the hierarchical smaa-promethee method applied to ......cities in the 2012-2015 period, taking into...
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https://doi.org/10.1007/s10489-021-02384-5
The hierarchical SMAA-PROMETHEEmethod applied to assessthe sustainability of European cities
Salvatore Corrente1 · Salvatore Greco1,2 · Floriana Leonardi1 · Roman Słowinski3,4
Accepted: 24 March 2021© The Author(s) 2021
AbstractMeasuring the level of sustainability taking into account many contributing aspects is a challenge. In this paper, weapply a multiple criteria decision aiding framework, namely, the hierarchical-SMAA-PROMETHEE method, to assess theenvironmental, social, and economic sustainability of 20 European cities in the period going from 2012 to 2015. Theapplication of the method is innovative for the following reasons: (i) it permits to study the sustainability of the mentionedcities not only comprehensively but also considering separately particular macro-criteria, providing in this way more specificinformation on their weak and strong points; (ii) the use of PROMETHEE and, in particular, of PROMETHEE II, avoidsthe compensation between different and heterogeneous criteria, that is arbitrarily assumed in value function aggregationmodels; finally, (iii) thanks to the application of the Stochastic Multicriteria Acceptability Analysis, the method providesmore robust recommendations than a method based on a single instance of the considered preference model compatible withfew preference information items provided by the Decision Maker.
Keywords Sustainability · Cities · Hierarchy of criteria · Non-compensatory aggregation · PROMETHEE II ·Robustness concerns
This article belongs to the Topical Collection: 30th AnniversarySpecial Issue
� Roman Sł[email protected]
Salvatore [email protected]
Salvatore [email protected]
Floriana [email protected]
1 Department of Economics and Business, Universityof Catania, Corso Italia, 55, 95129, Catania, Italy
2 Centre of Operations Research and Logistics (CORL),University of Portsmouth, Portsmouth Business School,Richmond Building, Portland Street, Portsmouth,PO1 3DE, United Kingdom
3 Institute of Computing Science, Poznan Universityof Technology, 60-965, Poznan, Poland
4 Systems Research Institute, Polish Academy of Sciences,01-447, Warsaw, Poland
1 Introduction
Nowadays cities are considered as the most important factorof environmental pollution and, as acknowledged by [54],although urban spaces are only 2% of the earth’s surface,they consume 60-80% of all goods. Consequently, overthe years many different objectives have been defined toreduce the pollution produced by cities and to make themdevelop concerning the environment. This is also the reasonfor which on September 25, 2015, the Agenda 2030 hasspecified, among the others, the sustainable developmentgoal (SDG) 11 regarding cities [1]. Therefore, the evaluationof the level of sustainability of cities became a crucialissue.
Even if there is no univocal definition of the termsustainability, three main types of sustainability arecommonly considered: environmental, economic, and social[39, 45]. Because the level of sustainability is measuredby means of several indicators, studying the sustainabilityof cities at both comprehensive and partial level can beconsidered a typical Multiple Criteria Decision Aiding(MCDA; [29]) problem [37].
/ Published online: 22 April 2021
Applied Intelligence (2021) 51:6430–6448
In this paper, we would like to promote the use ofa method recently proposed in the literature, called thehierarchical-SMAA-PROMETHEE method [3], to evaluatethe sustainability of cities but that can analogously beapplied to countries or regions. To this aim, we appliedthe method to study the sustainability of 20 Europeancities in the 2012-2015 period, taking into account 9different indicators grouped in three macro-criteria, that is,environmental, economic, and social. The method combinesthree MCDA methodologies, namely, the Multiple CriteriaHierarchy Process [16], the PROMETHEE II method [7],and the Stochastic Multicriteria Acceptability Analysis[34], taking advantage of their main potentialities. Thismethodological combination is innovative and yields anadded value to be shown by this study. The benefitsresulting from the application of the hierarchical-SMAA-PROMETHEE method in the considered context are thefollowing:
• The use of the PROMETHEE methods and, inparticular, of PROMETHEE II, permits to aggregate theevaluations on multiple criteria avoiding compensationbetween them. Indeed, following [38], in measuringsustainability “compensability should be avoided”.Moreover, PROMETHEE II provides a completeranking of the alternatives, permitting to define theposition got by each city.
• The use of the MCHP permits to get the rankinginformation not only at the comprehensive level butalso at environmental, economic, and social levels.In this way, by integrating the MCHP with thePROMETHEE II method one can rank-order the citiesnot only comprehensively, but also with respect to eachindividual macro-criterion, learning in this way whichare their weak and strong points.
• The use of SMAA permits to provide robust recom-mendations concerning the considered sustainabilityevaluation. Indeed, instead of choosing a single vectorof weights corresponding to the nine indicators, SMAAgives the possibility of ranking the considered citiesat both comprehensive and partial levels using a bigset of possible vectors of weights. The output infor-mation provided by SMAA is presented in statisticalterms specifying the probability with which a city getsa certain rank position or the frequency with which acity is preferred to another one. This statistical infor-mation can then be used to obtain a robust ranking ofthe considered cities at both comprehensive and partiallevels.
The paper is organized as follows: in the next Section,we shall briefly review the literature on sustainabilityevaluation of cities, countries, and regions; In Section 3,we remind the methodological background including, in
particular, the three methods composing the hierarchical-SMAA-PROMETHEE method. In Section 4, we applythe proposed method to evaluate the sustainability of 20European cities at both comprehensive and partial levels,showing the potential of the method; finally, in Section 5,we make conclusions and indicate some future researchdirections.
2 Literature review
The number of papers presenting applications of MCDAmethods to assess sustainability in different fields is quitelarge (see, for example, [15, 22, 24, 55, 62]). In thefollowing, without any ambition of being exhaustive, wereview a few of these papers regarding the sustainabilityevaluation of cities, countries, and regions. As will becomeevident later, they differ for the type of sustainability tobe studied, the chosen indicators, and the method used toperform the aggregation of the alternatives’ performances[57].
Munda and Saisana [39] compared 25 regions inthe Mediterranean area (17 Spanish, 4 Italian, and 4Greek) based on 29 indicators representing economic,social, and environmental aspects. Compensatory and non-compensatory aggregations have been used to underline thatthe obtained results depend on the chosen method; DataEnvelopment Analysis (DEA; [12]) has also been used tostudy the efficiency of the same regions.
Phillis et al. [44] evaluated the sustainability of 106 citiesand megacities all over the world by a fuzzy model calledSAFE (Sustainable Assessment by Fuzzy Evaluation). Thesustainability of these cities has been studied based on 46indicators belonging to two macro-input, that is, ecologyand well-being. A sensitivity analysis has been performedto highlight which indicators influence more the degree ofsustainability of the considered cities. The same model hasbeen used to compare the sustainability of 128 countriesconsidering 75 indicators in [43].
Using an intuitionistic fuzzy approach, [23] assessedthe environmental sustainability of 27 U.S. and Canadianmetropoles. 16 sustainability indicators were taken intoaccount in the paper while the analysis was performedbased on experts’ judgments used to assign weights to theseindicators.
Chen and Zhang [13] studied the sustainability of14 Chinese cities in Liaoning province considering 21indicators grouped in economic, social end environmentalmacro-criteria in the 2013-2017 period. Interaction betweenindicators, distinguished in static interaction and dynamictrend similarity, has been taken into account. Afternormalizing the evaluations of the cities by the min −max normalization, the IOWA (Induced Ordered Weighted
6431The hierarchical SMAA-PROMETHEE method applied...
Averaging; [63]) operator has been used to aggregate them;the IOWA operator has also been applied in [65] to analyzethe sustainable development of 13 Chinese cities in the2011-2016 period. To this aim, 18 criteria concerningeconomic, social, and environmental aspects have beentaken into account. Weights assigned to the differentindicators were used to express their interdependence.
Deng et al. [21] assessed the sustainability of four large-sized Chinese cities (Beijing, Chongqing, Shanghai, andTianjin) in three different years (2005, 2010, and 2015).The evaluations of the cities on 18 indicators divided intofour macro-areas have been aggregated by the arithmeticmean after the min − max normalization. The samepreference model has been used by [5] to evaluate thesustainability of 92 municipalities located in the Umbriaregion (Italy), using 18 indicators (9 environmental and 9socio-economic). After putting all evaluations in the [0,1]interval by a standardization method, trade-off weightsnecessary to apply in the weighted sum have been obtainedusing the SWING method [61].
