Enriching descriptive information in ranking and sorting problems with visualizations techniques

[Pre-print version] please cite as: Ph. Nemery, A. Ishizaka, M. Camargo and L. Morel, Enriching descriptive

Information in ranking and sorting problems with visualizations techniques, Journal of Modelling in Management, 7(2), 130-147, 2012

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Enriching descriptive Information in ranking and sorting problems with visualizations techniques

Ph. Nemery1, A. Ishizaka2, M. Camargo3 and L. Morel3

1 Department of Mathematics, University of Portsmouth, Lion Gate Building, Lion Terrace,

PO1 3HF Portsmouth, United Kingdom, [email protected] 2 Portsmouth Business School, University of Portsmouth, Richmond Building, Portland Street,

PO1 3DE Portsmouth, United Kingdom, [email protected] 3 ERPI, University of Nancy, Rue Bastien Lepage 8, 54010 Nancy Cedex, France,

[email protected]; [email protected]

Abstract

Purpose: Most of the proposed decision aid methods provide the user only with a prescriptive approach (quantitative analysis) without any descriptive approach (qualitative analysis). It is therefore not possible to justify and recommend way of improvements. In this paper, we introduce visualization techniques to complement prescriptive approaches.

Design/methodology/approach: Visual techniques have been developed for the FlowSort sorting method, namely the FS-GAIA and stacked bar diagrams.

Findings With visual techniques, fine details can be captured, e.g. detection of incomparability (with FS-GAIA) and the composition of a score (with stacked bar diagrams).

Research limitations/implications It is expected that, in the future, other multi-criteria decision methods will be complemented by prescriptive approaches.

Practical implications A real case study is introduced in order to illustrate the practicality of the visual techniques. In this paper, the innovation performances of small and medium enterprises from the French Lorraine region are assessed.

Social implications It is expected that the quality of the decisions taken are improved because better informed.

Originality/value The paper provides important new tools to enhance the quality of the decisions. A real case study has been used to shown the added value of these visual techniques. Keywords: Multicriteria Decision Aid, Sorting, Classification, Information Visualisation, GAIA, PROMETHEE, FlowSort



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1. Introduction Companies grow, prosper or fail as consequence of the decisions taken by their management and stakeholders. Decision making is therefore a vital contributor to the success of enterprises and administrations. Several multiple criteria decision making methods have been developed to help managers for ranking (Figueira et al. 2005) and sorting (M Doumpos and C Zopounidis 2002) problems. However, these methods provide often only a raw quantitative result (a ranking or a sorting) in a normative approach without any qualitative analysis to understand the structure of the results. It is therefore difficult to justify a decision and moreover to recommend ways of improvement. PROMETHEE is probably the unique ranking method that has been complemented with a descriptive method: the GAIA method (Brans and Mareschal 1994). However, to the best of our knowledge, no descriptive approach has been proposed in a sorting problem. The aim of this paper is thus to propose a descriptive approach which permits a decision maker to gain insight in a multicriteria sorting problem. Since the FlowSort sorting method is based on the PROMETHEE method, we extend the GAIA visualizations to this sorting method. These extensions lead to the FS-GAIA descriptive approach which inherits of the same features as the GAIA method. In particular, the FS-GAIA permits to detect easily if actions assigned to a same category are incomparable or indifferent to each other. Besides, it permits to confirm that there is a preference relation between actions assigned to different categories. The practical usefulness for decision makers of such complementary descriptive tools is illustrated on a real case study where the innovation performances of small and medium enterprises from the French Lorraine region are assessed. Building and sustaining the Technology Innovativeness Capabilities (TIC) of enterprises is a very important challenge (Chiesa, 1996; Guan and Ma, 2003; Burgelman et al., 2004; Wang et al, 2008). The TIC of an enterprise are at first measured to compare an enterprise to well-known norms or profiles (i.e. benchmarking). Based on these comparisons, a label is given to enterprise: passive, reactive, preactive or proactive. Based on the extracted information, recommendations are suggested to enhance the innovation capabilities of the enterprises. It is thus crucial to understand the TIC of an enterprise correctly. As illustrated by this case study, descriptive methods are very important in decision problems since they permit a decision maker to gain a better view and comprehension. The structure of the paper is as follows. First, we give a brief reminder of the PROMETHEE and GAIA methods. In Section 3, we present briefly the FlowSort method. Section 4 introduces FS-GAIA and section 5 is devoted to the case study. Finally, some further research directions are given in the conclusions.

