Investigating ideal-solution based multicriteria decision making techniques for sustainability evaluation of urban mobility projects

Transportation Research Part A 116 (2018) 247–259

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Transportation Research Part A journal homepage: www.elsevier.com/locate/tra

Investigating ideal-solution based multicriteria decision making techniques for sustainability evaluation of urban mobility projects

T

⁎

Anjali Awasthia, , Hichem Omranib, Philippe Gerberb a b

CIISE, Concordia University, EV-7.636, 1455 De Maisonneuve Blvd. West, Montreal H3G 1M8, Quebec, Canada CEPS/INSTEAD, 3 avenue de la Fonte, L-4364 Esch-Sur-Alzette, Luxembourg

A R T IC LE I N F O

ABS TRA CT

Keywords: Multicriteria decision making Urban mobility Sustainability evaluation TOPSIS VIKOR GRA Fuzzy numbers

Confronted with negative environmental impacts, rising fuel costs and increasing congestion, many cities are implementing sustainable mobility measures to improve the flow of passenger and goods. Examples of these measures are use of public transport, cycling, walking, energy efficient vehicles, biofuels. The challenge before transport decision makers is which one(s) to choose for implementation as often there is no or limited quantitative data available on the subject. Moreover, the context of each city, its geographic and transport conditions restrict the generalization of results obtained in experienced cities. In this paper, we are investigating application of ideal solution based multicriteria decision making (MCDM) techniques namely fuzzy TOPSIS, fuzzy VIKOR, and fuzzy GRA for sustainability evaluation of urban mobility projects. A real application for city of Luxembourg is provided. Three projects are evaluated namely implementation of a new tramway in the city center of Luxembourg, re-organization of existing bus lines in the city to perform optimized service, and implementation of electric vehicle car-sharing stations in the city. Sensitivity analysis is performed to determine the influence of input parameters on modeling results. The proposed work is one of the first few works to investigate application of ideal-solution based multicriteria decision making techniques for sustainability evaluation of urban mobility projects under uncertainty. Besides, the best alternative is selected using veto thereby overcoming the limitations of single MCDM methods.

1. Introduction Sustainable mobility is vital for modern cities to ensure seamless movement of goods and people while ensuring a healthier society and environment. It can be defined as “the ability to meet the needs of society to move freely, gain access, communicate, trade and establish relationships without sacrificing other essential human or ecological values today or in the future.” (Mobility, 2001 report). According to Black (2005), the current transport system is non-sustainable due to diminishing petroleum reserves, global atmospheric impacts, local air quality impacts, fatalities and injuries, congestion, noise, low mobility, biological impacts, and lack of equity. The goal of sustainable transport is to ensure that environment, social and economic considerations are factored into decisions affecting transportation activity (Transport Canada, 1999). More and more cities are becoming active in this direction and implementing measures that encourage sustainable mobility such as travel reduction, distance reduction, modal shift, technological innovation, use of public transport and soft modes of transport such as walking and biking, land use and transport integration, regulation instruments, use of electric and other alternative-fueled vehicles, carsharing, park-and-ride etc. (Banister, 2008, Hickman ⁎

Corresponding author. E-mail addresses: [email protected] (A. Awasthi), [email protected] (H. Omrani), [email protected] (P. Gerber).

https://doi.org/10.1016/j.tra.2018.06.007 Received in revised form 15 May 2018; Accepted 7 June 2018 0965-8564/ © 2018 Elsevier Ltd. All rights reserved.

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et al., 2013). The commonly used approaches for sustainability evaluation of urban mobility projects can be classified into: ● Life cycle analysis/assessment: Life cycle analysis (LCA) systematically looks at a product’s complete life cycle, from raw materials to final disposal of the product. It offers a “cradle to grave” look at a product or process, considering environmental aspects and potential impacts. The use of LCA to evaluate the environmental impact of transport system is growing (Goedkoop, 2000; Guinée, 2002). However, its main limitation is that it does not take into consideration social aspects. ● Cost benefit analysis (CBA) and Cost effectiveness analysis (CEA): CBA is a microeconomic approach that computes the benefits and costs of projects in dollar values by taking into account positive and negative impacts. On the other hand, CEA is often used where it may be inappropriate to monetize the effects. In the context of transportation, it compares costs and emissions impacts of potential transit strategies to reduce emissions. Use of CBA has been reported for sustainable transportation analysis by Browne and Ryan (2011), Eliasson (2009), Damart and Roy (2009), and Tudela et al. (2006). Tsamboulas and Mikroudis (2000) propose CEA for evaluation of environmental impacts and costs of transport initiatives. Kunreuther et al. (2003) use CEA for evaluation of mitigation measures. With CBA and CEA approaches (Kunreuther et al., 2003), it is extremely difficult to estimate directly external and social costs (e.g. air pollution, noise pollution, accidents, congestions and fuel costs). ● Assessment indicator models: The assessment indicator models use indicators to assess sustainability of transportation systems. According to Tao and Hung (2003), three categories of assessment indicator models are composite index models, multi-level index models and multidimension matrix models. The output of a composite index model is a single index representing degree of satisfying economical, social and environmental objectives (Maoh and Kanaroglou, 2009). For example, ecological footprint (Browne et al., 2008), green gross national product, etc. In multilevel index model, a series of indicators representing different goals and hierarchies are used. In multi-dimensional matrix model, interaction among different indicators is defined using logic architectures. Examples of these models are the Pressure-State-Response, Driving-Force-State response, Driving-Force-PressureState-Impact-Response, and Driving Force-Pressure-State-Exposure-Effect-Action. Assessment indicator models have been used for sustainable transport planning by Lima et al. (2014), Black et al. (2002), Haghshenas and Vaziri (2012), Jeon and Amekudzi (2005), Gudmundsson (2003), Litman (2009), Browne et al. (2008). Identification of right number and type of indicators that accurately represent the social, economic and environmental dimensions being measured is critical to effective functioning of these models. ● Multicriteria decision making (MCDM): MCDM constitutes both the framework for structuring decision problems, as well as a set of methods for generating preferences among alternatives. Examples of MCDM techniques are AHP, TOPSIS, PROMETHEE, ELECTRE etc. Their main advantage is the ability to take into account conflicting, multidimensional, incommensurable and uncertain effects of decisions explicitly (Beinat, 2001). The limitation is that the solutions generated are tradeoff among the multiple objectives and not optimal ones due to nature of the problem. MCDM technqiues have been widely used for sustainability evaluation of transportation projects (Hickman et al., 2012; Curiel-Esparza et al., 2016; Yedla and Shrestha, 2003; Awasthi and Chauhan, 2011). Recently, importance of integrating multiple stakeholders perspectives into multicriteria techniques has been emphasized by various researchers (Macharis and Bernardini, 2015). A detailed review of MCDM techniques has been provided in Section 2. The study conducted in this paper is inspired by Ministry of Luxembourg who is contemplating implementation of several sustainability initiatives to improve mobility and modal split towards public transport. Modal split represents the distribution (in percentage) of travellers with respect to usage of different modes of transport (e.g. bus, tram, private car, cycling). Modal split in favour of public transport will improve city sustainability. The Luxembourg authority (Ministry of Sustainable Development and Infrastructure) is aiming to achieve a modal split of 75/25 in 2020 (75% of trips by private vehicles and 25% by public transportation). In 2007, the modal split was 85.5/14.5 (MODU strategy). To achieve this target, the Luxembourg Government is planning several transport projects. Among them three projects are considered in our study. These projects are implementation of a new tramway in the city center of Luxembourg, re-organization of existing bus lines in the city to perform optimized service, and implementation of electric vehicle car-sharing stations in the city (Section 4). These transport projects will affect the mobility of people inside city centers and the trans-border commuters in particular (Schmitz et al., 2012). Therefore, it is important to perform careful evaluation of these projects to achieve sustainable mobility. The research questions we are trying to address in this paper are : ● ● ● ●