Yi et al. [64] evaluated the sustainability of 14 citiesin the Lianoling province of China in the 2011-2016period. A weighted sum has also been used in this caseto aggregate the evaluations of the considered cities on 21indicators using equal weighting. By stochastic simulations,the authors forecasted also the sustainability of the samecities in the following years.
The sustainability of 4 metropolitan areas (Bari, Bitonto,Mola, and Molfetta) in the south of Italy has been studiedby [10]. The AHP method [51] has been applied to the dataset composed of 35 indicators belonging to seven differentdimensions; AHP has been used in [20] and [46] as well. Onthe one hand, [20] evaluated the sustainability performanceof the 28 European countries from environmental andenergetic perspectives considering 9 indicators; on the otherhand, [46] proposed an approach aiming to assess thesustainability and livability of cities based on cognitivemapping. The analysis took into consideration 6 macro-criteria.
Zhang et al. [66] evaluated the sustainability of 13Chinese cities in the Jiangsu province with respect to30 indicators by using the Choquet integral [14]. Theevaluations of the considered cities have been normalizedby the min-max normalization, and then aggregatedconsidering weights assigned to the indicators and allpossible coalitions of criteria, objectively based on the dataat hand and, therefore, without any judgment of the DecisionMaker (DM). The Choquet integral has also been used inconjunction with cognitive mapping by [8] and [11]. In thefirst paper, the “greenness” of 20 Portuguese cities has beenevaluated, while, in the second, the “smartness” of the same
20 Portughese cities with respect to 6 macro-criteria hasbeen analyzed.
Evaluation of the urban sustainable development of16 Chinese cities in Anhui province has been performedbased on 39 indicators divided into economic, social, andenvironmental in [56]. The evaluations of the cities on theconsidered indicators have been computed by an integratedframework composed of the TOPSIS method [31] and thegrey relational analysis, while weights of criteria have beenobtained by the entropy method [67].
Paolotti et al. [41] assessed the sustainability level ofthe 20 Italian regions and the 17 Spanish autonomouscommunities on the basis of 18 indicators belonging toeconomic, social, and environmental macro-criteria. Theanalysis has been performed based on the preferences of 8experts (4 from Italy and 4 from Spain), while the resultshave been obtained by the GeoUmbriaSUIT [6] whichintegrates GIS and MCDA [35]. In particular, TOPSIS was usedagain as a preference model, while the weights necessary toapply the method have been obtained by SWING.
Antanasijevic et al. [2] measured the sustainability of 30European countries in the 2004-2014 period. The analysisinvolved 38 indicators grouped into 8 subgroups. Theauthors applied PROMETHEE II as a preference modeland provided a ranking of the considered countries for theperiod 2004-2014 and two shorter periods, being 2004-2009and 2010-2014, respectively. Analogously, PROMETHEEII has been used to assess the sustainable energy transitionreadiness level of 14 countries belonging to all continentsby [40]. 8 indicators have been considered in the studyand AHP has been used to get the weights of indicatorsnecessary to apply the PROMETHEE II method, which isadmittedly not a correct combination [48].
Finally, [52] applied ELECTRE III [25] to evaluate thesustainability of some megacities, such as New York andLos Angeles, considering their evaluations on 12 indicatorsbelonging to environmental, economic, social, and smartmacro-criteria.
The above literature review shows that in the performedstudies there was no MCDA method permitting at the sametime to consider sustainability of the cities at the globallevel as well as at the level of macro-criteria, using a non-compensatory aggregation, taking into account preferenceinformation expressed by the DM in an indirect way, andproviding robust recommendations following from not onlyone but a plurality of instances of the assumed preferencemodel compatible with available preference information.Therefore, in this paper, we would like to fill this gapin the literature by applying the hierarchical SMAA-PROMETHEE method addressing all the mentioned issuessimultaneously.
6432 S. Corrente et al.
3Methodological background
In this Section, we shall recall briefly the methods com-posing the hierarchical-SMAA-PROMETHEE method thatwill be applied in the considered case study, namely thePROMETHEE II (Section 3.1), the Multiple Criteria Hier-archy Process (Section 3.2), and the Stochastic MulticriteriaAcceptability Analysis (Section 3.3).
3.1 Multiple criteria decision aiding and thePROMETHEE II method
Multiple Criteria Decision Aiding (MCDA; [29]) methodsare designed to deal with ranking, choice, or sortingproblems. In this paper, we are interested in the rankingsince we aim to order several European cities from thebest to the worst with respect to their sustainability atboth comprehensive and partial levels, that is, economic,social, and environmental. In the following, by A we shalldenote the set of alternatives {a, b, c, . . .} and by G theset of m criteria {g1, . . . , gm} on which the alternatives areevaluated. For the sake of simplicity and without loss ofgenerality, we assume that each criterion gj is a real-valuedfunction, that is, gj : A → R, and that it has an increasingdirection of preference (the more gj (a), the better is a ongj ).
Considering the performance matrix being composed ofthe evaluations of the cities on the criteria at hand, the onlyobjective information that can be obtained is the dominancerelation D, such that for all a, b ∈ A, gj (a) � gj (b)
for all gj ∈ G and there is at least one gj ∈ G suchthat gj (a) > gj (b). The objectivity of this relation iscounterbalanced by its poverty, since in most of the casesneither a dominates b nor vice versa, which means thatmany alternatives are non-comparable by the dominancerelation. To make the alternatives more comparable, anaggregation method has to be used summarizing theinformation included in the performance matrix on onehand, and preference information provided by the DM onthe other hand. Historically, three different aggregationmethodologies have been considered: (i) value functionmethods belonging to Multiple Attribute Value Theory(MAVT; [33]), (ii) methods based on outranking relations,such as ELECTRE [25, 26] and PROMETHEE [4, 7], and(iii) methods based on induction of decision rules [27].In this paper, we will aggregate the evaluations of thealternatives on the considered criteria by using the secondapproach and, in particular, the PROMETHEE II method.We recall this method below.
PROMETHEE II builds a complete order of thealternatives at hand based on their comparison through thenet flow. The net flow of each alternative a is computed inthe following steps:
1. For each criterion gj and each pair of alternatives(a, b) ∈ A × A, the preference function Pj (a, b)
is computed first. It is a non-decreasing function ofthe difference gj (a) − gj (b) expressing the degreeof preference of a over b on gj . Six different typesof function Pj (a, b) have been defined by [7]. Themost frequently used is the V-shape function withindifference zone, defined as follows:
Pj (a, b) =
⎧⎪⎨
⎪⎩
0 if gj (a) − gj (b) � qj ,[gj (a)−gj (b)]−qj
pj −qjif qj < gj (a) − gj (b) < pj ,
1 if gj (a) − gj (b) � pj .
Pj (a, b) ∈ [0, 1] and, the greater Pj (a, b), the moregj is in favor of the preference of a over b. In thedefinition of Pj (a, b), qj and pj are, respectively, theindifference and the preference thresholds related to gj
(see [50]). They are such that 0 � qj < pj and qj isthe maximum difference between evaluation gj (a) andevaluation gj (b) compatible with their indifference ongj , while, pj is the minimum difference between gj (a)
and gj (b) compatible with the preference of a over b
on this criterion.2. For each (a, b) ∈ A×A, the preference function π(a, b)
is computed:
π(a, b) =m∑
j=1
wj · Pj (a, b)
where wj > 0 is a relative importance weight assigned
to criterion gj , j = 1, . . . m, such thatm∑
j=1
wj = 1.
Also π(a, b) ∈ [0, 1] and the greater π(a, b) the morea is preferred to b.
3. For each a ∈ A, the positive flow φ+(a), the negativeflow φ−(a) and the net flow φ(a) are computed:
φ+(a) = 1
|A| − 1
∑
b∈A\{a}π(a, b), φ−(a)
= 1
|A| − 1
∑
b∈A\{a}π(b, a), φ(a) = φ+(a) − φ−(a).
On the one hand, φ+(a) measures how much, inaverage, a is preferred to all other alternatives;consequently, the greater φ+(a), the better a. On theother hand, φ−(a) measures how much, in average, theother alternatives are preferred to a; consequently, thegreater φ−(a), the worse a. Finally, φ(a) provides abalance between the positive and the negative flowsand it represents the relative quality of a in the set ofalternatives A.
Based on the net flow of each alternative, PROMETHEEII builds a preference P II and an indifference I II relation,such that:
6433The hierarchical SMAA-PROMETHEE method applied...
• aP II b iff φ(a) > φ(b);• aI II b iff φ(a) = φ(b).