2. Ranking problem: the PROMETHEE and GAIA methods This section briefly describes the PROMETHEE and GAIA methods, which have permitted to tackle successfully ranking problems in several cases (Behzadian et al. 2010, Yatsalo et al. 2010). The PROMETHEE II method leads to a complete ranking of the actions based on their pair-wise comparisons. The GAIA method provides the decision maker with a visual



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representation of his decision problem by taking into account his preference parameters (Brans and Mareschal 1994).

Let us denote by A = {a1, a2, ..., an} the set of n actions of the ranking problem where the actions are evaluated on a set of q criteria denoted by F = { f1, f2,.., fq}. Without loss of generality we will suppose that all the criteria have to be maximized.

In order to pair-wise compare two actions a1 and a2 on criterion fj the difference dj(a1,a2) =

fj(a1) - fj(a2) is at first computed. This difference is then translated into a uni-criterion preference degree, noted Pj(a1, a2), such that (Brans and Mareschal, 1994):

- 0 ≤ Pj(a1, a2) ≤ 1,

- Pj(a1, a2) ≈ 0 when a1 is indifferent to a2 for criterion j,

- Pj(a1, a2) ≈ 1 when a1 is strictly preferred to a2 for criterion j.

The higher Pj(a1, a2), the stronger the preference of a1 over a2 according to the decision maker on the criterion j. The PROMETHEE method provides us with 6 types of preference functions which are given in (Brans and Mareschal, 1994). The linear preference function is illustrated in Figure 1.

Pj(a,b)

q p fj(a)-fj(b)

0

1

Figure 1 Representation of the linear preference function where q and p denote respectively the indifference and preference thresholds.

Considering the whole set of actions, a global score for action on criterion fl is defined as the PROMETHEE uni-criterion net flow:

(1)

This uni-criterion net flow score, always between -1 and 1, represents the strength (if near 1)

or the weakness (if near -1) of an action in regards of all the actions of A. These uni-

criterion net flows are then aggregated into a global score taking into account the decision

maker’s priorities: to each criterion fj a weight, noted (with ) is associated such that

. This leads to the net flow of action computed as follows:

(2)



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This score allows the decision maker to rank the actions from the best to the worst one and is referred to as the PROMETHEE II ranking. More information about the PROMETHEE methods may be found in (Brans and Mareschal 2005) and (Mareschal et al. 2008) for another interpretation of the net flow score. Besides, the uni-criterion net flows lead to the following matrix:

(3)

This matrix is similar to the performance table since each row of this matrix represents an action and each column represents a criterion. However, this matrix contains some preference information given by the decision maker since it incorporates the preference function and their parameters. It measures thus the intra criteria information. In order to represent the inter criteria information the decision maker can use the GAIA method (Brans and Mareschal, 1994), which is an improvement of the traditional multivariate statistical analysis (Stewart 1981). Here, actions will be represented by points, noted with αi: (Φ1(ai),..., Φj(ai),..., Φq(ai)) in a -dimensional space. The coordinates of the points are thus the values in each line of matrix Φ and representing the criteria’s variations. To graphically represent this matrix, the GAIA method, uses a principal component analysis (PCA) to find a plane which allows a 2-D visualization. For this purpose, the variance-covariance matrix of our decision problem, noted C, is at first computed. This matrix can be obtained by using the following relation:

nC = ΦT* Φ (4)

where ΦT denotes the transposition of Φ . Then, two eigenvectors, noted u and v, are chosen such that they have the greatest eigenvalues λ1 and λ2. These two eigenvectors are orthogonal ( ) and define the best plane, called the GAIA plane, to use for the projection of the points while minimizing the loss of information (Brans and Mareschal, 1994). As a -dimensional space is reduced to two dimension for visualisation purposes, some information is lost or distorted. The amount of information preserved in percents can be calculated as follows:

