intercriteria decision making approach to eu member states competitiveness analysis: temporal and...

InterCriteria Decision MakingApproach to EU Member States

Competitiveness Analysis:Temporal and Threshold Analysis

Vassia AtanassovaLyubka Doukovska

Deyan Mavrov Krassimir Atanassov

7th International IEEE Conferenceon Intelligent Systems24–26 September 2014, Warszawa

Specific problem statement

• A problem from the petrochemical industry:– A set of probes of crude oil from a new shipment

(oil from same locations inherently have different properties over time)

– Tested against a set of physical and chemical criteria:• molecular weight density• viscosity refractive index• content of hydrogen aniline point• cetane number

– To determine the properties of that shipment of crude oil– Hence the best way to utilize it in production:• kerosene, car fuel, plastics, dyes, bitumen, etc.

• A problem from the petrochemical industry:– From the set of all physical and chemical criteria, not all

are equal to measure:• e.g., measuring the cetane number is slow (> 3 days)

and difficult.– Any extra measurement delays the production and rises

the production costs.– Can we find some correlations in our data, so that we

eliminate the need of measurement of the cetane number,while keeping the precision of the decision making process as much as possible?

General problem statement

• A set of objects is evaluated against a set of criteria– Not all physical and chemical criteria are equal to

measure:• Some measurements are cheap, quick and easy• Other measurements are expensive, time-consuming

and/or difficult. We called them ‘cost-unfavourable criteria’ (CUC)

• We need to discover dependences between the criteria, and thus eliminate the need of making all the measurements, ideally eliminating the CUC.

• Precision is not to be compromised.

Proposed approach

• InterCriteria Decision Making, based on:– Index matrices– Intuitionistic fuzzy sets

1

1 1,1 1, 1,

,1 , ,

... ...

... ...

... ... ... ... ... ...

... ...

s n

s s

m m m s m s

c c cIM

o e e e

o e e e

( 1)

pairs of objects , , 2

( 1)i.e. pairwise

2comparisons between and

i j

i j

m mo o

m m

e e

• InterCriteria Decision Making, based on– Index matrices– Intuitionistic fuzzy sets

If R(ei,s; ej,s) is “>”, then µ++ (membership)

If R(ei,s; ej,s) is “<”, then ν++ (non-membership)

Otherwise, π++ (uncertainty)

, ,i s j se e

, , [0;1]s s s


Parameters α and β (α, β [0;1]) are used to measure the levels of consonance or dissonance between the involved criteria:• If (µ > α) AND (ν < β), then (α, β)-positive consonance• If (µ < β) AND (ν > α), then (α, β)-negative consonance• Otherwise, dissonance


We obtain back two IM-s for the positive and the negative consonances between the criteria, i.e.

1 1

1 1,1 1, 1, 1 1,1 1, 1,

,1 , , ,1 , ,

,1 , ,

... ... ... ...,

... ... ... ...

... ... ... ... ... ... ... ... ... ... ... ...

... ... ... ...

... ... ... ... ... ... ... ... ... ... .

... ...

i n i n

i n i n

i i i n i n i i i n i n

n n n i n n

c c c c c cIM IM

c c

c c

c

,1 , ,

.. ...

... ...n n n i n nc

Applications

• So far the approach is tested with: – Petrochemical data for crude oil• Results outline all the previously

known correlations between criteria

– Biomedical data about temperature curves of patients with multiplen myelom and carcinome• Results outline yet unknown relations, but the starting

data are yet scarce, work needed on problem formulation

– Data from the World Economic Forum’s Global Competitiveness Reports (2008-2014)• AFAWK, completely new and reliable results

which is actually good!

which is actually good!

not yet ready to

boast with

not yet ready to

boast with

encouraging!encouraging!

Application: EU Competitiveness

• World Economic ForumGlobal competitiveness reports (2008–2014)– 6 matrices × 28 objects × 12 criteria

Basic requirements1. Institutions 3. Macroeconomic stability2. Infrastructure 4. Health and primary education

Economy enhancers5. Higher education and training 6. Goods market efficiency 9. Technological readiness7. Labor market efficiency 10. Market size8. Financial market sophistication

Innovation and sophistication factors11. Business sophistication 12. Innovation

11, 12

5, 6, 7, 8, 9, 10

1, 2, 3, 4

• World Economic ForumGlobal competitiveness reports (2008–2014)

• WEF’s general message to policy makers:Identify and strengthen the transformativeforces that will drive future economic growth.