The above two relations constitute a weak order (P II andI II are transitive and P II ∪ I II is reflexive and complete;see. e.g., [47]) in the set of alternatives, so one gets a rankingrecommendation from the best to the worst alternative withpossible ex-aequo.
3.2 Themultiple criteria hierarchy process
In real-world applications of MCDA, the evaluation criteriaare not always considered at the same level but they arestructured hierarchically. This means that it is possibleto distinguish a root criterion being the comprehensiveobjective of the problem, some macro-criteria descendingfrom the root criterion hierarchically, until the elementarycriteria being placed at the bottom of the hierarchy tree.The basic evaluations of the alternatives are made onthe elementary criteria only, and they are aggregated tomacro-criteria up the hierarchy tree, until the comprehensivecriterion.
To deal with such a hierarchical structure of the familyof criteria in MCDA, the Multiple Criteria HierarchyProcess (MCHP) has been proposed in [16]. In particular,its application to the PROMETHEE methods has beenpresented in [17]. The integration of the MCHP and thePROMETHEE II method permits to define a preferenceand an indifference relation not only at the comprehensivelevel (that is, at the root criterion level) but also at partiallevels that correspond to macro-criteria (that is, at particularnodes of the hierarchy tree). To describe the integration ofPROMETHEE II with MCHP, we shall use the followingnotation: gt represents an elementary criterion, while theset of indices of elementary criteria is denoted by EL;gr represents a generic macro-criterion in the hierarchy,while E(gr) is a subset of EL composed of the indicesof elementary criteria descending from gr. In particular, g0represents the root-criterion. For the sake of simplicity andwithout loss of generality we assume that macro-criteria,as well as elementary criteria, can descend from only onemacro-criterion at the level above (see [17] for more detailson this point).
To adapt the PROMETHEE II method to the MCHP, it isenough to perform the following replacements in steps 1–3presented in the previous Subsection:
1→1’. The preference function Pj (a, b) that was definedfor each criterion gj and for each ordered pair ofalternatives (a, b) ∈ A × A has now to be defined foreach elementary criterion gt and for each ordered pair ofalternatives (a, b); of course, if the V-shape is the usedpreference function, indifference qt and preference pt
thresholds have to be defined for each gt, t ∈ EL.
2→2’. After a weight wt is assigned to each elementarycriterion gt, t ∈ EL, so that wt > 0 for all t ∈ EL
and∑
t∈EL
wt = 1, for each macro-criterion gr, the partial
preference function πr(a, b) is defined for each orderedpair of alternatives (a, b) ∈ A × A as follows:
πr(a, b) =∑
t∈E(gr)
wt · Pt(a, b).
Of course, πr(a, b) ∈⎡
⎣0,∑
t∈E(gr)
wt
⎤
⎦ and, the greater
πr(a, b), the more a is preferred to b on gr.3→3’. For each alternative a ∈ A and for each macro-
criterion gr, the partial positive, negative, and net flowsare defined as follows:
φ+r (a) = 1
|A| − 1
∑
b∈A\{a}πr(a, b),
φ−r (a)= 1
|A| − 1
∑
b∈A\{a}πr(b, a), φr(a) = φ+
r (a) − φ−r (a).
Based on the net flows, a marginal preference relation P IIr
and a marginal indifference relation I IIr are defined for each
macro-criterion gr as follows:
• aP IIr b ⇔ φr(a) > φr(b);
• aI IIr b ⇔ φr(a) = φr(b).
3.3 Stochastic multicriteria acceptability analysis
As described in the previous Subsection, the application ofPROMETHEE II involves that the weights of elementarycriteria wt, as well as the indifference qt and preferencethresholds pt, have to be specified by the DM. Assumingthat the discriminating thresholds are technical, and assuch, they are fixed, the final ranking recommendation atboth comprehensive level and partial levels depends on thechoice of the weights wt. Indeed, different values of wt
imply, in general, different values of the positive, negative,and net flows and, consequently, different relations betweenthe considered alternatives. To avoid a single, and thereforeto some extent arbitrary, choice of weights, [19] proposedthe SMAA-PROMETHEE method, later extended to thehierarchical-SMAA-PROMETHEE method by [3]. Thehierarchical-SMAA-PROMETHEE method integrates theStochastic Multicriteria Acceptability Analysis (SMAA) inthe hierarchical PROMETHEE II method (see [34] for thepaper introducing SMAA and [42] for a recent survey of theSMAA applications). As result, one gets a recommendationin statistical terms specifying the probability with which analternative gets a particular position in the ranking or on theprobability with which an alternative is preferred to anotherone at the comprehensive and partial levels. Such a ranking
6434 S. Corrente et al.
recommendation is more robust than the ranking obtainedfor a single vector of weights.
Defining by W ={
(w1, . . . , w|EL|
) ∈ R|EL|+ :
∑
t∈EL
wt = 1
}
the
whole space of vectors of weights and by WDM the subsetof W composed of the vectors of weights compatible withsome preferences provided by the DM, the application ofSMAA starts sampling several weights vectors from WDM .The hierarchical-PROMETHEE II method is then appliedfor each (w1, . . . , w|EL|) ∈ WDM getting a preference andan indifference relation at both comprehensive and partiallevels. Based on these computations, the following indicesare then obtained:
• The rank acceptability index bkr (a): it is the probability
with which an alternative a reaches the kth position inthe ranking corresponding to criterion gr,
• The pairwise winning index pr(a, b): it is the probabil-ity with which alternative a is preferred to alternative b
on gr. Of course, based on pr(a, b) and pr(b, a) the fre-quency of indifference between a and b on gr can alsobe computed as 1 − pr(a, b) − pr(b, a).
3.4 The SMAA-PROMETHEEmethod in detail
In this Section, we shall present in detail the different stepsof the SMAA-PROMETHEE method summarized in theflow chart in Fig. 1.
Step 0: The set of criteria to be taken into accountin the problem are structured hierarchically: a rootcriterion being representative of the problem itself is
defined, as well as few macro-criteria descending from it,continuing down until the elementary criteria on whichthe alternatives will be evaluated and that are located atthe bottom of the hierarchy tree.
Step 1: In this step, the DM is asked to provide somepreference information:
Step 1.1: With the help of the analyst, all technicalparameters are fixed. These regard selection ofthe shape of the preference function Pt(·, ·) foreach elementary criterion gt that, as mentioned inSection 3.1, can be of six different types, as wellas indifference qt and preference pt thresholds foreach gt if the V-shape with indifference is assumed aspreference function,
Step 1.2: The DM elicits some preference informationby comparing criteria in terms of their importance(for example, “gr1 is more important than gr2”or “gr1 and gr2 have the same importance”, etc.)or comparing some alternatives pairwise in termsof preference (for example, “a is preferred to b”or “a and b are indifferent”, etc.). These piecesof preference information are translated into linearconstraints involving the weights of the elementarycriteria and, therefore, reducing the space W of thecompatible weights vector giving rise to the WDM
space.
Step 2: The analyst checks if the preference informationprovided by the DM is consistent, that is, if there existsat least one instance of the assumed preference model(the PROMETHEE II in our case) compatible with the
Fig. 1 Flow chart of the steps ofthe SMAA-PROMETHEEmethod
6435The hierarchical SMAA-PROMETHEE method applied...
Fig. 2 Criteria considered in thecase study and structured in ahierarchical way
preferences provided by the DM. We shall call suchan instance compatible model in the following. If thereexists at least one compatible model and, therefore,WDM �= ∅, one can pass to step 3, otherwise the DM,with a help of the analyst, has to check the cause of theincompatibility and to resolve it in the revised preferenceinformation [36].
Step 3: A certain number of compatible models issampled by means of, e.g., the Hit-And-Run method [53,59] (to have an idea of the number of compatible modelsthat need to be sampled to get a certain precision in theobtained results, see [58]).
Step 4: Apply the hierarchical-PROMETHEE II methodfor each sampled vector of weights obtaining, therefore,a complete ranking of the alternatives at hand both atthe comprehensive level as well as for each consideredmacro-criterion.
Step 5: Based on the rankings obtained in the previousstep, the SMAA methodology is applied to compute theindices presented in Section 3.3, that is, the rank accept-ability index of each alternative on each rank position,and the pairwise winning index between two alternatives.Both indices can be computed at comprehensive and atpartial levels. The rank acceptability indices of the alter-natives can also be aggregated to obtain a final rankingof the alternatives at hand, as will be shown in the nextSection.