(5)

The coordinates of , the projections of the points, on the GAIA plane will be:



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where denotes the transposition of αi which is a row of Φ . In order to represent the intra criteria information, each criterion fj will be projected on the GAIA plane by considering each criterion axis cj as follows:

ej:(0,0,…,1,0,…,0) j = 1,2,…,q

The angle between the projections of two criteria is a measure of similarity or conflict between two criteria. The smaller is the angle, the more similar are two criteria. On the contrary, the angle will be greater when criteria are conflicting given the data set. Finally, the information on the weights chosen by the decision maker can be added by finding the projection of the weights vector: w:(w1, w2, …, wj, …, wq) The vector obtained is called decision stick, noted D, as it represents the decision maker’s priorities: D: (w*u, w*v). Having a GAIA plane such as illustrated in Figure 2, the decision maker may easily draw conclusions about his ranking problem. Actions that are close on the plane will often have very similar rows in the matrix Φ (e.g., a1 and a2). The decision maker can thus quickly identify actions that have similar or conflicting (e.g., a1 and a5) performance. Moreover, the decision maker can easily compare criteria between each other since their position is an indication of their conflicting or correlated behaviour. For instance, in Figure 2, the criteria c1

and c2 are very close to each other which means that they discriminate the actions in the same manner (they are thus correlated). On the other hand, c2 and c4 are in opposite directions: they are conflicting. The possibility to compare actions to the different criteria by their position in the plane, allows the decision maker to regroup actions and to have a better understanding of the results obtained (Brans and Mareschal 2005).

Figure 2 Illustration of the GAIA plane.

Let us remark that (Hayez et al. 2009) and (Nemery et al. 2010) presented some variants of this GAIA plane in order to minimize the information loss.



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3. Sorting problem: the FlowSort method In a sorting problem, the decision maker wants to assign a set of actions A = {a1, a2, ..., an} to K predefined categories C1,…,CK . Moreover, there is a complete order on the categories such that category C1 is the best and CK is the worst category. An example of a sorting problem is the assignment of projects into 2 categories: the accepted or rejected projects. Several real-world decision problems have been addressed through sorting models, including financial decision-making problems, environmental decisions, marketing decisions, and even medical decisions (diagnosis) (M Doumpos and C Zopounidis 2002, M. Doumpos and C. Zopounidis 2002). An important requirement in a sorting problem is that the assignment of the actions must be independent. In other words, the assignment of an action to a category must not depend on the assignment of another action (i.e. the actions are not pairwise compared to each others). This is a fundamental difference with the ranking problem. The following paragraphs describe briefly the FlowSort sorting method which is based on the PROMETHEE method (section 2). In the FlowSort method (Nemery and Lamboray 2008), the K categories are predefined either by limiting profiles or central profiles. In the former case, each category is defined by an upper and a lower boundary. The category Cj is thus defined by the upper limiting profile rj and the lower profile rj+1 of the limiting profiles set noted R={r1,…,rK+1}. In the latter case, the categories are defined by a central element. For simplicity, only the case of limiting profiles is presented in this paper. Since the categories are completely ordered, each limiting profile dominates all the next : i.e. r1 > r2 > … > rK+1. Formally, the profiles respect thus the following condition if we suppose that the q criteria have to be maximized: Condition 1:

The FlowSort method is the outcome of the following main idea: an action to be sorted is compared to solely the reference profiles by means of a ranking method. The category, to which the action is assigned, is deduced from its relative position with respect to solely the reference profiles. Let us stress that the ranking method is applied on the data-set consisting of one action to be assigned and the reference profiles. In the FlowSort method, the PROMETHEE II ranking method is used to assign the actions to the categories. The steps of the assignment are briefly given below. The methodology and its properties are explained more in details in (Nemery and Lamboray 2008). Let us note the set of reference profiles and an action ai to be classified. The action ai is first pairwise compared to all the reference profiles and then a complete ranking is computed.



