000) 3.2. New approaches E LECTRE M ETHODS

New approaches

J.R. Figueira 3. Some recent developments (>2000) 3.1. Methodological 3.2. New approaches

1

Bi-polar outranking relations implemented in RUBIS software (Bisdorff et al., 2007, 2008).

2

The weights of the interaction coefficients and the modifications in the concordance index (Figueira et al., 2009).

3

Handling with the reinforced preference and the counter-veto ´ effects (Roy and Słowinski, 2009).

4

E LECTRE T RI -C, T RIN , N C (Almeida-Dias et al., 2010a, 2010b).

5

The possible and the necessary approach for E LECTRE methods (E LECTRE -GKMS) by Greco et al., (2009, 2010).

3.3. Axiomatic and meaningfulness analysis 3.4. Other aspects



3. Some recent developments (>2000) 3.3 Axiomatic and meaningfulness E LECTRE M ETHODS

Axiomatic and meaningfulness

J.R. Figueira 3. Some recent developments (>2000) 3.1. Methodological

1

Axiomatic analysis of E LECTRE I method by using conjoint measurement theory (Greco et al., 2001).

2

Representing preferences through conjoint measure and the decision rule approach (Greco et al., 2002).

3

An axiomatic analysis based on a general conjoint measure framework with application to a variant of E LECTRE T RI (Bouyssou and Marchant, 2007a,b).

4

An axiomatic analysis of the concordance-discordance relations (Bouyssou and Pirlot, 2009).

5

Representing preferences by decision rules (Greco et al., 2002).

6

The meaningfulness of E LECTRE methods (Martel and Roy, 2006).

3.2. New approaches 3.3. Axiomatic and meaningfulness analysis 3.4. Other aspects



3. Some recent developments (>2000). 3.4 Other aspects E LECTRE M ETHODS

Other aspects

J.R. Figueira 3. Some recent developments (>2000) 3.1. Methodological 3.2. New approaches 3.3. Axiomatic and meaningfulness analysis 3.4. Other aspects

4. Applications

1 The relative importance of criteria (Figueira and Roy, 2002). 2 Concordant outranking with criteria of ordinal significance (Bisdorff, 2004). 3 Evolutionary approaches (Leyva-López et al., 2008; Doumpos et al., 2009).

4.1. Some applications areas 4.2. Real-world applications


4 The E PISSURE method for the assessment of non-financial performances (André and Roy, 2007; André, 2009). 5 Group decision aiding (Damart et al., 2007; Greco et al., 2009, 2010).

4. Applications 4.1. Some applications areas E LECTRE M ETHODS

Areas


1

Agriculture and Forest Management.

2

Energy.

3

Environment and Water Management.

4

Finance.

5

Medicine.

6

Military.

7

Project selection (call for tenders).

8

Transportation.

9

...




4. Applications 4.2. Concrete cases (1) E LECTRE M ETHODS J.R. Figueira 3. Some recent developments (>2000)

Areas Sorting cropping systems (Arondel and Girardin, 2000).




Land-use suitability assessment (Joerin et al., 2001). Greenhouse gases emission reduction (Georgopoulou, 2003). Risk zoning of an area subjected to mining-inducing hazards (Merad et al., 2004). Participatory decision-making on the localization of waste-treatment plants (Norese, 2006).

4. Applications 4.2. Concrete cases (1) E LECTRE M ETHODS

Areas

J.R. Figueira 3. Some recent developments (>2000) 3.1. Methodological

Material selection of bipolar plates for polymer electrolyte membrane fuel cell (Shanian and Savadogo).

3.2. New approaches 3.3. Axiomatic and meaningfulness analysis

Assisted reproductive technology (Matias, 2008).

3.4. Other aspects



Promotion of social and economic development (Autran-Gomes et al., 2009). Sustainable demolition waste management strategy (Roussat et al., 2009). Assessing the risk of nano-materials (Tervonen et al., 2009).

5. Concluding remarks E LECTRE M ETHODS

Concluding remarks


1

E LECTRE methods have a long history of successful real-world applications with impact on the life of populations (see Figueira et al., 2005)).

2

When applying E LECTRE methods analysts should pay attention to the characteristics of the context and also to the (theoretical) weaknesses of these methods. Note that all the MCDA methods have theoretical limitations.

3

Software implementations of high quality along with friendly interfaces render possible the application to a vast range of applications.

4

Research on E LECTRE methods is not a death field. It stills evolving and rapidly, namely over of the first years of this new millennium.




E LECTRE M ETHODS J.R. Figueira 3. Some recent developments (>2000) 3.1. Methodological 3.2. New approaches 3.3. Axiomatic and meaningfulness analysis 3.4. Other aspects



Thank You! (very much for your attention)

ELECTRE METHODS (PART I)

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