4 Case study
In this Section, we shall apply the hierarchical-SMAA-PROMETHEE method to assess the sustainability of 20European cities in the period 2012-2015 at a comprehensivelevel as well as at Environmental (ENV), Economic (ECO),and Social (SOC) ones. Comprehensively, 9 elementarycriteria have been taken into account, three for eachmacro-criterion at hand. In particular, Passenger Cars (PC),Amount of Waste Generated (AWG), and CO2 emissions(CO2) are elementary criteria of ENV ; Employment Rate(ER), Unemployment Rate (UR), and GDP per capita(GDP) are elementary criteria descending from ECO;finally, Percentage of Population Owning a House (POH),Population Density (PD) and Criminal Rate (CR) are
elementary criteria descending from SOC. The hierarchy ofcriteria is shown in Fig. 2, while the reference to the data sourceas well as their preference direction is shown in Table 1.
In Table 2, there are evaluations of the 20 consideredcities on the elementary criteria in the year 2015 only.The whole data set and the whole set of results can bedownloaded by clicking on the following link: Supplemen-tary Results(http://www.antoniocorrente.it/wwwsn/images/allegati articoli/SMAA%20Results%20Sustainability%20Cities.xlsx).
The indifference and preference thresholds for each elemen-tary criterion, equal for all considered years, are shown in Table 3.
Using the notation introduced in Section 3.3we have that EL = {(1, 1), . . . , (3, 3)} and,therefore, the whole set of weights is W ={
(w(1,1), . . . , w(3,3)
) ∈ R9+ :
∑
t∈EL
wt = 1
}
. For our anal-
ysis, let us assume that Environmental macro-criterionis more important than Social one which, in turn, ismore important than Economic macro-criterion. Thispreference information is translated into the followingconstraints on the weights: W1 > W3 and W3 > W2.Transforming the strict inequalities in weak ones bymeans of an auxiliary variable ε and observing thatW1 = w(1,1) +w(1,2) +w(1,3), W2 = w(2,1) +w(2,2) +w(2,3)and W3 = w(3,1) + w(3,2) + w(3,3), the two constraintsbecome
w(1,1) + w(1,2) + w(1,3) � w(3,1) + w(3,2) + w(3,3) + ε
and w(3,1) + w(3,2) + w(3,3) � w(2,1) + w(2,2) + w(2,3) + ε.
Moreover, to impose that there is no dictator criterion, thatis, there is no criterion having importance greater than thesum of the remaining ones, we impose the no-dictatorshipcondition [49] at all levels of the hierarchy, obtaining thefollowing constraints:
1. W1 � W2 + W3 ⇔ w(1,1) + w(1,2) + w(1,3) �w(2,1) + w(2,2) + w(2,3) + w(3,1) + w(3,2) + w(3,3)
1,2. w(1,1) � w(1,2) + w(1,3); w(1,2) � w(1,1) + w(1,3);
w(1,3) � w(1,1) + w(1,2),3. w(2,1) � w(2,2) + w(2,3); w(2,2) � w(2,1) + w(2,3);
w(2,3) � w(2,1) + w(2,2),
1Let us observe that g3 and g2 cannot be dictator criteria inconsequence of the preference information provided by the DM.Indeed, on one hand, W3 < W1 implies that W3 < W1 + W2 and, onthe other hand, W2 < W3 implies that W2 < W1 + W3.
6436 S. Corrente et al.
4. w(3,1) � w(3,2) + w(3,3); w(3,2) � w(3,1) + w(3,3);w(3,3) � w(3,1) + w(3,2).
To summarizing, the space WDM of weights vectorscompatible with the mentioned preference information isdefined by the following set of constraints:
w(1,1) + w(1,2) + w(1,3) � w(3,1) + w(3,2) + w(3,3) + ε
w(3,1) + w(3,2) + w(3,3) � w(2,1) + w(2,2) + w(2,3) + ε
w(1,1) � w(1,2) + w(1,3), w(1,2) � w(1,1) + w(1,3), w(1,3) � w(1,1) + w(1,2)
w(2,1) � w(2,2) + w(2,3), w(2,2) � w(2,1) + w(2,3), w(2,3) � w(2,1) + w(2,2)
w(3,1) � w(3,2) + w(3,3), w(3,2) � w(3,1) + w(3,3), w(3,3) � w(3,1) + w(3,2)
wt � ε, ∀t ∈ EL∑
t∈EL
wt = 1.
⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬
⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭
EDM
Solving the LP problem: ε∗ = max ε, subject to EDM ,we find that EDM is feasible and ε∗ = 0.0833 meaningthat there is at least one weights vector compatible withthe preference we provided as a hypothetical DM. Applyingthe HAR method, we sampled 100,000 compatible weightvectors, applying for each of them the hierarchicalPROMETHEE II method and obtaining for each weightsvector a total ranking of the considered cities, not onlyat the comprehensive level but also at partial levels. Asexplained in Section 3.3, applying the SMAA methodologyto the hierarchical PROMETHEE II method, we get therank acceptability indices of all cities at comprehensiveand partial levels. In Tables 4, 5, 6 and 7 we show therank acceptability indices at the comprehensive level, aswell as at the levels of the three considered macro-criteria,according to the provided preference information2.
Looking at data in Tables 4-7 and 8a-b, the followingdetailed observations can be done
• Comprehensive level: Luxembourg, Oslo, Bern, Riga,and Prague are the only five cities that can take thefirst ranking position. In particular, Luxembourg is theone being in the first place more frequently (b1
0(LU) =42.66%), followed by Oslo (b1
0(OS) = 25.746%), Bern(b1
0(BL) = 14.432%), Riga (b10(RI) = 12.774%)
and Prague (b10(PR) = 4.388%). Moreover, looking
at the sum of the rank acceptability indices of thesame countries for the first three positions, we havethe confirmation that Luxembourg and Oslo are thetwo best cities since this sum is equal to 85.623% forLuxembourg and 83.585% for Oslo meaning that, inalmost all cases, both cities reach one of the first threepositions in the ranking. Regarding Prague, instead,this sum is equal to 35.003% that means that it canreach the first three positions in the ranking but notvery frequently. To further compare these five cities,
2We did not compute the rank acceptability indices got by Paris atthe comprehensive and Environmental levels because its evaluation onPassenger Cars was not available.
in Table 8 we provide the pairwise winning indicesamong them. Luxembourg is preferred to the other fourconsidered cities with a probability at least equal to59.599% being the probability with which it is preferredto Oslo. Analogously, Oslo is preferred to the otherfour cities with a probability at least equal to 40.401%being the probability with which it is preferred toLuxembourg. Indeed, again, we have the confirmationthat the two cities are the best.
Regarding, instead, the tail of the ranking, Londonand Athens are the two cities more frequently in the lastpositions since the other three, that is, Rome, Berlin,and Madrid can be ranked last with very marginalprobabilities. Similar to what has been done for thefirst three positions in the ranking, we look at thesum of the rank acceptability indices correspondingto the last three positions in the ranking. This sum isequal to 98.957% for London and 93.052% for Athens,meaning that the two cities are almost always in thesepositions independently on the weights assigned to theelementary criteria;
• Environmental level: The information extracted fromTable 5 is quite easy to be interpreted since there isonly one city that can be ranked first, that is Bern, andone city that is always the last ranked, that is London.Moreover, one can observe that the results are quitestable and do not change very much with the weightsof the three elementary criteria descending from theenvironmental macro-criterion since all cities can takeat most 5 positions and at least one of them is filledwith a probability close to 50% and, in many cases, evenhigher;
• Economic level: At the economic level only three citiescan be ranked first, that is, Stockholm, Oslo, andLuxembourg with probabilities of 77.242%, 20.616%,and 2.142%, respectively. Moreover, in the cases inwhich Stockholm is not ranked first, it is in thesecond (b22(ST ) = 17.256%) or in the third position(b32(ST ) = 5.502%) showing, therefore, great stability.
6437The hierarchical SMAA-PROMETHEE method applied...