Transition 2-3Transition 1-2 Stage 2

Efficiency driven economy

Stage 3

Innovation driven economy

Stage 1

Factor driveneconomy

• Example: Poland, 2013–2014

• Example with the WEF’s GCRs Positive consonance

2008-2009 vs. 2013-2014µ 1 2 3 4 5 6 7 8 9 10 11 12

1 1.000 0.844 0.685 0.757 0.788 0.833 0.603 0.828 0.823 0.497 0.794 0.802

2 0.844 1.000 0.627 0.751 0.749 0.743 0.529 0.741 0.775 0.582 0.831 0.807

3 0.685 0.627 1.000 0.616 0.638 0.664 0.653 0.648 0.693 0.434 0.651 0.667

4 0.757 0.751 0.616 1.000 0.780 0.720 0.550 0.704 0.725 0.524 0.765 0.772

5 0.788 0.749 0.638 0.780 1.000 0.746 0.622 0.728 0.757 0.558 0.767 0.796

6 0.833 0.743 0.664 0.720 0.746 1.000 0.627 0.817 0.802 0.505 0.786 0.765

7 0.603 0.529 0.653 0.550 0.622 0.627 1.000 0.664 0.611 0.389 0.563 0.590

8 0.828 0.741 0.648 0.704 0.728 0.817 0.664 1.000 0.820 0.476 0.733 0.751

9 0.823 0.775 0.693 0.725 0.757 0.802 0.611 0.820 1.000 0.548 0.817 0.815

10 0.497 0.582 0.434 0.524 0.558 0.505 0.389 0.476 0.548 1.000 0.648 0.601

11 0.794 0.831 0.651 0.765 0.767 0.786 0.563 0.733 0.817 0.648 1.000 0.860

12 0.802 0.807 0.667 0.772 0.796 0.765 0.590 0.751 0.815 0.601 0.860 1.000

µ 1 2 3 4 5 6 7 8 9 10 11 12

1 1.000 0.735 0.577 0.720 0.807 0.836 0.733 0.749 0.854 0.503 0.804 0.844

2 0.735 1.000 0.479 0.661 0.749 0.677 0.537 0.590 0.786 0.661 0.804 0.799

3 0.577 0.479 1.000 0.421 0.519 0.558 0.627 0.675 0.550 0.413 0.548 0.556

4 0.720 0.661 0.421 1.000 0.730 0.683 0.590 0.563 0.677 0.497 0.712 0.690

5 0.807 0.749 0.519 0.730 1.000 0.735 0.622 0.632 0.775 0.579 0.815 0.847

6 0.836 0.677 0.558 0.683 0.735 1.000 0.749 0.712 0.788 0.466 0.759 0.751

7 0.733 0.537 0.627 0.590 0.622 0.749 1.000 0.741 0.685 0.399 0.624 0.624

8 0.749 0.590 0.675 0.563 0.632 0.712 0.741 1.000 0.712 0.497 0.688 0.680

9 0.854 0.786 0.550 0.677 0.775 0.788 0.685 0.712 1.000 0.526 0.810 0.831

10 0.503 0.661 0.413 0.497 0.579 0.466 0.399 0.497 0.526 1.000 0.611 0.598

11 0.804 0.804 0.548 0.712 0.815 0.759 0.624 0.688 0.810 0.611 1.000 0.873

12 0.844 0.799 0.556 0.690 0.847 0.751 0.624 0.680 0.831 0.598 0.873 1.000

• Example with the WEF’s GCRs Negative consonance

2008-2009 vs. 2013-2014ν 1 2 3 4 5 6 7 8 9 10 11 12

1 0.000 0.114 0.241 0.140 0.140 0.077 0.275 0.116 0.116 0.458 0.148 0.127

2 0.114 0.000 0.304 0.156 0.190 0.167 0.365 0.220 0.180 0.384 0.127 0.138

3 0.241 0.304 0.000 0.265 0.265 0.209 0.204 0.270 0.225 0.495 0.270 0.241

4 0.140 0.156 0.265 0.000 0.108 0.140 0.294 0.201 0.169 0.381 0.138 0.111

5 0.140 0.190 0.265 0.108 0.000 0.135 0.233 0.198 0.164 0.378 0.156 0.130

6 0.077 0.167 0.209 0.140 0.135 0.000 0.209 0.090 0.095 0.397 0.114 0.127

7 0.275 0.365 0.204 0.294 0.233 0.209 0.000 0.212 0.259 0.497 0.315 0.265

8 0.116 0.220 0.270 0.201 0.198 0.090 0.212 0.000 0.132 0.476 0.217 0.196