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Considering ai and the set of reference profiles, a global uni-criterion netscore for ai on criterion fl is defined as follows:

(6)

where represents the numbers of elements belonging to the particular set

This uni-criterion net flow score (always between -1 and 1) represents the strength (if near 1) or the weakness (if near -1) of an action in regards of solely the reference profiles of R. We can thus calculate the PROMETHEE II ranking for this set with the following net flows:

(7)

The assignment of action to the class Ch is based on its relative position with respect to the reference profiles rh and rh+1 :

(8)

Alongside the category to which an action is assigned, the net score of each action compared solely to reference profiles, gives the decision maker an idea of the strength or weakness of an action.

4. The FS-GAIA plane In this section, we will present the different steps to represent the sorting problem in a 2-D plane. Therefore, let us consider that x represents either an action to be sorted or one of the

profiles. We define the vector [ ] representing the q unicriterion net flows

of x in regards of the profiles R. This permits us to define the following matrix:

(9)

This matrix has q columns corresponding to q criteria and n+K+1 rows. The first n rows correspond to the actions to be assigned whereas the K+1 following ones to the limiting profiles. This matrix is not similar to the performance table nor the matrix (3). It corresponds to the behaviour of the actions in regards to the reference profiles solely (while taking into preference information such as the preference functions, etc). However, it measures also the intra criteria information. In order to represent the intra criteria information contained in this matrix, the decision maker may use a plane similar to the GAIA plane representing the behaviour of the actions in regards to the reference profiles. This plane is called the FS-GAIA plane and will be obtained as follows.



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The actions and profiles will be represented by points, noted with

in a -dimentional space. The coordinates of the points are thus

the values in each line of matrix and represent the behaviour of x on each criterion in regards of the profiles. To graphically represent this matrix, the principal component analysis (PCA) is used to find a plane which allows a 2-D visualization. For this purpose, the variance-covariance matrix of the sorting problem, noted , is at first computed. This matrix can be obtained by using the following relation:

(10)

where denotes the transposition of . Then, two eigenvectors, noted and , are chosen such that they have the greatest eigenvalues and These two eigenvectors are orthogonal ( ) and define the best plane, called the FS-GAIA plane, to use for the projection of the points while minimising the loss of information. Similarly to the GAIA plane, the obtained plane will be the one that holds the maximum amount of information after the projection. Intuitively, the amount of information preserved can be obtained analogously:

(11)

The coordinates of , the projections of the points, on the FS-GAIA plane will be:

where denotes the transposition of which is a row of . In order to represent the intra criteria information, each criterion will be projected on the

FS-GAIA plane. To do that we just need to obtain the projections of each axis , where:

The angle between the projections of two criteria is a measure of the similarity or the conflict between two criteria. The smaller is the angle, the more similar are two criteria. On the contrary, this angle will be large when criteria are conflicting. Analogously, the information on the weights chosen by the decision maker can be added by projecting , the weights vector on the FS-GAIA plane. This leads

to .



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Figure 3 FS-GAIA plane representing the actions, the reference profiles and the criteria

Figure 3 is a representation of the FS-GAIA plane. Let us first remark that in the sorting context, the reference profiles respect the condition of dominance (Condition 1), which implicates a high correlation between the criteria. As a consequence, the limiting profiles will be almost aligned along the decision stick and the biggest angle between the criteria will be smaller than 90 degrees. The perpendicular projections on the decision stick permits to define stripes which are an indication of the different categories. An FS-GAIA plane, such as in

Figure 3, helps a decision maker to draw conclusions about the behaviour of actions. Indeed, actions that are similar will also have similar rows in the matrix (9) and therefore its projection on the FS-GAIA plane will be close (e.g., a1 and a2). Moreover, the decision maker can compare criteria between each other since their position is an indication of their conflicting or correlated behaviour. The possibility to compare actions to the different criteria by their position in the plane, allows the decision maker to regroup actions and to have a better understanding of the results obtained. For instance, in Figure 3, the criteria c1 and c2 are close to each other which means that they discriminate the actions in the same manner (they are thus correlated). On the other hand, c1 and c3 are not close: they are conflicting. If an action is indifferent to a reference profile it will indeed have the same position as the reference profile in the FS-GAIA Plane. Although two actions may be assigned to the same category, they can behave in a different way. These are so-called incomparable actions: they lay in a same stripe but are distant.