Table1
Eva
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Considering the tail of the ranking, Athens is surelythe worst among the twenty analyzed cities since itfills always the last position. Looking at the second-worst city w.r.t. economic aspects, this has to be chosenbetween Lisbon, Madrid, and Rome since they are theonly three cities that can be ranked at the last but oneplace of the ranking with probabilities of 62.056%,36.873%, and 1.071%, respectively (see Table 6);
• Social level: Warsaw, Luxembourg, and Oslo are theonly three cities that can be ranked first consideringthe social macro-criterion. In particular, from Table 7,one can observe that they have a probability tobe ranked first equal to 67.87%, 20.972%, and11.158%, respectively. However, Luxembourg and Oslopresent the highest probability in correspondence of arank position different from the first. Indeed, Oslo’shighest probability is 37.273% and it is obtained incorrespondence of the second place, while Luxembourghas the highest probability in correspondence of thesixth place, meaning that this is the rank position thatis occupied more frequently from this city. To furthercompare these three cities, we extract their pairwisewinning indices shown in Table 8b from which onecan observe that Warsaw is preferred to the other twocities with a probability at least equal to 79.028%,while Oslo and Luxembourg are preferred to eachother with quite similar probabilities since Oslo ispreferred to Luxembourg in 51.547% of the cases,while Luxembourg is preferred to Oslo in the remaining48.453% of the cases.
Considering the tail of the ranking, London andParis are the only two cities that can be ranked lastand they have the highest probability to be ranked last(b20
3 (LO) = 97.686%) and last but one (b193 (PA) =
80.841%), respectively.
To summarize the results of the rank acceptabilityindices of the cities at the comprehensive and partial levels,following [32], we can calculate the expected rank ERr(a)
of each city a:
ERr(a) = −|A|∑
k=1
k · bkr (a).
Based on ERr(a), the cities are then ranked from the best(the one having the greatest ERr(a)) to the worst (the onehaving the smallest ERr(a)).
In Table 9, we show the positions got by each city inthe ranking obtained according to the expected rank at thecomprehensive and partial levels. Looking at the data, onecan appreciate the finer results provided by the MCHP atthe macro-criteria levels. Indeed, while some cities, such asPrague or Oslo, take more or less the same position at thecomprehensive level and each macro-criterion, others take
6438 S. Corrente et al.
Table 2 Evaluations of the considered cities on elementary criteria in year 2015
ENV ECO SOC
PC AWG CO2 ER UR GDP POH PD CR
Rome (RO) 2,728,054.166 2,146.624 25,868.311 65.8 10.6 41,475 72.9 716.6 55.98
London (LO) 6,294,246.092 5,730.346 77,033.686 77.7 4.7 58,827 63.5 1830.9 50.37
Lisbon (LI) 1,195,859.779 1,294.769 14,164.325 70.9 12.5 34,782 74.8 698.7 34.73
Budapest (BU) 958,076.036 1,114.946 14,020.051 72.3 5.3 37,399 86.3 462.3 41.56
Paris (PA) NA 6,188.958 62,628.929 69.5 10.1 61,883 64.1 994 54.90
Vienna (VI) 1,550,756.578 1,565.488 21,602.468 70.4 8.5 46,787 55.7 304.3 30.52
Berlin (BERL) 2,839,085.775 3,201.384 49,358.037 78 4.6 37,601 51.9 290.2 32.55
Madrid (MA) 3,213,640.511 2,985.525 38,254.224 69.7 16.7 43,074 78.2 830.8 35.60
Athens (AT) 1,751,838.628 1,757.541 24,965.637 55 25.2 32,167 75.1 1,871.5 50.54
Prague (PR) 1,038,880.789 130.067 4,083.880 77.8 3.1 48,160 78 378 32.93
Copenhagen (CO) 876,842.31 1,603.495 13,054.794 78.5 6.3 54,197 62.7 561 26.80
Amsterdam (AM) 1,361,481.631 1,406.588 26,407.374 77.5 6.1 60,857 67.8 811.8 33.14
Riga (RI) 324,543.514 380.013 3,465.98 76.9 6.8 30,682 80.2 153.5 38.51
Oslo (OS) 682,479.995 557.665 11,550.834 79.1 4 64,673 82.8 178.7 39.91
Warsaw (WA) 1,621,188.597 879.116 25,275.365 77.9 4.8 49,722 83.7 361.9 30.75
Stockholm (ST) 1,106,009.075 996.609 9,804.747 82.5 6.3 61,754 66.2 315.6 45.98
Bern (BERN) 220,797.145 299.151 1,921.322 81.7 4.7 51,912 43.4 527.9 21.12
Bruxelles (BR) 1,311,091.76 1,076.621 23,130.854 65.6 11 54,634 71.4 799 52.85
Helsinki (HE) 734,696.173 726.145 11,700.913 77.1 7.5 49,760 72.7 309.9 35.63
Luxembourg (LU) 369,401.927 342.887 9,248.308 70.9 6.3 88,312 73.2 217.8 26.17
NA=Not Available
completely different rank positions in the four consideredrankings. For example, London, is 3rd according to theeconomic ranking, while it is the 19th in the comprehensiveand environmental rankings and the 20th in the socialranking. Analogously, while Bern is the first according tothe environmental aspect, it is the 4th at the comprehensivelevel, the 5th on the economic aspect, and, finally, the 13thon the social aspect. In this way, from a policy-makingpoint of view, it is possible to consider the weak and strongpoints of each city, so that the policymakers can developstrategies preserving the strong points and, at the same time,improving the weak ones.
Since the analysis has been performed separately for eachyear from 2012 to 2015, it can be beneficial to look at theevolution in time of the positions got by each city in therankings obtained at the comprehensive and partial levels.
In Table 10a-c we reported the evolutions of the expectedranks over the 2012-2015 period at the comprehensive levelas well as for economic and social macro-criteria. We didnot include the same table for the environmental macro-criterion since the ranking is the same in all years apart from2015 where Paris is not considered because of missing dataon some elementary criteria. In parentheses, we reportedthe number of rank positions a city has increased (↑) ordecreased (↓) with respect to the previous year. More indetail, one could observe the following:
• Comprehensive level: In 2013 many cities have changedtheir rank position with respect to the previous year.However, this is mainly because four of them wereexcluded from the 2012 analysis because of missingdata on some elementary criteria. Considering, instead,
Table 3 Indifference and preference thresholds for the elementary criteria
PC AWG CO2 ER UR GDP POH PD CR
qt 100,000 500 6,000 2.5 3 4,000 5.5 150 7
pt 500,000 1,000 11,000 6 7 10,000 13 450 16
6439The hierarchical SMAA-PROMETHEE method applied...
Table4
Ran
kA
ccep
tabi
lity
Indi
ces
ofth
eci
ties
atth
eco
mpr
ehen
sive
leve
l:20
15da
ta
b1 0(·)
b2 0(·)
b3 0(·)
b4 0(·)
b5 0(·)
b6 0(·)
b7 0(·)
b8 0(·)
b9 0(·)
b10 0
(·)b
11 0(·)
b12 0
(·)b
13 0(·)
b14 0
(·)b
15 0(·)
b16 0
(·)b
17 0(·)
b18 0
(·)b
19 0(·)
Rom
e(R
O)
00
00
00
00
00
00
00
14.9
2952
.537
25.4
36.
977
0.12
7
Lon
don
(LO
)0
00
00
00
00
00
00
00
1.06
36.
432
23.5
0569
Lis
bon
(LI)
00
00
00
00
0.15
90.
472
28.9
0951
.312
18.6
420.
506
00
00
0
Bud
apes
t(B
U)
00
00
00.
444
11.1
3622
.389
34.1
2230
.528
1.38
10
00
00
00
0
Vie
nna
(VI)
00
00
00
00
00
2.47
420
.459
66.1
810
.887
00
00
0
Ber
lin(B
ER
L)
00
00
00
00
00
00
0.10
310
.07
66.8
9512
.034
4.19
26.
703
0.00
3
Mad
rid
(MA
)0
00
00
00
00
00
00
07.
038
28.3
8349
.453
15.0
240.
102
Ath
ens
(AT
)0
00
00
00
00
00
00
00.
965
5.98
314
.493
47.7
9130
.768
Prag
ue(P
R)
4.38
89.
527
21.0
8836
.725
28.2
720
00
00
00
00
00
00
0
Cop
enag
hen
(CO
)0
00
00
05.
188
33.6
2225
.11
35.9
560.
124
00
00
00
00
Am
ster
dam
(AM
)0
00
00
00
00
1.38
166
.605
27.5
774.
386
0.05
10
00
00
Rig
a(R
I)12
.774
14.9
8223
.871
24.7
3623
.073
0.53
60.
028
00
00
00
00
00
00
Osl
o(O
S)25
.746
32.2
0725
.632
12.7
993.
616
00
00
00
00
00
00
00
War
saw
(WA
)0
00
00
05.
537
30.3
9933
.925
29.9
370.
202
00
00
00
00
Stoc
khol
m(S
T)
00
00.
006
0.42
61.