9 0.116 0.180 0.225 0.169 0.164 0.095 0.259 0.132 0.000 0.399 0.122 0.116

10 0.458 0.384 0.495 0.381 0.378 0.397 0.497 0.476 0.399 0.000 0.307 0.336

11 0.148 0.127 0.270 0.138 0.156 0.114 0.315 0.217 0.122 0.307 0.000 0.079

12 0.127 0.138 0.241 0.111 0.130 0.127 0.265 0.196 0.116 0.336 0.079 0.000

ν 1 2 3 4 5 6 7 8 9 10 11 12

1 0.000 0.220 0.386 0.188 0.132 0.077 0.185 0.172 0.090 0.452 0.138 0.111

2 0.220 0.000 0.466 0.228 0.172 0.228 0.362 0.317 0.146 0.286 0.135 0.138

3 0.386 0.466 0.000 0.476 0.405 0.344 0.286 0.251 0.394 0.537 0.394 0.389

4 0.188 0.228 0.476 0.000 0.143 0.169 0.283 0.307 0.201 0.397 0.175 0.198

5 0.132 0.172 0.405 0.143 0.000 0.153 0.272 0.259 0.135 0.341 0.098 0.079

6 0.077 0.228 0.344 0.169 0.153 0.000 0.135 0.169 0.101 0.439 0.143 0.159

7 0.185 0.362 0.286 0.283 0.272 0.135 0.000 0.146 0.209 0.505 0.267 0.275

8 0.172 0.317 0.251 0.307 0.259 0.169 0.146 0.000 0.206 0.415 0.217 0.233

9 0.090 0.146 0.394 0.201 0.135 0.101 0.209 0.206 0.000 0.405 0.119 0.101

10 0.452 0.286 0.537 0.397 0.341 0.439 0.505 0.415 0.405 0.000 0.328 0.344

11 0.138 0.135 0.394 0.175 0.098 0.143 0.267 0.217 0.119 0.328 0.000 0.071

12 0.111 0.138 0.389 0.198 0.079 0.159 0.275 0.233 0.101 0.344 0.071 0.000

Consonances vs. criteria

1

11 12

9

11

1111 1212

995

2

6

11

1111 1212

9955

22

66

11

1111 1212

9955

22

66

4

7

8

11

1111 1212

9955

22

66

44

77

88

10

3

Threshold analysis

Results for fixed thresholds α = 0.7, β = 0.3.

Year C1 C2 C4 C5 C6 C7 C8 C9 C11 C12 Rel Uniq

2008–2009 8 8 8 8 8 0 8 8 8 8 36 9

2009–2010 8 7 8 8 8 0 6 8 7 8 34 9

2010–2011 8 5 5 7 7 0 2 6 7 7 27 9

2011–2012 7 5 1 6 7 1 3 7 7 6 25 10

2012–2013 9 5 6 7 8 3 4 8 7 7 32 10

2013–2014 9 5 3 7 7 4 3 7 7 6 29 10

Observations on thresholds

• General observations• 3 pillars, ‘3. Macroeconomic stability’, ‘7. Labor market

efficiency’ and ‘10. Market size’ tend to avoid positive consonances with the rest pillars.

• Under a certain value for threshold α (respectively, above a certain value for threshold β), all pillars start correlating, which is ineffective. (9/12 at α = 0.775).

• Analysing data for too few pillars in positive consonance is not effective either (2/12 or 3/12 at α = 0.85).

• It is useful to focus on (0.775; 0.225) to (0.825; 0.175).

• Specific observations• Pillar ‘7. Labor market efficiency’ starts correlating with

the rest pillars only after year 2011–2012, and only in the low values of α from 0.7 to 0.75.

• Pillar ‘8. Financial market sophistication’ after year 2009–2010 tends to be more weakly correlated.

• Pillars ‘11. Business sophistication’ and ‘12. Innovation’ have shown the greatest and most stable positive consonance between each other, as well as with the other pillars.