D

r3

r1

a4

c3

r2

r4

c2

c1

a5 a1

a2

a3

C1

C2

C3



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5. Case Study Building and sustaining the Technology Innovativeness Capabilities (TIC) of enterprises is a very important challenge. The assessment of these capabilities enables to identify their current level of innovativeness. In this study, we will evaluate the innovation capability of a set of 20 small and medium enterprises of East France based on the capabilities/criteria defined in (Morel and Boly 2004): creativity (CR), product development (PD), human resource management (HRM), strategy (ST), project management (PM) and knowledge management (KM). The SMEs will be ranked and sorted in a second exercise. In both cases, qualitative analysis will be composed with the support of visualization techniques.

5.1. Ranking of SMEs

The evaluations of these SMEs on these six criteria (which have to be maximized) were assessed by independent external experts of the companies (namely the two last authors) in an interview of about two hours with a top manager. For each criterion, a set of questions has been prepared but deviations from the agenda were made in order to explore new and particular practice raised in the course of each interviews. After the interview, the two experts rated the company on each criterion on a scale 0 to 100 %. As the questionnaire was prepared at length, a consensus was found quickly for each score. The final performance of each company is given in Table 1. Let us first consider that these 20 companies need to be ranked from the most innovative to the less one. In order to use the PROMETHEE method, the experts have decided the following preference parameters: the indifference threshold is 0 and preference threshold is 0.25 on all criteria. The weights of the criteria, determined by the experts, are given at the bottom of Table 1. Table 1 Performances of the enterprises on the 6 criteria

CR PD HRM ST PM KM

E1 0.27 0.25 0.25 0.37 0.02 0.19 E2 0.35 0.56 0.38 0.82 0.14 0.19 E3 0.27 0.15 0.38 0.56 0 0.09 E4 0.17 0.21 0.12 0.41 0.11 0.19 E5 0.3 0.3 0.12 0.13 0 0 E6 0.25 0.4 0.24 0.33 0.14 0 E7 0.47 0.11 0 0.48 0.16 0 E8 0.5 0.13 0.37 0.57 0.37 0.34 E9 0.5 0.75 0.5 0.95 0.62 0.41

E10 0.33 0.05 0.24 0.6 0.24 0.52 E11 0.55 0.55 0.63 0.43 0.5 0.41 E12 0.47 0 0.38 0.34 0.13 0.15 E13 0.17 0.2 0.25 0.07 0.12 0.09 E14 0.36 0 0.25 0.37 0.13 0 E15 0.19 0 0.12 0.04 0 0.07 E16 0.27 0.2 0.12 0.32 0.12 0.09 E17 0.48 0.64 0.38 0.21 0.13 0.24 E18 0.19 0.26 0.24 0.17 0 0.23 E19 0.08 0.26 0.25 0.11 0.25 0.07 E20 0.25 0.05 0.25 0.36 0 0.25

W 0.175 0.107 0.068 0.232 0.194 0.224



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Based on the preference parameters, we obtain the PROMETHEE II ranking given in Figure 4 representing the net flow scores of the 20 SMEs. E9 is the most innovative SME whereas E15 is the less innovative one. The Figure 5 represents a stacked bar diagram of the contribution of each weighted unicriterion net flow to the total net score. The black bullet corresponds to the total net flow (the sum of the positive and negative unicriterion net flows). This figure permits us to understand the weakness and strengths of each SME compared with its competitors. We may for instance remark that E9 behaves well on all the criteria with the highest contribution coming from the criteria Strategy (ST), Project Managament (PM) and Knowledge Management (KM). E7 behaves very well on the criteria Creativity (CR) and Strategy (ST) but is weak on the criteria Human Ressource Management (HRM), Knowledge Managament (KM) and Process Development (PD).