268
76.0
6913
.516
6.68
41.
726
0.30
50
00
00
00
0
Ber
n(B
ER
N)
14.4
3215
.085
14.6
4516
.258
29.2
668.
501
1.73
90.
074
00
00
00
00
00
0
Bru
xelle
s(B
R)
00
00
00
00
00
00.
652
10.6
8978
.486
10.1
730
00
0
Hel
sink
i(H
E)
00
00
10.4
4789
.25
0.30
30
00
00
00
00
00
0
Lux
embo
urg
(LU
)42
.66
28.1
9914
.764
9.47
64.
90.
001
00
00
00
00
00
00
0
6440 S. Corrente et al.
Table5
Ran
kA
ccep
tabi
lity
Indi
ces
ofth
eci
ties
atth
eE
nvir
onm
enta
llev
el:2
015
data
b1 1(·)
b2 1(·)
b3 1(·)
b4 1(·)
b5 1(·)
b6 1(·)
b7 1(·)
b8 1(·)
b9 1(·)
b10 1
(·)b
11 1(·)
b12 1
(·)b
13 1(·)
b14 1
(·)b
15 1(·)
b16 1
(·)b
17 1(·)
b18 1
(·)b
19 1(·)
Rom
e(R
O)
00
00
00
00
00
00
00
010
00
00
Lon
don
(LO
)0
00
00
00
00
00
00
00
00
010
0
Lis
bon
(LI)
00
00
00
00
11,2
288
,555
0,22
50
00
00
00
0
Bud
apes
t(B
U)
00
00
00
8,01
980
,491
11,4
90
00
00
00
00
0
Vie
nna
(VI)
00
00
00
00
00
00
20,5
9979
,401
00
00
0
Ber
lin(B
ER
L)
00
00
00
00
00
00
00
00
47,4
6352
,537
0
Mad
rid
(MA
)0
00
00
00
00
00
00
00
052
,537
47,4
630
Ath
ens
(AT
)0
00
00
00
00
00
00
010
00
00
0
Prag
ue(P
R)
02,
1516
,246
49,3
1727
,098
5,18
90
00
00
00
00
00
00
Cop
enag
hen
(CO
)0
00
00
04,
661
6,82
977
,29
11,2
20
00
00
00
00
Am
ster
dam
(AM
)0
00
00
00
00
00
22,2
5166
,854
10,8
950
00
00
Rig
a(R
I)0
97,8
52,
150
00
00
00
00
00
00
00
0
Osl
o(O
S)0
00
32,2
8767
,713
00
00
00
00
00
00
00
War
saw
(WA
)0
00
00
00
00
013
,861
63,8
8812
,547
9,70
40
00
00
Stoc
khol
m(S
T)
00
00
00
87,3
212
,68
00
00
00
00
00
0
Ber
n(B
ER
N)
100
00
00
00
00
00
00
00
00
00
Bru
xelle
s(B
R)
00
00
00
00
00,
225
85,9
1413
,861
00
00
00
0
Hel
sink
i(H
E)
00
00
5,18
994
,811
00
00
00
00
00
00
0
Lux
embo
urg
(LU
)0
081
,604
18,3
960
00
00
00
00
00
00
00
6441The hierarchical SMAA-PROMETHEE method applied...
Table6
Ran
kA
ccep
tabi
lity
Indi
ces
ofth
eci
ties
atth
eE
cono
mic
leve
l:20
15da
ta
b1 2(·)
b2 2(·)
b3 2(·)
b4 2(·)
b5 2(·)
b6 2(·)
b7 2(·)
b8 2(·)
b9 2(·)
b10 2
(·)b
11 2(·)
b12 2
(·)b
13 2(·)
b14 2
(·)b
15 2(·)
b16 2
(·)b
17 2(·)
b18 2
(·)b
19 2(·)
b20 2
(·)
Rom
e(R
O)
00
00
00
00
00
00
00
00.
663
74.4
8723
.779
1.07
10
Lon
don
(LO
)0
025
.467
60.8
6413
.607
0.04
60.
016
00
00
00
00
00
00
0
Lis
bon
(LI)
00
00
00
00
00
00
00
00.
296
1.98
335
.665
62.0
560
Bud
apes
t(B
U)
00
00
00
00
00
00.
6812
.909
12.7
8235
.729
36.2
271.
673
00
0
Pari
s(P
A)
00
00
00.
032
0.28
52.
245
0.91
67.
997
35.7
8415
.899
23.2
536.
798
6.79
10
00
00
Vie
nna
(VI)
00
00
00
00
00
02.
938
19.0
7654
.305
23.6
810
00
00
Ber
lin(B
ER
L)
00
00
0.06
20.
010.
380.
036
6.40
314
.419
31.4
3139
.595
2.07
15.
593
00
00
00
Mad
rid
(MA
)0
00
00
00
00
00
00
00
1.67
321
.521
39.9
3336
.873
0
Ath
ens
(AT
)0
00
00
00
00
00
00
00
00
00
100
Prag
ue(P
R)
00
0.05
92.
044
3.07
715
.874
23.4
4434
.408
20.0
561.
038
00
00
00
00
00
Cop
enag
hen
(CO
)0
00
00
43.2
6551
.259
5.39
20.
084
00
00
00
00
00
0
Am
ster
dam
(AM
)0
041
.146
31.8
4821
.826
3.80
60.
919
0.05
10.
404
00
00
00
00
00
0
Rig
a(R
I)0
00
00
00
00
0.14
712
.239
24.4
5631
.817
7.36
715
.46
8.51
40
00
0
Osl
o(O
S)20
.616
74.8
714.
454
0.05
90
00
00
00
00
00
00
00
0
War
saw
(WA
)0
00
00
1.31
88.
475
54.5
1532
.214
3.47
80
00
00
00
00
0
Stoc
khol
m(S
T)
77.2
4217
.256
5.50
20
00
00
00
00
00
00
00
00
Ber
n(B
ER
N)
04.
513
16.7
883.
729
42.1
9328
.389
4.07
10.
317
00
00
00
00
00
00
Bru
xelle
s(B
R)
00
00
00
00
00
04.
726
10.1
9413
.155
18.3
3952
.627
0.33
60.
623
00
Hel
sink
i(H
E)
00
00
00
00
2959
.378
11.6
220
00
00
00
00
Lux
embo
urg
(LU
)2.
142
3.36
6.58
41.
456
19.2
357.
2611
.151
3.03
610
.923
13.5
438.
924
11.7
060.
680
00
00
00
6442 S. Corrente et al.
Table7
Ran
kA
ccep
tabi
lity
Indi
ces
ofth
eci
ties
atth
eSo
cial
leve
l:20
15da
ta
b1 3(·)
b2 3(·)
b3 3(·)
b4 3(·)
b5 3(·)
b6 3(·)
b7 3(·)
b8 3(·)
b9 3(·)
b10 3
(·)b
11 3(·)
b12 3
(·)b
13 3(·)
b14 3
(·)b
15 3(·)
b16 3
(·)b
17 3(·)
b18 3
(·)b
19 3(·)
b20 3
(·)
(RO
)0
00
00
00
00
01.
113
2.15
2.12
78.
358
5.21
672
.74
8.29
60
00
Lon
don
(LO
)0
00
00
00
00
00
00
00
00
02.
314
97.6
86
Lis
bon
(LI)
00
00
00
019
.796
39.4
724.
771
5.70
319
.783
10.4
750
00
00
00
Bud
apes
t(B
U)
01.
496.
298
24.4
763.
377
28.8
4619
.189
2.50
22.
441
3.95
27.
429
00
00
00
00
0
Pari
s(P
A)
00
00
00
00
00
00
00
00
016
.845
80.8
412.
314
Vie
nna
(VI)
00.
027
0.53
20.
960.
669
0.92
79.
213
24.8
447.
189
6.33
721
.491
17.2
5410
.557
00
00
00
0
Ber
lin(B
ER
L)
00
00.
029
0.40
40.
193
0.46
24.
369
19.2
566.
336
6.40
611
.583
17.1
5223
.364
9.01
21.
242
0.19
20
00
Mad
rid
(MA
)0
00
00
0.01
55.
864
25.0
1314
.098
9.44
34.
796
5.01
716
.216
.77
2.78
40
00
00
Ath
ens
(AT
)0
00
00
00
00
00
00
1.41
81.
418
5.76
111
.029
63.5
2916
.845
0
Prag
ue(P
R)
01.
8716
.559
12.7
7762
.847
5.32
10.