Temporal analysis

α β C1 C2 C4 C5 C6 C7 C8 C9 C11 C12 Rel Uniq

0.85 0.153 0 0 1 1 0 0 1 1 3 5 6

0.825 0.1753 0 0 1 1 0 0 2 1 4 6 6

0.8 0.25 1 0 3 1 0 0 3 5 4 11 7

0.775 0.2255 3 0 4 2 0 0 6 5 5 15 7

0.75 0.255 3 0 4 4 0 0 6 6 6 17 7

0.725 0.2758 4 1 7 6 0 2 6 6 6 23 9

0.7 0.39 5 3 7 7 4 3 7 7 6 29 10

Results for fixed year 2013–2014.

Observations on pillars in time

• After pillars 11 and 12, pillar ‘1. Institutions’ is the third most correlating criterion. 4th and 5th best are pillars ‘9. Technological readiness’ and ‘6. Goods market efficiency’.

• With (α; β) running from (0.8; 0.2) to (0.7; 0.3), the positive consonances of pillar ‘2. Infrastructure’ gradually fall in time.

• Pillar ‘8. Financial market sophistication’ was in positive consonances with α > 0.75 only in years 2008–2010.

• Pillar ‘5. Higher education and training’ shows higher levels of positive consonance than pillar ‘4. Health and primary education’ for different runs of (α; β).

• Pillar ‘7. Labor market efficiency’ starts exhibiting only in 2013-2014 for α > 0.75.

What needs to be done?

• A more detailed and profound analysis of these data should be done by professional economists, taking into consideration various factors like – beginning of the world financial crisis, – accession of new Member States to the European Union, – certain changes in legislation,– technological breakthroughs.

• In some pillars, effects should only be expected to occur after certain periods of time, which makes it necessary to continue the present research.

InterCriteria Decision MakingApproach to EU Member States

Competitiveness Analysis:Trend Analysis

Vassia AtanassovaLyubka Doukovska

Dimitar KarastoyanovFrantišek Čapkovič

7th International IEEE Conferenceon Intelligent Systems24–26 September 2014, Warszawa

Next step: Defining the IF thresholds

• How to determine the thresholds α, β?– In previous research we took some predefined pairs

like (0.85; 0.15), (0.8; 0.2), (0.75; 0.25) …– Problem: when β = 1 – α, results are ‘incomparable’:• When (α, β) = (0.85; 0.25), α yields 2 pairs, β yields 19• When (α, β) = (0.80; 0.20), α yields 11 pairs, β yields 29• …• When (α, β) = (0.65; 0.35), α yields 39 pairs, β yields 51

– We need to find such α, β so that they yield similar results. And if we fix α, what should β be?

• How to determine the thresholds α, β?• Our problem needs reformulation:

If the decision maker wishes to focusonly on the k most positively correlated criteria

out of the totality of n criteria, what valuesof the thresholds α and β shall he/she select?

• Reminder: This problem statement is in line with WEF’s address to policy-makers to: ‘identify and strengthen the transformative forcesthat will drive future economic growth’’

Proposed solution

µ 1 2 3 4 5 6 7 8 9 10 11 12

1 0.735 0.577 0.720 0.807 0.836 0.733 0.749 0.854 0.503 0.804 0.844

2 0.735 0.479 0.661 0.749 0.677 0.537 0.590 0.786 0.661 0.804 0.799

3 0.577 0.479 0.421 0.519 0.558 0.627 0.675 0.550 0.413 0.548 0.556

4 0.720 0.661 0.421 0.730 0.683 0.590 0.563 0.677 0.497 0.712 0.690

5 0.807 0.749 0.519 0.730 0.735 0.622 0.632 0.775 0.579 0.815 0.847

6 0.836 0.677 0.558 0.683 0.735 0.749 0.712 0.788 0.466 0.759 0.751

7 0.733 0.537 0.627 0.590 0.622 0.749 0.741 0.685 0.399 0.624 0.624

8 0.749 0.590 0.675 0.563 0.632 0.712 0.741 0.712 0.497 0.688 0.680

9 0.854 0.786 0.550 0.677 0.775 0.788 0.685 0.712 0.526 0.810 0.831

10 0.503 0.661 0.413 0.497 0.579 0.466 0.399 0.497 0.526 0.611 0.598

11 0.804 0.804 0.548 0.712 0.815 0.759 0.624 0.688 0.810 0.611 0.873

12 0.844 0.799 0.556 0.690 0.847 0.751 0.624 0.680 0.831 0.598 0.873

C i

1 0.8542 0.8043 0.6754 0.7305 0.8476 0.8367 0.7498 0.7499 0.854

10 0.66111 0.87312 0.873

,max ( , )i j

j j iC C

C i

1 0.8542 0.8043 0.6754 0.7305 0.8476 0.8367 0.7498 0.7499 0.854

10 0.66111 0.87312 0.873

,max ( , )i j

j j iC C

Sort by value(descending for α )