Determine the criteria to choose for sustainability evaluation (ex-ante) of urban mobility projects. Perform sustainability evaluation of urban mobility projects using ideal-solution based multicriteria decision making techniques. Determine the stability of model results with respect to variation in input parameters using sensitivity analysis. Model decision makers preferences under uncertainty using linguistic assessments and fuzzy set theory.

The rest of the paper is organized as follows. In Section 2, we present the related literature. The solution approach is provided in Section 3. Section 4 presents the numerical application of the proposed approach. Finally, in Section 5 we provide the conclusions and steps for future work. 2. Related literature This section is dedicated to detailed literature review of multicriteria decision making methods for sustainability evaluation of 248

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urban transportation projects. MCDM technqiues have been widely used for sustainability evaluation of transportation projects (Zak, 2011, Hickman et al., 2012, Pérez et al., 2014, Curiel-Esparza et al., 2016). Multicriteria decision making (MCDM) constitutes both the framework for structuring decision problems, as well as a set of methods for generating preferences among alternatives. According to Belton and Stewart (2002), there are three broad categories of MCDM techniques namely value measurement models, goal, aspiration, reference level (or ideal-solution based) models, and outranking models (the French school). The value measurement models assign a numerical score (or value) V for each alternative. These scores are aggregated sum of criteria weights and alternatives values for these criteria. An alternative a is preferred to b (a ≻ b) if and only if V(a) > V(b). Examples of value measurement models are Analytical Hierarchy Process (AHP), Analytical Network Process (ANP), Simple Aggregated Weighting (SAW). AHP has been used for evaluating environmentally sustainable transport system in Delhi (Yedla and Shrestha, 2003), evaluating passenger transportation projects (Jones et al., 2013), optimal land use and transport planning (Vold, 2005), and design of optimal transport strategies (Zhang et al., 2006). Awasthi and Chauhan (2011) apply AHP-Demspter Shafer theory for sustainability evaluation of passenger transport systems. A hybrid method based on AHP and belief theory has been investigated in Awasthi and Omrani (2009). Sayers et al., (2003) use simple aggregate weighting (SAW) for transport options evaluation. Campos Gouvêa et al. (2009) propose a SAW based approach for sustainable mobility evaluation in urban areas. Ivanović et al. (2013) apply Analytic Network Process (ANP) for multicriteria evaluation of transportation projects. Shang et al.(2004) perform road transport project selection using ANP. Brey et al. (2007) use Data Envelopment Analysis (DEA) for evaluation of automobiles with alternative fuels. Teng and Tzeng (1996) use fuzzy multicriteria approach for ranking urban transportation investment alternatives. Avineri et al. (2000) use fuzzy set theory (weighted average and noncompensatory decision rules) for transportation project selection The strength of value measurement models is their simplicity, flexibility, ability to handle both quantitative and qualitative criteria, and consideration of multiple decision makers preferences. The limitation is concerning the selection of right decision maker (s) (number and type) for decision making and assignment of criteria weights. The goal, aspiration, reference level (or ideal-solution based) models rank alternatives based on their closeness to achieve a determined goal, aspiration level or ideal solution. An ideal solution is a theoretical solution where all all the criteria have been respectively maximized or minimized. Ratio of Euclidean distances to the ideal and anti-ideal solutions is computed. The best solution is closest to the ideal solution and farthest from the anti-ideal solution. Examples of this category of models are Technique for Ordered Preference by Similarity to Ideal Solution (TOPSIS), VIKOR (in Serbian: VlseKriterijumska Optimizacija I Kompromisno Resenje) VIKOR, and GRA (Grey Relational Analysis). Tzeng et al. (2005) use TOPSIS and VIKOR for choice of “clean technologies” for vehicles. Bai et al (2015) use rough set theory and VIKOR for sustainable transport fleet appraisal. Awasthi et al. (2011) use fuzzy TOPSIS for evaluating sustainable transportation systems. The strength of goal, aspiration or reference (ideal-solution) based methods is that they are quantitative in nature and suitable for being implemented directly into LP solvers. Their main criticism is regarding the assignment of weights, the determination of goals and the normalization of the variables. The outranking models compare the alternatives pair-wise for each criteria to determine to what extent one of the alternatives can be said to outrank another. Aggregate preference functions are computed for alternatives based on this information. An alternative a outranks an alternative b if there is enough evidence to conclude that a is at least as good as b when taking all criteria into account. Two main families of methods in this category are PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluation) and ELECTRE (in French: ELimination Et Choix Traduisant la REalité. Turcksin et al. (2011) apply combined AHP-PROMETHEE approach for selecting the most appropriate policy scenario to stimulate a clean vehicle fleet. Concordance analysis has been used for transportation investment planning (Giuliano, 1985) and evaluating automobile restraint policies (Won, 1990). Brand et al. (2002) apply NAIADE (Novel Approach to Imprecise Assessment and Decision Environments) for choice of “clean technologies” for vehicles. Vermote et al. (2014) apply MAMCA methodology for evaluation of regional light rail scenarios. The strength of outranking models is the ability to provide a deep insight in the problem structure and treatment of decision makers uncertainties in various ways using preference functions and thresholds. The limitation is that they cannot be used when there are many alternatives due to large number of pairwise comparisons required. In this paper, our focus is on the use of goal, aspiration and reference level (or ideal solution based) multicriteria decision making methods. The reason being their ability to quantitatively evaluate the alternatives, ability to handle large number of alternatives and criteria, and generation of alternative rankings based on proximity to ideal solution. Three techniques of this family are chosen namely TOPSIS, VIKOR and GRA and coupled with fuzzy set theory for sustainability evaluation of urban transportation projects. Our goal is to observe if the rankings generated by the three methods are consistent and how should the decision regarding the best project(s) selection be made using these techniques.