626
00
00
00
00
00
00
0
Cop
enag
hen
(CO
)0
00
00
00
0.00
92.
5642
.028
32.1
0111
.321
10.3
571.
608
0.01
60
00
00
Am
ster
dam
(AM
)0
00
00
00
00
5.37
611
.219
5.11
28.
586
24.7
541
.249
3.70
80
00
0
Rig
a(R
I)0
3.46
964
.234
20.3
188.
901
3.06
30.
015
00
00
00
00
00
00
0
Osl
o(O
S)11
.158
37.2
736.
628
23.5
8418
.147
0.53
70.
270.
932
1.47
10
00
00
00
00
00
War
saw
(WA
)67
.87
29.6
242.
346
0.13
10.
029
00
00
00
00
00
00
00
0
Stoc
khol
m(S
T)
00
00
00
011
.458
2.87
13.8
073.
105
14.4
0413
.732
10.5
4628
.437
1.63
80.
003
00
0
Ber
n(B
ER
N)
00.
231
0.55
50.
321.
048
0.6
3.64
36.
857
7.89
87.
956.
637
13.3
7610
.814
13.1
78.
817
5.97
77.
275
4.83
20
0
Bru
xelle
s(B
R)
00
00
00
00
00
00
00.
016
3.05
18.
934
73.2
0514
.794
00
Hel
sink
i(H
E)
00
00
032
.317
60.7
184.
222.
745
00
00
00
00
00
0
Lux
embo
urg
(LU
)20
.972
26.0
162.
848
17.4
054.
578
28.1
810
00
00
00
00
00
00
0
6443The hierarchical SMAA-PROMETHEE method applied...
Table 8 Pairwise winning indices between few cities at comprehensivelevel as well as at macro-criteria level
(a) Comprehensive
p0(·, ·) PR RI OS BERN LU
PR 0 41.109 15.644 50.202 18.079
RI 58.891 0 28.925 53.512 27.192
OS 84.356 71.075 0 67.836 40.401
BERN 49.798 46.488 32.164 0 20.081
LUX 81.921 72.808 59.599 79.919 0
(b) Social
p3(·, ·) OS WA LU
OS 0 11.158 51.547
WA 88.842 0 79.028
LU 48.453 20.972 0
the years 2013-2014, one can see that the ranking isalmost the same since all cities maintain the same rankposition or they change by one or at most 2 ranks. Themain changes can be observed for Riga which is 5th in2013 and 2014 but goes to 3rd place in 2015;
• Economic level: Differently from the comprehensivecase, more changes can be observed w.r.t. the economicaspect. While Lisbon and Athens fill always the sameposition in the four considered years, all the other
Table 9 Rank positions of each city at the comprehensive and partiallevels according to their expected rank: 2015 data
Comprehensive Environmental Economic Social
Rome (RO) 16 16 17 16
London (LO) 19 19 3 20
Lisbon (LI) 12 10 19 9
Budapest (BU) 8 8 15 6
Paris (PA) NA NA 12 19
Vienna (VI) 13 14 14 8
Berlin (BERL) 15 18 11 12
Madrid (MA) 17 17 18 10
Athens (AT) 18 15 20 18
Prague (PR) 5 4 7 5
Copenaghen (CO) 10 9 6 11
Amsterdam (AM) 11 13 4 15
Riga (RI) 3 2 13 4
Oslo (OS) 2 5 2 2
Warsaw (WA) 9 12 9 1
Stockholm (ST) 7 7 1 14
Bern (BERN) 4 1 5 13
Bruxelles (BR) 14 11 16 17
Helsinki (HE) 6 6 10 7
Luxembourg (LU) 1 3 8 3
NA=Not Available
Table 10 Comparison of the expected ranks over the period 2012-2015both at comprehensive and partial level
2012 2013 2014 2015
(a) Comprehensive
Rome (RO) 12 16 (↓ 4) 16 16
London (LO) 16 19 (↓ 3) 18 (↓ 1) 19 (↑ 1)
Lisbon (LI) 8 13 (↓ 5) 12 (↓ 1) 12
Budapest (BU) 4 8 (↓ 4) 8 8
Paris (PA) 15 20 (↓ 5) 20 NA
Vienna (VI) 9 12 (↓ 3) 13 (↓ 1) 13
Berlin (BERL) 11 15 (↓ 4) 15 15
Madrid (MA) 13 17 (↓ 4) 17 17
Athens (AT) 14 18 (↓ 4) 19 (↓ 1) 18 (↑ 1)
Prague (PR) 2 4 (↓ 2) 4 5 (↓ 1)
Copenaghen (CO) 5 9 (↓ 4) 10 (↓ 1) 10
Amsterdam (AM) 7 11 (↓ 4) 11 11
Riga (RI) NA 5 5 3 (↑ 2)
Oslo (OS) 1 2 (↓ 1) 1 (↑ 1) 2 (↓ 1)
Warsaw (WA) 6 10 (↓ 4) 9 (↑ 1) 9
Stockholm (ST) 3 6 (↓ 3) 7 (↓ 1) 7
Bern (BERN) NA 3 3 4 (↓ 1)
Bruxelles (BR) 10 14 (↓ 4) 14 14
Helsinki (HE) NA 7 6 (↑ 1) 6
Luxembourg (LU) NA 1 2 (↓ 1) 1 (↑ 1)
(b) Economic
Rome (RO) 15 16 (↓ 1) 17 (↓ 1) 17
London (LO) 7 6 (↑ 1) 3 (↑ 3) 3
Lisbon (LI) 19 19 19 19
Budapest (BU) 16 17 (↓ 1) 16 (↑ 1) 15 (↑ 1)
Paris (PA) 11 11 11 12 (↓ 1)
Vienna (VI) 12 13 (↓ 1) 13 14 (↓ 1)
Berlin (BERL) 13 12 (↑ 1) 12 11 (↑ 1)
Madrid (MA) 17 18 (↓ 1) 18 18
Athens (AT) 20 20 20 20
Prague (PR) 9 9 10 (↓ 1) 7 (↑ 3)
Copenaghen (CO) 8 7 (↑ 1) 7 6 (↑ 1)
Amsterdam (AM) 3 4 (↓ 1) 5 (↓ 1) 4 (↑ 1)
Riga (RI) 18 15 (↑ 3) 14 (↑ 1) 13 (↑ 1)
Oslo (OS) 1 2 (↓ 1) 2 2
Warsaw (WA) 10 10 9 (↓ 1) 9
Stockholm (ST) 2 1 (↑ 1) 1 1
Bern (BERN) 4 3 (↑ 1) 4 (↓ 1) 5 (↓ 1)
Bruxelles (BR) 14 14 15 (↓ 1) 16 (↓ 1)
Helsinki (HE) 6 8 (↓ 2) 8 10 (↓ 2)
Luxembourg (LU) 5 5 6 (↓ 1) 8 (↓ 2)
(c) Social
Rome (RO) 12 16 (↓ 4) 17 (↓ 1) 16 (↑ 1)
London (LO) 16 20 (↓ 4) 20 20
Lisbon (LI) 9 14 (↓ 5) 12 (↑ 2) 9 (↑ 3)
Budapest (BU) 2 4 (↓ 2) 3 (↑ 1) 6 (↓ 3)