C i

11 0.87312 0.873

1 0.8549 0.8545 0.8476 0.8362 0.8047 0.7498 0.7494 0.733 0.675

10 0.661

,max ( , )i j

j j iC C

C i

11 0.87312 0.873

1 0.8549 0.8545 0.8476 0.8362 0.8047 0.7498 0.7494 0.733 0.675

10 0.661

,max ( , )i j

j j iC C

Number of

correlating criteria

Number of pairs of correlating

criteria

Criteria ordered by

positive consonance

True when α ≥

2 1 11 0.873 12

4 2 1 0.854 9

5 3 5 0.847 6 11 2 0.804 7 13 6 0.788 9 20 7 0.749

8 10 25 4 0.730 11 37 3 0.675 12 39 10 0.661

k = 4

Number of



criteria

Criteria ordered by

positive consonance

True when α ≥

2 1 11 0.873 12

4 2 1 0.854 9

5 3 5 0.847 6 11 2 0.804 7 13 6 0.788 9 20 7 0.749

8 10 25 4 0.730 11 37 3 0.675 12 39 10 0.661

Number of



criteria

Criteria ordered by negative

consonance

True when β ≤

2 1 11 0.071 12

4 2 1 0.077 6

5 3 5 0.079 6 4 9 0.09 8 13 2 0.135

7 9 17 4 0.143

10 19 8 0.146 11 38 3 0.251 12 45 10 0.286

k = 4

Some calculations

• Results for year 2008–2009

Number of correlating

criteria


criteria

Criteria ordered by

positive consonance

True when α ≥


criteria

Number of pairs of



consonance

True when β ≤

2 1 11 0.860 2 1 1 0.077 12 6

4 2 1 0.844 4 2 11 0.079 2 12

5 3 6 0.833 5 3 8 0.09 6 5 8 0.828 6 4 9 0.095 7 6 9 0.823 8 5 4 0.108 8 14 5 0.796 5 9 18 4 0.780 9 8 2 0.114

10 37 3 0.693 11 35 3 0.204 11 41 7 0.664 7 12 45 10 0.648 12 54 10 0.307

• Results for year 2013–2014


criteria


criteria

Criteria ordered by

positive consonance

True when α ≥


criteria

Number of pairs of



consonance

True when β ≤

2 1 11 0.873 2 1 11 0.071 12 12

4 2 1 0.854 4 2 1 0.077 9 6

5 3 5 0.847 5 3 5 0.079 6 11 2 0.804 6 4 9 0.090 7 13 6 0.788 8 13 2 0.135 9 20 7 0.749 7

8 9 17 4 0.143 10 25 4 0.730 10 19 8 0.146 11 37 3 0.675 11 38 3 0.251 12 39 10 0.661 12 45 10 0.286

• Results for period 2008–2014


criteria


criteria

Criteria ordered by

positive consonance

True when α ≥


criteria

Number of pairs of



consonance

True when β ≤

2 1 11 0.836 2 1 11 0.091 12 12

4 2 1 0.821 4 2 1 0.092 6 6

6 5 5 0.804 5 3 5 0.109 9 6 4 9 0.124

7 7 2 0.789 7 8 4 0.139 8 18 8 0.745 8 9 2 0.144 9 21 4 0.725 9 18 8 0.163

10 25 7 0.693 10 26 7 0.190 11 34 3 0.672 11 34 3 0.239 12 44 10 0.622 12 48 10 0.306

Next step: Interconnected criteria

• Can we detect some dependences between the increase of the threshold values and the interconnectedness between the correlating criteria?– Interconnectedness / Density / Homogeneity

• This will give another way of determining the threshold values: No need to shortlist k out of n criteria, but select with the “most strongly correlating criteria”, no matter their number.

Fig. 1. Results for year 2008–2009.