3. Solution approach The proposed solution approach comprises of following steps. 1. 2. 3. 4.

Identification of criteria for sustainability evaluation of urban mobility projects Seeking linguistic assessments for criteria and alternatives from decision makers under lack of quantitative data Application of fuzzy TOPSIS, fuzzy VIKOR and fuzzy GRA for ranking urban mobility projects Conducting sensitivity analysis to determine the stability of model results to variation in input parameters. These steps are described in detail as follows: 249

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Table 1 Evaluation criteria. Category

Criteria

Explanation

Direction

Economic

Revenues (C1) Investment costs (C2)

B C

Operating costs (C3) Travel cost (for users) (C16)

Profits for the transport operator Land costs, infrastructure costs, equipment costs, utilities, purchase costs etc. for the transport operator Labour, maintenance, fuel costs etc. for the transport operator Ticket price, Trip cost for the customer

Environmental

Fossil fuel consumption (C4) Air pollution – GHG emissions (C5) Air pollution – Local pollutants (C6) Noise (C7)

Fossil fuel consumed per trip GHG emissions per trip Local pollutants per trip Noise per trip

C C C C

Social

Number of potential users (C14) Social equity (C8) Impact on city congestion reduction (C9) Land consumption by the project (C10) Impact of transport project on land use (C11) Number of private cars replaced (C12) Number of public parkings replaced(C13)

More users towards public transport are favorable Affordability of transport service Less congestion implies less stress and better health for society Land consumed for installing new project infrastructure Creation of new commerce, residences from project implementation

B B C C C

Implying less private car trips by transfer to public transport Freeing of city land occupied by parkings

C B

Travel time between locations (C15) Reachability to major locations (C17) Service reliability (C18) Spatial accessibility (C19) Frequency of transport (C20) Service area network (C21) Connectivity to multimodal transport (C22) Park and Ride facility (C23)

Fast transport service or less travel time is preferred Ease of reaching major locations Timeliness, no breakdowns Distribution of transport service stops geographically Number of times the transport service is offered Size of transport service area network Connectivity to other modes of transport e.g. metro, bus, train from the service stops

C B B B B B B

Parking availability for private car drivers to embark on public transport for next step of journey Protection offered against accidents Proetction offered against thefts Capacity utilization of vehicles offered by transport service Ability of transport service to accommodate special needs of users Indicator of hygiene Ability to handle customer complaints, queries by transport service Access of transport services by www, phone Ability to expand transport service network to meet growing demand

B

Technical

Safety (C24) Security (C25) Vehicle occupancy (C26) Suitability to disabled customers (C27) Modern and clean facilities (C28) Staff service quality (C29) Integration with IT (C30) Possibility of network expansion (C31)

C C

B B B B B B B B

B: Benefit, C: Cost.

3.1. Selection of evaluation criteria The first step involves selection of criteria for evaluating sustainability of urban mobility projects. Four category of criteria are proposed namely economic, social, enviornmental and technical. The sources used to generate these criteria are comprehensive literature review (Jeon and Amekudzi, 2005, Jonsson, 2008, Litman, 2009, Meyer and Miller, 2001, Nathanail, 2008, Richardson, 2005, Sayers et al., 2003), discussion with experts in sustainable mobility (3 academic researchers, 4 transportation experts from ministry of sustainable development and infrastructure), and our practical experience with city transportation projects (ECOSYMPA, SUCCESS, MOEBIUS) in Europe. The final list contains 31 criteria (Table 1). In Table 1 above, the criteria C2–C7, C9–C12 and C15–C16 are the cost (C) category criteria that is, the lower the value, the more sustainable the alternative (or urban mobility project). The remaining criteria are benefit (B) type criteria, that is, the higher the value, the more sustainable the urban mobility project.

3.2. Generating qualitative criteria and alternative ratings. For sustainability evaluation of the projects under study (Section 1), we need quantitative data on social-economic-environmental-technical criteria. Since these projects are new and implemented for the first time in Luxembourg context, there is almost none or very limited quantitative data available, thereby making the evaluation process difficult. To address this situation, a decision making committee comprising of subject matter experts can be formed who can use linguistic or qualitative ratings such as Good, Very Good, Poor, Very Poor etc. for assessing the alternatives and the criteria. Later, these qualitative assessments are transformed into fuzzy triangular numbers (Pedrycz, 1994, Klir and Yuan, 1995) using conversion schemes provided in Tables 2 and 3 for further processing.