Figure 4 Representation of the PROMETHEE II ranking based on the net flows

Figure 5 Stacked bar diagram of the weighted unicriterion net flows of the 20 enterprises. The black dot represents the net flows of each SME



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Figure 6 represents the GAIA plane (with =71%) of the 20 SMEs. The Decision Stick (D) points in the direction of E9 and E11 point which means that these SMEs are the best ones. On the other hand, E15, in the opposite direction, is the last ranked SME. From the GAIA plane, we can thus, as in Figure 5, conclude that E7 behaves well on the criteria ST and CR (the arrows representing those criteria points in the same direction as E7) but is very weak on the criteria HRM, PD and PM (these criteria point in the opposite direction as E7). We may also remark that E6 and E7 have opposite features. This is also visible in Figure 5 for experienced eyes. The advantage of Figure 6 is a full picture, which represents all the SMEs on the same graph. This permits to compare easily several SMEs at the same time. Moreover, it enables the discovering of clusters of SMES (such as the cluster E19, E5, E13, E18, E6; or the cluster E20, E14, E7) which have all a similar behaviour.

Figure 6 Representation of the GAIA plane ( =71%) for the set of 20 SMEs

5.2. Sorting of SMEs

In this section, we now suppose that the decision maker wants to sort the SMEs into predefined categories. The aim is to compare each SME to well-known norms or profiles of the innovation sector for benchmarking purposes. In the innovation field, we can find 4 categories of SMEs (Godet and Roubelat 1996; Rejeb et al, 2008): the proactive, preactive, reactive and passive enterprises. The 20 SMEs are thus not anymore pairwise compared to each other but to limiting profiles whose performances are given in Table 2 and represented in Figure 7 with dashed lines.



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Table 2 Performances of the limiting profiles defining the 4 categories

CR PD HRM ST PM KM

R1 1 1 1 1 1 1 R2 0.75 0.75 0.75 0.75 0.75 0.75 R3 0.5 0.5 0.5 0.5 0.5 0.5 R4 0.25 0.25 0.25 0.25 0.25 0.25 R5 0 0 0 0 0 0

Figure 7 Graphical representation of the performances of the SMEs E10, E11, E17 and E2 and the limiting profiles (dashed lines)

The assignments of the 20 enterprises are given in Table 1. Most sorting methods provide only this raw result. However, the FlowSort sorting method is complemented with visualisation techniques, which may provide some further interesting information for the decision maker. Table 1 Assignments of the 20 SMEs

Category 1 /

Category 2 E9

Category 3 E2, E8, E10, E11, E17

Category 4 E1, E3, E4, E5, E6, E7, E12, E13, E14, E15, E16, E18, E19, E20

Figure 8 represents the net scores of each SME compared to the reference profiles only. We may see that E2 and E8 have the same net scores compared to the limiting profiles and are indeed assigned to the same category. Let us remark that they received a different ranking with PROMETHEE II : respectively third and fifth! On the other hand, although there is a high



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difference between the net scores of E11 (-0.021) and E17 (-0.310), both actions are assigned to the same category. Let us analyse the individual behaviour of E2 and E17 in regards of the reference profiles. Both SMEs are assigned to the same category. From Figure 9, we remark that E2 scores very well on Strategy. On the other hand, it is very poor on Project Management and is not very well on Knowledge Management and Creativity. From Figure 10, we conclude that E17 lacks particularly on Product Development, Project Management and Knowledge Management. It does not score as well as E2 on the Strategy criterion. We might conclude that although E2 and E17 are assigned to the same category, they behave in a different way.

Figure 8 Representation of the assignments of the enterprises (colours) as well as their net flows in regards of the reference profiles

The different behaviour is confirmed in the individual GAIA-planes for E2 (Figure 11) and E17 (Figure 12). In both cases, the SMEs are respectively compared solely to the limiting profiles.

Figure 10 Stacked bar diagram of the unicriterion netscores of E17 and the five limiting profiles Ri

Figure 9 Stacked bar diagram of the unicriterion netscores of E2 and the five limiting profiles Ri



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E2 performs very well on the criteria strategy, product development but poorly on the criteria Knowledge Managements, Process Management and Human Resource Management. On the other hand, E17 performs very well on Product Development, Creativity and Human Resource Management but poorly on Strategy, Knowledge Management and Process Management.