0.4

0.6

0.8

1.0

0 10 20 30 40 50 600.4

0.6

0.8

1.0

0 10 20 30 40 50 600.4

0.6

0.8

1.0

0 10 20 30 40 50 60

0.4

0.6

0.8

1.0

0 10 20 30 40 50 600.4

0.6

0.8

1.0

0 10 20 30 40 50 600.4

0.6

0.8

1.0

0 10 20 30 40 50 60

• On this basis we can conclude that for year 2013‒2014, we can see that four groups of criteria are formed:

• 5 strongly correlating, with from 0.847 to 0.873: ‘11. Business sophistication’, ‘12. Innovation’, ‘1. Institutions’, ‘9. Technological readiness’ and ‘5. Higher education and training’;

• 2 weakly correlating, with from 0.788 to 0.804:‘2. Infrastructure’ and ‘6. Goods market efficiency’;

• 3 weakly non-correlating, with from 0.730 to 0.749: ‘7. Labor market efficiency’, ‘8. Financial market sophistication’and ‘4. Health and primary education’; and

• 2 strongly non-correlating, with from 0.661 to 0.675: ‘3. Macroeconomic stability’ and ’10. Market size’.

• With the data from this case, involving 12 criteria only, the decision maker can easily make the above observation without further calculations or application of other sophisticated methods.

• In cases involving a much greater number of criteria, application of cluster analysis methods may prove unavoidable.

The bigger picture: Trends

Combined results for the years 2008–2014, based on dependencies between number of pairs in correlation (axis x) and level of positive consonance (axis y).

Positive consonance

Linear function: y1 = ‒0.0051x + 0.85916th order polynomial: y2 = 9e‒10x6 ‒ 1e‒7x5 + 8e‒6x4 ‒ 0.0002x3 + 0.0028x2 ‒ 0.0203x + 0.8822

Positive consonance

Combined results for the years 2008–2014, based on dependencies between number of pairs in correlation (axis x) and level of negative consonance (axis y).

Negative consonance

Negative consonance

Linear function: y3 = 0.0042x + 0.07516th order polynomial: y4 = ‒3e‒12x6 ‒ 4e‒10x5 ‒ 6e‒8x4 + 1e‒5x3 ‒ 0.0004x2 + 0.009x + 0.0658

Conclusions

• In the present work, we show that taking into consideration the proximity between the InterCriteria exhibited consonance is another approach for selecting the desired subset of criteria different from:– either taking predefined values of the thresholds α and β,– or shortlisting the first k out of n criteria

• In some applications it may prove more appropriate.• Further research has potential to reveal more

knowledge about the nature of the evaluation criteria involved and their development in future.

References

• Atanassov, K. (1986) Intuitionistic fuzzy sets. Fuzzy Sets and Systems. Vol. 20 (1), pp. 87–96.• Atanassov K. (1991) Generalized Nets. World Scientific, Singapore.• Atanassov, K. (1999) Intuitionistic Fuzzy Sets: Theory and Applications. Physica-Verlag,

Heidelberg.• Atanassov, K. (2012) On Intuitionistic Fuzzy Sets Theory. Springer, Berlin.• Atanassov K., D. Mavrov, V. Atanassova (2013). InterCriteria decision making. A new approach

for multicriteria decision making, based on index matrices and intuitionistic fuzzy sets. Proc. of 12th International Workshop on Intuitionistic Fuzzy Sets and General ized Nets, 11 Oct. 2013, Warsaw, Poland (in press).

• Atanassova, V., D. Mavrov, L. Doukovska, K. Atanassov, (2014) Discussion on the threshold values in the InterCriteria Decision Making Approach. Notes on Intuitionistic Fuzzy Sets, Vol. 20, No. 2, 94–99.

• Atanassova, V., L. Doukovska, K. Atanassov, D. Mavrov (2014) InterCriteria Decision Making Approach to EU Member States Competitiveness Analysis. Proc. of 4th Int. Symp. on Business Modelling and Software Design, Luxembourg, 24–26 June 2014, pp. 289–294.

• World Economic Forum (2008–2013). The Global Competitive ness Reports. http://www.weforum.org/issues/global-competitiveness.

Thank you!

18th International Conferenceon Intuitionistic Fuzzy Sets10-11 May 2014, Sofia

The research work is partly supportedby the project AComIn

“Advanced Computing for InnovationGrant 316087, funded by the

FP7 Capacity Programme

intercriteria decision making approach to eu member states competitiveness analysis: temporal and...

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