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Table 2 Linguistic ratings for alternatives. Linguistic Term

Membership Function

Very poor (VP) Poor (P) Fair (F) Good (G) Very Good (VG)

(1,1,3) (1,3,5) (3,5,7) (5,7,9) (7,9,9)

Table 3 Linguistic ratings for criteria. Linguistic Term

Membership Function

Very Low Low Medium High Very High

(1,1,3) (1,3,5) (3,5,7) (5,7,9) (7,9,9)

3.3. Sustainability evaluation using ideal-solution based MCDM techniques Three techniques from the family of ideal-solution based MCDM techniques are chosen for sustainability evaluation of urban mobility projects namely TOPSIS, VIKOR and GRA and coupled with fuzzy set theory for application. These techniques differ in the way in which the overall scores are generated. The following sections illustrate the steps involved. Let us consider a set of m alternatives (urban mobility projects) called A = {A1 , A2 , ...,Am } which are to be evaluated against a set of n criteria, C = {C1, C2, ...,Cn} . The fuzzy performance ratings of decision maker Dk (k = 1, 2, ...,K ) for each alternative Ai(i = 1,2,...,m) x ijk where: with respect to criteria Cj (j = 1, 2, ...,n) are denoted by ∼ ∼ k k k k ∼ Rk = x ij = (aij , bij , cij ), i = 1, ...,m ; j = 1, 2, ...,n; k = 1, 2, ..with membership function μ R∼k (x ) . The aggregate fuzzy ratings of alternatives is obtained by averaging the crisp scores obtained from the decision makers K 1 x = ∑∼ x k , i = 1, ...,m ; j = 1, 2, ...,n i.e.∼ ij

K

ij

k=1

∼k = (ak , bk , c k ) denote the fuzzy criteria weight by decision maker D (k = 1, 2, ..,K ) . The aggregate fuzzy criteria weight is Let w k j j j j given by ∼= 1 w j K

K

∑ w∼jk, j = 1, 2, ...,n k=1

The crisp value x ij for a fuzzy alternative rating ∼ x ij = (aij , bij , cij ) is obtained using:

x ij =

aij + 4bij + cij 6

∼ = (a , b , c ) is given byw = aj + 4bj + cj The crisp value wj for a fuzzy criteria weight w j j j j j 6 The decision matrix for the alternatives (D ) and the criteria (W ) is constructed

(4) (5)

W = (w1, w2, ...,wn ) Once these matrices are obtained, the next step is generate overall criteria scores for evaluateng the alternatives.

3.3.1. Fuzzy VIKOR The fuzzy VIKOR technique involves fuzzy assessments of criteria and alternatives in VIKOR. Its foundation lies in finding a compromise solution (Opricovic, 1998). It measures the closeness of the alternative with respect to the positive ideal solution for evaluation. Step 1: Defuzzify the elements of fuzzy decision matrix for the criteria weights and the alternatives into crisp values. 251

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Step 2: Determine the best f j∗and the worst values f j−of all criteria ratings j = 1,2,…,n

f j∗ = max{x ij} and f j− = min{x ij}

(7)

i

i

Step 3: Compute the values Si and Ri using the following equations n

Si =

f j∗ −x ij

∑ wj f ∗ −f − j=1

j

and Ri = max wj

j

j

f j∗ −x ij f j∗ −f j−

(8)

Step 4: Compute the values Qi as following

Qi = ν

Si−S ∗ R −R∗ + (1−v ) −i ∗ S −−S ∗ R −R

(9)

where:

S ∗ = mini Si; S − = max i Si; R∗ = mini Ri ; R− = max i Ri ;

(10)

And ν is the weight for the strategy of maximum group utility and 1-ν is the weight of the individual regret. Step 5: Rank the alternatives, sorting by the values S, R and Q in ascending order. Step 6: Propose as a compromise solution the alternative ( A(1) ) which is the best ranked by the measure Q(minimum) if the following two conditions are satisfied C1: Acceptable advantage

Q (A(2) )−Q (A(1) ) ⩾ DQ where

A(2)

(11)

is the alternative with second position in the ranking list by Q and J is the number of alternatives. (12)

DQ = 1/ J −1

C2: Acceptable stability in decision making The alternative A(1) must also be the best ranked by S or/and R. The compromise solution is stable within a decision making process, which could be the strategy of maximum group utility (whenν > 0.5 is needed), or “by consensus ν≈0.5”, or “with veto” (ν < 0.5). Please note that ν is the weight of the decision making strategy of maximum group utility. If one of the conditions is not satisfied, then a set of compromise solutions is proposed, which consists of: ● Alternatives A(1) and A(2) if only the condition C2 is not satisfied Or ● Alternatives A(1) , A(2) , ....,A(M ) if the condition C1 is not satisfied; A(M ) is determined by the relation Q (A(M ) )−Q (A(1) ) < DQ for maximum M (the position of these alternatives are in closeness). 3.3.2. Fuzzy TOPSIS The fuzzy TOPSIS technique involves fuzzy assessments of criteria and alternatives in TOPSIS (Hwang and Yoon, 1981). The TOPSIS technique chooses an alternative that is closest to the positive ideal solution and farthest from the negative ideal solution. A positive ideal solution is composed of the best performance values for each criterion whereas the negative ideal solution consists of the worst performance values. Step 1: Defuzzify the elements of fuzzy decision matrix for the criteria weights and the alternatives into crisp values. Step 2: Normalize the fuzzy decision matrix. The raw data are normalized using linear scale transformation to bring the various criteria scales into a comparable scale. The normalized decision matrix R is given by:

R = [rij]mxn , i = 1, 2, ...,m ; j = 1, 2, ...,n

(13)

where

rij =

=

x ij−Min {x ij , i = 1, 2, ...,m} Max {x ij , i = 1, 2, ...,m}−Min {x ij , i = 1, 2, ...,m}

Max {x ij , i = 1, 2, ...,m}−x ij Max {x ij , i = 1, 2, ...,m}−Min {x ij , i = 1, 2, ...,m}

, ∀ j = 1, 2, ...,n (Benefit type criteria)

, ∀ j = 1, 2, ...,n (Cost type criteria)

(23)

(24)

Step 2: Compute the weighted normalized matrix The weighted normalized matrix V for criteria is computed by multiplying the weights (wj ) of evaluation criteria with the normalized decision matrix rij .