Paris (PA) 14 19 (↓ 5) 19 19
6444 S. Corrente et al.
Table 10 (continued)
2012 2013 2014 2015
Vienna (VI) 11 9 (↑ 2) 8 (↑ 1) 8
Berlin (BE) 7 10 (↓ 3) 11 (↓ 1) 12 (↓ 1)
Madrid (MA) 6 12 (↓ 6) 10 (↑ 2) 10
Athens (AT) 15 18 (↓ 3) 18 18
Prague (PR) 5 5 4 (↑ 1) 5 (↓ 1)
Copenaghen (CO) 10 13 (↓ 3) 14 (↓ 1) 11 (↑ 3)
Amsterdam (AM) 8 15 (↓ 7) 15 15
Riga (RI) NA 7 6 (↑ 1) 4 (↑ 2)
Oslo (OS) 1 1 2 (↓ 1) 2
Warsaw (WA) 3 3 1 (↑ 2) 1
Stockholm (ST) 4 6 (↓ 2) 13 (↓ 7) 14 (↓ 1)
Bern (BERN) NA 11 9 (↑ 2) 13 (↓ 4)
Bruxelles (BR) 13 17 (↓ 4) 16 (↑ 1) 17 (↓ 1)
Helsinki (HE) NA 8 7 (↑ 1) 7
Luxembourg (LU) NA 2 5 (↓ 3) 3 (↑ 2)
cities are subject to changes in their rank positions.In particular, on the one hand, a positive trend canbe observed for London (which gains one position in2013 and three positions in 2014), Berlin (which gainsone position in 2013 and 2015), Copenaghen (whichgains one position in 2013 and 2015), and Stockholm(which gains one position in 2013); on the other hand,a negative trend can instead be observed for Rome(which loses one position in 2013 and 2014), Paris(which loses one position in 2015), Vienna (which losesone position in 2013 and 2015), Madrid (which losesone position in 2013), Oslo (which loses one positionin 2013), Warsaw (which loses one position in 2014),Bruxelles (which loses one position in 2014 and 2015),Helsinki (which loses two positions in 2013 and 2015)and, finally, Luxembourg (which loses one position in2014 and two positions in 2015); the other cities havea fluctuating trend since they gain and lose positionsduring the years;
• Social level: As already observed for the comprehensivelevel, in 2013 many cities have changed their rankposition with respect to the previous year because in2012 four cities have not been considered in the rankingbecause of missing data on some elementary criteriadescending from the social macro-criterion; apart fromLondon, Paris, Athens, and Amsterdam which maintainthe same position in the three years, all the other citieschange their position over the years. In particular, on theone hand, a positive trend can be observed for Lisbon(it gains two positions in 2014 and three positions in2015), Vienna (it gains one position in 2014), Madrid (itgains two positions in 2014), Riga (it gains one position
in 2014 and two positions in 2015), Warsaw (it gainstwo positions in 2014), Helsinki (it gains one positionin 2014); on the other hand, a negative trend can beobserved for Berlin (it loses one position in 2014 and2015), Oslo (it loses one position in 2014), Stockholm(it loses seven positions in 2014 and one position in2015); the other cities have a fluctuating trend sincethey gain and lose positions during the years.
5 Conclusions
Sustainability and, consequently, sustainable developmentis a wide concept universally acknowledged but notunivocally defined. Several definitions of sustainabledevelopment have been provided over the years, startingfrom the first dated 1713 and provided by Von Carlowitz[60]. The most used is the one contained in the Brundtlandreport, dated 1987, for which it is “...a development thatmeets the needs of the present without compromising theability of the future generations to meet their own needs”[9]. As three main types of sustainability are commonlyacknowledged [45], that is, Environmental, Social andEconomic, the measuring of sustainability of a project, acity, or a country, is a problem that has to be addressed usingsome Multiple Criteria Decision Aiding (MCDA) methods.
In this paper, we applied a recently developed MCDAmethod, namely, the hierarchical-SMAA-PROMETHEEmethod, to evaluate the sustainability of 20 European citiesin the 2012-2015 period. Nine elementary criteria belongingto the environmental, social, and economic macro-criteriahave been taken into account to evaluate the sustainabilityof the cities at the comprehensive level as well as at threepartial levels. The preference model used to aggregate themultiple criteria evaluations is the one of PROMETHEE II,which permits to avoid the effect of compensation betweencriteria. The compensability of indices used to measuresustainability is in fact undesirable, as shown in [30] and[38]. The use of PROMETHEE II permits to rank order allconsidered cities from the best to the worst, not only at thecomprehensive level but also at the level of each macro-criterion. To provide a robust ranking recommendation,the Stochastic Multicriteria Acceptability Analysis (SMAA)[34] has been applied. The application of SMAA permits tofind the frequency with which a city is reaching a certainrank position at the comprehensive and partial levels, takinginto account a large set of the instances of the assumedpreference model compatible with the preferences providedby the Decision Maker. In our study, these instances aredefined by vectors of criteria weights drawn randomly froma feasible set. The results of SMAA were summarized usingthe expected rank score proposed by [32], providing a finalranking of the cities.
6445The hierarchical SMAA-PROMETHEE method applied...
Based on the results of our case study, we believethat the proposed method can be a useful tool forpolicymakers for at least two reasons. Firstly, it givesthe possibility to identify the weak and strong points ofeach city looking at its rank position got at partial levels.Indeed, apart from information about the rank positionof a particular city reached at the comprehensive level,the hierarchical-SMAA-PROMETHEE method gives alsoinformation about its position in the rankings taking intoaccount the Environmental, Social and Economic aspectsseparately. This permits to identify weak points (the macro-criteria on which the city gets low-rank positions) and strongpoints (the macro-criteria on which the city gets high-rankpositions). Secondly, comparing the rank position got by acity in different years, one can observe the consequencesof implemented policies, and arrive to conclude which onesshould be maintained (in case a city has improved or, atleast, not deteriorated its rank position over the years) andwhich ones should be revised and improved (in case a cityhas seen its rank position going down during the years).
In our future research, we would like to apply the sameframework considering a greater number of cities as well asa wider period. Moreover, from the methodological pointsof view it would be interesting to take into account somepossible interactions between the different criteria [18] and,finally, to explain and justify the obtained results using theDominance-based Rough Set Approach [27, 28].
Acknowledgments The authors would like to thank the two anony-mous Reviewers whose comments have helped to considerablyimprove this manuscript.
The first two authors wish to acknowledge the support of theMinistero dell’Istruzione, dell’Universita e della Ricerca (MIUR)- PRIN 2017, project “Multiple Criteria Decision Analysis andMultiple Criteria Decision Theory”, grant 2017CY2NCA. Moreover,Salvatore Corrente wishes to acknowledge the support of the researchproject “Multicriteria analysis to support sustainable decisions” ofthe Department of Economics and Business of the University ofCatania, while Salvatore Greco acknowledges also the research project“Analysis and measurement of the competitiveness of enterprises,and territorial sectors and systems: a multicriteria approach” of theDepartment of Economics and Business of the University of Catania.The research of Roman Słowinski was supported by the PolishMinistry of Education and Science, grant no. 0311/SBAD/0709.
Open Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in any medium or format, aslong as you give appropriate credit to the original author(s) and thesource, provide a link to the Creative Commons licence, and indicateif changes were made. The images or other third party material in thisarticle are included in the article’s Creative Commons licence, unlessindicated otherwise in a credit line to the material. If material is notincluded in the article’s Creative Commons licence and your intendeduse is not permitted by statutory regulation or exceeds the permitteduse, you will need to obtain permission directly from the copyrightholder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
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Salvatore Corrente receiveda Master degree in Math-ematics in 2008 and PhDin Pure and Applied Math-ematics in 2016 from theDepartment of Mathematicsand Computer Science of theUniversity of Catania. He iscurrently researcher at theDepartment of Economics andBusiness of the University ofCatania. His research inter-ests concern Multiple CriteriaDecision Making and Interac-tive Evolutionary Multiobjec-tive Optimization. He received
the Bernard Roy Award 2020 for his contribution to multicriteriadecision aiding methodology from the European Working Group onMultiple Criteria Decision Aiding.
Salvatore Greco is a Profes-sor at the Department of Eco-nomics, Catania Universityand a part time Professor atthe University of Portsmouth.He has been invited professorat many universities amongwhich Poznan Technical Uni-versity and University of ParisDauphine. He is the electedpresident of the INFORMSMCDM Section and coordina-tor of the EWG on MCDA. Hereceived the Gold medal of theMCDM International Societyin 2013.
Floriana Leonardi received aBachelor degree in Economicsfrom the University of Cataniain 2020 discussing a thesison multicriterial analysis. Shescurrently attending the firstyear of the Master degreein Economics and EconomicPolicy at the University ofBologna.
Roman Słowinski is a Pro-fessor and Founding Chair ofthe Laboratory of IntelligentDecision Support Systems atPoznan University of Technol-ogy, and a Professor in theSystems Research Institute ofthe Polish Academy of Sci-ences. As an ordinary mem-ber of the Polish Academyof Sciences he is its VicePresident, elected for the term2019-2022. He is a mem-ber of Academia Europaeaand Fellow of IEEE, IRSS,INFORMS and IFIP. Recipi-ent of the EURO Gold Medal
by the European Association of Operational Research Societies(1991), and Doctor HC of Polytechnic Faculty of Mons (Belgium,2000), University Paris Dauphine (France, 2001), and Technical Uni-versity of Crete (Greece, 2008). In 2005 he received the Annual Prizeof the Foundation for Polish Science, and in 2020 - the ScientificAward of the Prime Minister of Poland. Since 1999, he is the principaleditor of the European Journal of Operational Research (Elsevier).
6448 S. Corrente et al.