Similarly to the Figure 5 in the ranking context, we propose a visualisation rendering the differences in behaviour of the actions. This is provided in the stacked bar diagram of Figure , representing the weighted unicriterion net flows of each SME compared to the profiles. It explains thus the contribution of each criterion to the net score. From Figure 13, it is clear that E2 and E17, although assigned to the same category, present different features. Indeed, the Strategy criterion (ST) is the most positive contributor for E2 whilst it is the second most negative contributor for E17 (as shown previously in figure 9 and 10). On the other hand, we may remark that E16 and E14 have similar behaviours.

Figure 11 GAIA plane including E2 and the limiting profiles

Figure 12 GAIA plane including E17 and the limiting profiles



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Figure 13 permits a decision maker to compare the behaviour of two actions. However, it is difficult to compare of several actions simultaneously. It does not allow a decision maker to discover eventual subgroups inside a same category. Moreover, it is not possible to represent the limiting profiles in this figure. Therefore, we will present in next paragraph a modified GAIA-plane containing all this information in a two-dimensional plane.

5.3. FS-GAIA plane

Figure 14 represents the FS-GAIA plane of the 20 SMEs compared to the limiting profiles. Let us first remark that the FS-GAIA plane differs significantly from the GAIA-plane (Figure 6). E9 and E11 behave in a ranking context similarly when compared to the rest of the SMEs (Figure 6) but differently when compared to solely the limiting profiles (see Figure 14). In the sorting context, there is a main difference between E11 and E9 on the criterion Strategy. This is indicated in the FS-GAIA plane by the fact that E11 is in the opposite direction as the criterion axis, on the contrary of E9. E9 is very far away from the limiting profiles R2 and R3 which means that it behaves differently on the different criteria. We can see that E9 performs much better on the criterion strategy than on the other criteria. From Figure 14, it is easy to identify the different zones corresponding to the different categories. It is possible to make further distinction in the categories. For example, in category 3, enterprises E10, E17, E8, E2 and E11 behave differently as indicated by their wide dispersion on the plane. Moreover, we can remark that E11 is on the limit between category 2 and category 3. E11 has similar performances to the limiting profile R3. E17 and E10 present a completely different profile although their final scores are almost equal. E17 behaves well on the Project Development criterion but very poorly on criterion Strategy whereas E8 behaves inversely on these criteria. The same reasoning might be applied on the enterprises E11 and E10. This is confirmed in Figure 7, where only the raw performances of these actions are represented.

Figure 13 Stacked bar diagram of the weighted unicriterion flows of the 20 SMEs compared individually to the limiting profiles



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Figure 14 also highlights a little cluster of purples enterprises (E4, E1, E12, E6, E20, E14, E16). These enterprises behave in the same way compared to the reference profiles. E19, E13, E5 and E15 do not belong to this group. Their net scores on the criteria are generally lower (and they are thus closer to the R5 in the FS-GAIA plane). The FS-GAIA plane can detect heterogeneity within classes of actions: class 3 and 4 may be

further subdivided. This permits to evolve from a set of completely ordered classes towards

a partially ordered set of classes.

6. Conclusion Multi-Criteria Decision Methods have been designed to solve sorting problems, ranking

problems and its particular case: choice problems. If a problem needs to be further analysed,

redefined, justified or improved, then descriptive methods needs to be used. They permit to

gain an insight to the problem and capture fine details. The PROMETHEE family is well

equipped for this further analysis with GAIA. In this paper, we have introduced two other

visualisation techniques: FS-GAIA and stacked bar diagrams. Their effectiveness has been

validated in a case study, where SMEs have been sorted into four ordered categories:

proactive, preactive, reactive and passive enterprises. FlowSort provides more information

than a simple ranking because, in our case study, the best ranked company needs still to

improve in order to achieve the best category: the proactive companies. This information

would not been available in PROMETHEE, where an action can be the best, but the best of

the worst. Further analysis for improvement can be provided with FS-GAIA and stacked bar

diagrams. In particular, incomparability can be visually detected in the FS-GAIA.

Figure 14 FS-GAIA plane for the 20 SME compared to the 5 limiting profiles



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A further development would be an interactive visualisation tool to assess the sensitivity of

an action when performances are varied. Another research direction would be to develop

visualisation techniques for other multi-criteria decision aids methods as AHP, MAUT or

ELECTRE.