V = [vij]mxn , i = 1, 2, ...,m ; j = 1, 2, ...,n where vij = rij (.) wj

(16) 252

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Step 3: Compute the positive ideal solution (PIS) and the negative ideal solution (NIS) for each criteria:

A∗ = (v1∗, v2∗, ...,vn∗) where v∗j = {(max{vij}/ j ∈ J ∗), (min{vij}/ j ∈ J −)/ i = 1, 2, ...m} A− = (v1, v2, ..,vn ) where

v−j

= {(min{vij}/ j ∈ J ∗), (max{vij}/ j ∈ J −)/ i = 1, 2, ..m}

*

(17) (18)

-

where J is the set of benefit attributes and J is the set of cost attributes. Step 4: Compute the distance of each alternative from PIS and NIS: The distance (di∗, di−) of each weighted alternative i = 1, 2. .., m from the PIS and the NIS is computed as follows: n

di∗ =

∑ d v (vij, v∗j ), i = 1, 2, ...,m (19)

j=1 n

di− =

∑ d v (vij, v−j ), i = 1, 2, ...,m (20)

j=1

where d v (a, b) is the distance measurement between two crisp numbers a and b and

∼ d v (∼ a, b) =

1 [(a1−b1)2 + (a2−b2)2 + (a3−b3)2] 3

(21)

Step 5: Compute the closeness coefficient (CCi ) of each alternative. The closeness coefficient CCi represents the distances to the positive ideal solution (A*) and the negative ideal solution (A−) simultaneously. The closeness coefficient of each alternative is calculated as:

CCi =

di−

di− , i = 1, 2, ...,m + di∗

(22)

Step 6: Rank the alternatives In this step, the different alternatives are ranked according to the closeness coefficient (CCi ) in decreasing order. The best alternative (highest rank) is closest to the PIS and farthest from the NIS. 3.3.3. Fuzzy grey relational analysis The fuzzy GRA technique involves fuzzy assessments of criteria and alternatives in GRA (Grey Relational Analysis, Deng, 1982). It uses the correlation between the alternative and the ideal alternative (reference sequence) to generate alternative rankings. The closer the alternative is to the ideal alternative, the better it is. Step 1: Normalize the data using the following equations:

∼ rij =

=

x ij−Min {x ij , i = 1, 2, ...,m} Max {x ij , i = 1, 2, ...,m}−Min {x ij , i = 1, 2, ...,m}

Max {x ij , i = 1, 2, ...,m}−x ij Max {x ij , i = 1, 2, ...,m}−Min {x ij , i = 1, 2, ...,m}

= 1−

, ∀ j = 1, 2, ...,n (Benefit type criteria)

, ∀ j = 1, 2, ...,n (Cost type criteria)

x ij−x∗j Max {Max {x ij , i = 1, 2, ..,m}−x∗j , x∗j −Min {x ij , i = 1, 2, ...,m}}

(23)

(24)

, ∀ i, =1, 2, ...,m ; j

= 1, 2, ...,n (The closer to the goal type criteria) Step 2: Calculate the reference sequence for the normalized criteria. The reference sequence X0 = (x 01, x 02 , x 03 , ...,x 0j , x 0n )contains the ideal value for each criterion. For cost category criteria, it is the lowest value whereas for the benefit category criteria, it is the highest value. Our aim is to find the alternative whose comparability sequence is closest to the reference sequence. Step 3: Calculate the grey relational coefficient γ (x 0j , x ij ) between x ij and x 0j to determine the closeness of x ij to x 0j . The larger the grey relational coefficient, the closer x ij and x 0j are. The grey relational coefficient is calculated as follows:

γ (x 0j , x ij ) =

Δmin + ζ Δmax Δij + ζ Δmax

∀ i = 1, 2, ...,m ; j = 1, 2. ..,n

Δij = |x 0j−x ij | Δmin = Min {Δij , i = 1, 2, ...,m ; j = 1, 2. ..,n}, Δmax = Max {Δij , i = 1, 2, ...,m ; j = 1, 2. ..,n},

(26)

where ζ is the distinguishing coefficient, ζ ∈ [0, 1]. The purpose of distinguishing coefficient is to expand or compress the range of grey relational coefficient. Step 4: Calculate the grey relational grade Γ(X0 , Xi ) between X0 and Xi . The grey relational grade represents the level of correlation between the reference sequence and the comparability sequence and is given by. 253

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Γ(X0 , Xi ) =

∑ wj γ (x 0j , xij), i = 1, 2, ...,m (27)

j=1

n

where wj is the weight of the attribute j and ∑ wj = 1. j=1

Step 5: Select the alternative with the highest grey relational grade. 3.3.4. Distinction among the three methods The VIKOR and GRA methods use linear normalization whereas TOPSIS method uses vector normalization. VIKOR and GRA use distance from the ideal solution whereas TOPSIS method uses distances from the ideal and anti-ideal solutions for calculating the best ranking alternative. Also, the relative importance of these distances is not considered in TOPSIS. VIKOR uses city-block distance metric whereas TOPSIS and GRA used Euclidean distances. The aggregation function for generating alternative rankings also differs across the three methods. 3.3.5. Best alternative selection Once the rankings for the alternatives (urban mobility projects) using the three methods (fuzzy TOPSIS, fuzzy VIKOR, fuzzy GRA) is obtained, the best alternative can be selected using the veto rule. In other words, the alternative (s) that is ranked highest by the majority of techniques will be finally chosen. If no clear majority is observed, then a number of other measures can be used such as Spearman’s rank correlation coefficient (Sheshkin, 2004), Kendall’s coefficient of concordance (Hajkowicz and Higgins, 2008), Z (Rao, 2007), agreement between the top three ranked alternatives, and number of ranks matched (as the % of the number of considered alternatives). 3.4. Sensitivity analysis The goal of sensitivity analysis is to determine the stability of model results to variation in input parameters (criteria weights in our case). In order to assess the impact of criteria weights on the rankings of the three alternatives obtained from fuzzy TOPSIS, fuzzy VIKOR and fuzzy GRA, we conducted thirty nine experiments. ● Experiments 1–4 consider each category of criteria one at a time. In other words, the first experiment considers only the economic criteria, the second experiment considers only environmental criteria, the third experiment only social criteria and the last experiment contains only technical criteria. The weight of criteria in each category being equal. ● Experiments 5–35 consider each criteria one at a time with weight equal to 1, the weights of other criteria being equal to 0. This leads to 31 experiments. ● Experiment 36 considers all criteria weights as equal, the total criteria weight being equal to 1. ● Experiment 37 considers only the cost category criteria (C2–7, C9–12, C15–16) and allocates them equal weights. ● Experiment 38 considers only the benefit category criteria (C1, C9, C13–14, C17–31) and allocated them equal weights. ● The last experiment 39 allocates random weights to the 31 criteria (Table 1) based on decision makers ratings, the total criteria weight being equal to 1. 4. Practical application In this section, we demonstrate the application of proposed solution for ex-ante evaluation of three sustainable mobility projects considered for possible implementation by the Ministry of Sustainable Development and Infrastructure, Luxembourg for ameliorating modal split in the city. These transport projects are: 1. Creation of a new tramway in the city center of Luxembourg (A1) The Luxtram will implement a new tram system for Luxembourg City in 2017 in order to strengthen the public transport system and render it more sustainable. The tramway project aims to reach a daily traffic of 100,000 passengers. The line Findel - Cloche d'Or, 16 km long with 23 stations, will provide 300 places in 2021. This tramway is a possible solution to the increasing congestion of the city of Luxembourg, especially related to the mobility of cross-border workers: by 2020, the flow from Germany and Belgium are expected to grow by 25% and by 10%, the flow from France (Lorraine). The tram will increase the capacity of public transport and replace the many buses that connect the main axis Central Station -Downtown - Luxexpo – Airport. It will make travel by public transport faster, comfortable and attractive, preserve the environment and ameliorate the quality of life by offering a better capacity (number of passengers carried per hour) than the current bus network, reduce air pollution and particulate emissions, redefine the public space and urban landscape and serve as complementary offer to other modes of transport such as walking, cycling, bus and train. 2. Reorganization of existing bus lines in the city to perform optimized service (A2) The tramway project involves implementation of several measures like the reorganization of bus lines and train networks to 254

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achieve a better correspondence of transport supply and demand. The bus network will build on the tram network at multiple intermodal points which will free the central tram axis of all regional bus lines. The new tangential lines connect the different areas without going through the City center. This allows the user to save time by opting for more direct routes. This multiplication of interchange points will permit to pass from a star-shaped system towards an interconnected network. 3. Implementation of electric vehicle car-sharing stations in the city (A3) In an effort to reduce CO2 emissions, the Luxembourg government announced in March 2013 its objective for 10% of the country’s car fleet (40,000 vehicles) to be electric by 2020. This will involve implementation of 850 new charging stations across the nation. A pilot project ‘eMovin’ was launched in the country’s northern region, in the five communes of the Nordstad in May 2013. It offers an entirely electric car-sharing service to its residents and businesses, alongside electric power-assisted bicycles and charging stations for electric vehicles. This is alongside a larger roll-out of electric charging stations by Enovos Luxembourg. The purpose is to provide the infrastructure to encourage the use of electric vehicles. Charged with electricity produced from renewable sources, it reduces carbon emissions linked to car use. Eventually, this pilot project will lead to a progressive nation-wide roll-out of this carsharing scheme. (www.Letzgreen.lu).

4.1. Input data A committee of seven decision makers comprising of three academic experts and four transport experts from deptt of sustainable development and infrastructure, ministry of Luxembourg is formed to evaluate the three projects. The academic experts (D1, D4, D5) have several years of project experience with sustainable mobility projects in Europe. The other four transport experts (D2, D3, D6, D7) from the deptt of sustainable development and infrastructure have several years of work and project experience with planning and implementation of sustainable mobility projects. The decision makers provide qualitative ratings to the criteria (Table 4) and the alternatives (Table 5) using linguistic scales provided in Tables 2 and 3. The criteria ratings obtained are presented in Table 4. Table 4 Linguistic Assessments for criteria. Criteria

D1

D2

D3

D4

D5

D6

D7

Category

Economic Environmental Social Technical

L VL L M

VL VL VL VL

VL VL VL L

M VL L L

VL L VL L

L M H L

VL VL VL L

Economic

C1 C2 C3 C16

L L VL VL

M M L VL

M M L L

M L L VL

M M L VL

H L L M

L VL VL VL

Environmental

C4 C5 C6 C7

VL VL L L

VL VL VL VL

L L L L

L L L L

VL VL VL L

M VL M H

VL VL VL VL

Social

C14 C8 C9 C10 C11 C12 C13

L M L M H L M

VL VL VL L VL VL VL

VL VL VL VL VL VL VL

L VL L M L VL VL

L VL VL M M L L

L VH M H M M M

VL VL VL VL VL L L

Technical

C15 C17 C18 C19 C20 C21 C22 C23 C24 C25 C26 C27 C28 C29 C30 C31

L L VL L VL M M L M H VH M H L M M

VL VL VL VL VL L VL VL VL L L VL VL L VL L

VL VL VL VL VL VL VL VL VL M L VL VL VL VL L

VL M L L VL L M L M M L L L M M M

VL VL VL VL L M M L VL M L VL M L L L

VL L M L L M H M H H H M H H H M

VL VL VL VL VL L VL VL VL L L VL VL VL VL VL

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Table 5 Linguistic Assessments for alternatives. Criteria

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24 C25 C26 C27 C28 C29 C30 C31