ACKNOWLEDGEMENTS

We gratefully acknowledge two anonymous reviewers for the valuable feedback and constructive

criticism.

Bibliography Behzadian, M., Kazemzadeh, R. B., Albadvi, A. and Aghdasi, M. (2010), "PROMETHEE: A

comprehensive literature review on methodologies and applications", European Journal of Operational Research, Vol. 200 No. 1, pp. 198-215.

Brans, J.-P. and Mareschal, B. (1994), "The PROMCALC & GAIA decision support system for

multicriteria decision aid", Decision Support Systems, Vol. 12 No. 4-5, pp. 297-310. Brans, J.-P. and Mareschal, B. (2005), "PROMETHEE methods", in Figueira, J., Greco, S. and

Ehrgott, M. (Eds.), Multiple Criteria Decision Analysis: State of the Art Surveys, Springer, New York, 163-198.

Burgelman, R., Maidique, M.A., Wheelwright, S.C., (2004). “Strategic Management of

Technology and Innovation”. McGraw-Hill, New York, pp. 8–12. Chiesa, V., Coughlan, P., & Voss, C. A. (1996). “Development of a technical innovation audit”,

Journal of Product Innovation Management, 13(2), 105-136. Doumpos, M. and Zopounidis, C. (2002a), "Multi-criteria classification methods in financial

and banking decisions", International Transactions in Operational Research, Vol. 9 No. 5, pp. 567-581.

Doumpos, M. and Zopounidis, C. (2002b), Multicriteria decision-aid classification methods,

Applied Optimisation, New York: Kluwer Academic Publishers. Figueira, J., Greco, S. and Ehrgott, M., eds. (2005), Multiple criteria decision analysis : state of

the art surveys, Springer, New York. Godet, M. and Roubelat, F. (1996), "Creating the future: The use and misuse of scenarios",

Long Range Planning, Vol. 29 No. 2, pp. 164-171.



19

Guan, J., Ma, N., (2003), “Innovative capability and export performance of Chinese firms”, Technovation 23 (9), 737–747.

Hayez, Q., Mareschal, B. and De Smet, Y. (2009), "New GAIA Visualization Methods", in

Information Visualisation 2009 proceedings of the 13th International Conference in Barcelona, IEEE Computer Society, Los Alamitos, pp. 247-251.

Mareschal, B., De Smet, Y. and Nemery, P. (2008), "Rank Reversal in the PROMETHEE II

Method : Some New Results", in Industrial Engineering and Engineering Managemen proceedings of the IEEE International Conference in Singapore, IEEE Engineering Management Society, Singapore, pp. 959- 963.

Morel, L. and Boly, V. (2004), "Mastering innovativeness potential: the results of an expert

consultation", Revista Eletrônica de Administração, Vol. 10 No. 6., pp. 165-180. Nemery, P. and Lamboray, C. (2008), "FlowSort: a flow-based sorting method with limiting or

central profiles", TOP, Vol. 16 No. 1, pp. 90-113. Nemery, P., Lidouh, K. and Mareschal, B. (2010), "On the use of taking weights into account

in the GAIA map", International Journal of Information and Decision Sciences, to appear.

Rejeb, H.B., Morel-Guimarães, L., Boly, V., Assiélou, N.G. (2008), “Measuring innovation best

practices: Improvement of an innovation index integrating threshold and synergy effects”, Technovation, 28 (12), pp. 838-854.

Stewart, T. (1981), “A Descriptive Approach to Multiple-Criteria Decision Making”, Journal of

the Operational Research Society, 32(1), 45-53. Wang, C., Lu, I., Chen, C. , (2008), “Evaluating firm technological innovation capability under

uncertainty”. Technovation. 28(6), 349-363. Yatsalo, B., Didenko, V., Tkachuk, A., Gritsyuk, G., Mirzeabasov, O., Slipenkaya, V., Babutski,

A., Pichugina,I., Sullivan T., Linkov, I. (2010) “Multi-criteria spatial decision support system DECERNS: application to land use planning”, International Journal of Information Systems and Social Change, 1(1), 11-30.

Enriching descriptive information in ranking and sorting problems with visualizations techniques

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