A1

A2

A3

D1

D2

D3

D4

D5

D6

D7

D1

D2

D3

D4

D5

D6

D7

D1

D2

D3

D4

D5

D6

D7

M H M VL VL VL L L M L VL H H VL L L L L VL VL M L L VL M VL VL VL M L L

L L L L L L L VL VL M M VL VL VL VL VL VL VL VL M VL VL VL M M VL VL VL M VL VL

H L M VH VH VH VL L L M L VL VL M L L L L L L M L L M M L L L M M H

L VL L VL VL VL L L L VL VL L VL L VL L VL VL VL L L VL VL VL L VL VL VL L L L

H H H L L L L VH VH L VL H L L M L L L M VL H L L L M M L VL M L L

VL L L VL VL VL L VL VL M L H M VL VL VL VL VL VL VL M VL L VL L VL VL VL VL VL L

M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M

M VL VL M M M H M M M L H H L M M L VL L L L L M M M M L M L M VL

L L L L L L L VL VL M M VL VL VL VL VL VL VL VL M VL VL VL M M VL VL VL M VL L

H M M VL VL VL VL L L M L VL VL M L L L L L VL M L L M M L L M M M H

L L VL L L L M VL VL M M L VL L VL L VL VL VL VL VL L L VL L VL VL L L L VL

H M M M L L M H M L M H M H H L H H M M M H H M M H M M M L M

VL VL M L L L L VL L VL VL H M VL L VL VL L VL VL VL VL VL VL VL M L VL VL VL VL

M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M

VH L L VL VL VL L H H VL M VH VH H VH H M H M M VL H H H L H H M H H VL

L L L L L L L VL L M M VL VL VL VL VL VL VL VL M VL VL VL M M M M VL M VL VL

H M M VH VH VH VL L M M M VL M M H M M M M M H L M M M L L L VL VL L

VL L VL VL VL VL L L H H H VL M VL VL L VL L VL M L L L VL M H L L L VL L

M L M L L L L VH H L M H M VH H M H L M H M L M M M H VH M M M M

VL VL VL VL VL VL L L H L L M VH M L L VL L L VL M L L L VL VH VH VL VL VL VL

M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M

4.2. Alternative rankings Table 6 presents the ranking results from the three methods. The first row presents the ranking results from fuzzy GRA. It can be seen that alternative A1 has the highest grey relational grade followed by A2 and A3. The second row presents the ranking results from fuzzy TOPSIS. It can be seen that A2 > A3 > A1 based on closeness coefficient (CCi) values. The third row presents the results from fuzzy VIKOR. It can be seen that the three alternatives receive equal rankings. Using the dominance (veto or majority winner rule), it can be seen that alternatives A2 and A1 score rank 1 two times each and are therefore declared as winners for this specific experiment (random weights of criteria).

4.3. Sensitivity analysis In order to determine the stability of model results with respect to variation in criteria weights, sensitivity analysis employing 39 experiments (Section 3.4) is conducted. The results are presented in Table 7. Based on the veto results obtained from the three methods, it can be seen that alternative A1 (implementation of a new tramway in the city center of Luxembourg) scores the highest (22 votes) followed by A3 (13 votes) and A2 (12 votes), and is therefore recommended for implementation.

Table 6 Ranking results.

Fuzzy GRA Fuzzy TOPSIS Fuzzy VIKOR

Γ(X0 , Xi ) CCi Si Ri Qi

A1

A2

A3

Alternative Ranking

Winner by Veto rule

0.7506 0.5078 0.5857 0.0488 0.5

0.617 0.5103 0.5327 0.0587 0.1489

0.551 0.5089 0.4077 0.0587 0.5

A1 > A2 > A3 A2 > A3 > A1 A2 = A3 = A1

A2 = A1

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Table 7 Sensitvity analysis. ID

Expt

F-VIKOR

F-TOPSIS

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

wC1-C4 = 0.25, wC5-C31 = 0 wC5-C8 = 0.3, wC1-4,9-C31 = 0 wC9-C15 = 0.142, wC1-8,16-C31 = 0 wC16-C31 = 0.06, wC1-15 = 0 wC1 = 1, wC2-31 = 0 wC2 = 1, wC1,3-31 = 0 wC3 = 1, wC1-2,4-31 = 0 wC4 = 1, wC1-3,5-31 = 0 wC5 = 1, w-4,6-31 = 0 wC6 = 1, wC1-5,7-31 = 0 wC7 = 1, wC1-6,7-31 = 0 wC8 = 1, w-7,9-31 = 0 wC9 = 1, wC1-8,10-31 = 0 wC10 = 1, wC1-9,11-31 = 0 wC11 = 1, wC1-10,12-31 = 0 wC12 = 1, wC1-11,13-31 = 0 wC13 = 1, wC1-12,14-31 = 0 wC14 = 1, wC1-13,14-31 = 0 wC15 = 1, wC1-14,16-31 = 0 wC16 = 1, wC1-15,17-31 = 0 wC17 = 1, wC1-16,18-31 = 0 wC18 = 1, wC1-17,19-31 = 0 wC19 = 1, wC1-18,20-31 = 0 wC20 = 1, wC1-19,21-31 = 0 wC21 = 1, wC19-20,22-31 = 0 wC22 = 1, wC1-21,23-31 = 0 wC23 = 1, wC1-22,24-31 = 0 wC24 = 1, wC1-23,25-31 = 0 wC25 = 1, w-24,26-31 = 0 wC26 = 1, wC1-25,27-31 = 0 wC27 = 1, w-26,28-31 = 0 wC28 = 1, w-27,29-31 = 0 wC29 = 1, wC1-28,30-31 = 0 wC30 = 1, wC1-29,31 = 0 wC31 = 1, w,3-30 = 0 wC1-31 = 0.0323 wc2-7,9-12,15-16 = 0.0833, wc1,8,13-14,17-31 = 0 wc2-7,9-12,15-16 = 0, wc1,8,13-14,17-31 = 0.0526 wC1-31 = random

N/A N/A N/A N/A A3 = A1 = A2 A1 = A2 > A3 A1 = A2 > A3 A2 = A1 = A3 A1 = A3 = A2 A1 = A3 = A2 A2 = A1 = A3 A2 = A1 = A3 A3 = A1 > A2 A2 = A3 = A1 A3 = A2 > A1 A1 = A2 = A3 A1 = A2 = A3 A1 = A2 = A3 A3 = A2 > A1 A3 = A2 > A1 A1 = A2 > A3 A1 = A2 = A3 A1 = A2 = A3 A1 = A2 = A3 A2 = A3 > A1 A1 = A2 > A3 A1 = A2 > A3 A1 = A2 > A3 A2 = A3 = A1 A1 = A2 = A3 A1 = A2 = A3 A1 = A3 > A2 A2 = A3 = A1 A1 = A3 = A2 A3 = A2 > A1 N/A N/A

A1 A3 A3 A2 A3 A1 A1 A2 A3 A3 A2 A2 A3 A3 A3 A2 A2 A1 A3 A3 A1 A1 A1 A1 A2 A1 A1 A1 A3 A1 A1 A1 A2 A1 A3 A2 A3

38 39

F-GRA

Winner by Veto

A3 A2 A1 A3 A2 A3 A3 A3 A2 A2 A3 A3 A1 A1 A1 A3 A3 A3 A1 A1 A3 A3 A3 A3 A1 A3 A3 A3 A1 A3 A3 A2 A1 A2 A1 A1 A1

A3 > A2 > A1 A2 > A1 > A3 A1 > A2 > A3 A1 > A2 > A3 A3 > A1 = A2 A3 > A2 > A1 A3 > A2 > A1 A3 = A1 > A2 A2 > A1 = A3 A1 = A3 > A2 A2 > A1 > A3 A2 > A1 > A3 A1 > A2 = A3 A1 > A2 > A3 A3 > A1 = A2 A1 > A2 > A3 A1 > A2 > A3 A1 > A2 > A3 A1 > A2 > A3 A1 > A2 > A3 A1 > A2 > A3 A1 > A2 > A3 A2 > A3 > A1 A2 > A3 > A1 A1 > A2 > A3 A1 > A2 > A3 A1 > A2 > A3 A2 = A3 > A1 A1 > A2 > A3 A1 > A2 > A3 A1 > A3 > A2 A2 > A3 > A1 A1 > A3 > A2 A3 > A2 > A1 A1 > A2 > A3 A1 > A2 > A3 A1 > A2 > A3

– – – – A3 A1 A1 A2 = A1 = A3 A3 = A2 A1 = A3 A2 A2 A1 = A3 A3 = A1 A3 A1 = A2 A1 = A2 A1 A3 A3 A1 A1 A1 = A2 A1 = A2 A2 A1 A1 A1 = A2 A1 = A3 A1 A1 A1 A2 = A1 A1 = A3 A3 – –

N/A

A2 > A1 > A3

A1 > A2 > A3

–

A2 = A3 > A1

A2 > A3 > A1

A3 > A2 > A1

A2 = A3

> > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >

A2 A1 A2 A1 A1 A2 A2 A1 A1 A1 A1 A1 A2 A2 A2 A1 A1 A2 A2 A2 A2 A2 A2 A2 A3 A2 A2 A2 A2 A2 A2 A3 A3 A3 A2 A3 A2

> > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >

5. Findings and results discussion Based on the proposed study, following findings were observed: ● The technical category received highest weight followed by economic, social and environmental category. The criteria revenues (C1), noise (C7), land consumption by the project (C10) and security (thefts) (C25) scoring the highest in their respective categories. ● From the technical perspective, alternative A1 (implementation of a new tramway in the city center of Luxembourg) scored highest followed by A2 (re-organization of existing bus lines in the city to perform optimized service) and A3 (implementation of electric vehicle car-sharing stations in the city). Alternative A1 scored highest on criteria reachability to major locations (C17), service reliability (C18), connectivity to multimodal transport (C22), park and ride facility (C23), vehicle occupancy (C26), suitability to disabled customers (C27), modern and clean facilities (C28), spatial accessibility (C19), frequency of transport (C20), safety (C24), staff service quality (C29), security (C25), integration with IT (C30). Alternative A2 scored highest on criteria service area network (C21), spatial accessibility (C19), frequency of transport (C20), safety (C24), staff service quality (C29). Alternative A3 scored highest on criteria travel time between locations (C15), possibility of network expansion (C31), security (C25), and integration with IT (C30). ● From economic perspective, both alternative A1 and A3 scored equal. Alternative A1 scored highest on investment costs (C2) and operating costs (C3) while alternative A3 scored highest on travel cost (for users) (C16) and revenues (C1) ● From environmental perspective, alternative A2 and A3 scored equal and were rate better than A1. Alternative A3 scored highest on air pollution – local pollutants (C6), air pollution – GHG emissions (C5), and fossil fuel consumption (C4) while alternative A2 scored highest on criteria noise (C7), air pollution – GHG emissions (C5), and fossil fuel consumption (C4). Alternative A1 scored 257

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highest on air pollution – local pollutants (C6), and fossil fuel consumption (C4). ● From social perspective, alternative A1 scored better over alternatives A2 and A3. Alternative A1 scored highest on number of potential users (C14), impact on city congestion reduction (C9), land consumption by the project (C10), number of public parkings replaced (C13), and number of private cars replaced (C12). Alternative A2 scored highest on social equity (C8), number of public parkings replaced (C13), number of private cars replaced (C12) while alternative A3 scored highest on impact of transport project on land use (C11), impact on city congestion reduction (C9), and land consumption by the project (C10) ● From overall sustainability perspective, alternative A1 scored the highest (22 votes) followed by A3 (13 votes) and A2 (12 votes) and was therefore recommended for implementation. Based on the above findings, following recommendations are generated for policy planners and transport decision makers. ● The evaluation process should involve all stakeholders associated with the project. In the current study, only few stakeholders participated due to time and resource limitations. Future researchers are encouraged to include all (multiple) stakeholders perspectives in the decision making process to achieve win-win situation for all. ● The current study involved three techniques fuzzy TOPSIS, fuzzy VIKOR and fuzzy GRA and used veto results for best alternative selection. Since different MCDM techniques may not always generate similar rankings, it is recommended to apply more than one technique for sustainable mobility project evaluation for validation of model results and improving decision quality. ● For holistic assessment of sustainable mobility projects, four categories of evaluaton critera should be considered : economic, social, environmental and technical. ● In our study, the evaluation criteria for sustainable mobility projects were chosen based on literature review and discussion with academic researchers and members from Ministry of Sustainable development and infrastructure, Luxembourg. It is possible, that these criteria are biased towards the three projects under consideration and specific context of the Luxembourg city, municipal priorities etc. Future studies should consider revising this list. The evaluation criteria should be developed considering all stakeholders perspectives, suited to their project requirements, city context and other circumstances. 6. Conclusions and future works In this paper, we investigate the application of three ideal-solution based multicriteria decision making (MCDM) techniques namely Fuzzy TOPSIS, Fuzzy VIKOR, and Fuzzy GRA for sustainability evaluation of urban mobility projects. A three step approach is proposed. In the first step, we perform selection of evaluation criteria using literature review and discussion with academic experts. In the second step, we generate criteria and alternative ratings using qualitative data which is later transformed into fuzzy triangular numbers for further processing through ideal-solution based multicriteria decision making techniques in step 3. A numerical application for city of Luxembourg is provided. Three sustainable mobility projects are evaluated namely implementation of a new tramway in the city center of Luxembourg, re-organization of existing bus lines in the city to perform optimized service, and implementation of electric vehicle car-sharing stations in the city. The results of our study yield implementation of a new tramway in the city center of Luxembourg as the best alternative for implementation. The strength of the proposed framework is (a). ability to perform sustainability evaluation under limited or no quantitative information (b). possibility to include multiple stakeholders point of view in decision making and (c). generate final alternative ranking using veto thereby overcoming the limitations of single MCDM methods. The limitations of the work are (a) use of limited number and type of respondents (stakeholders) and (b). lack of real data for validating the results of proposed models. Based on the proposed work, several future works are possible. 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