As

Aa

b

a

ARRA

KWUMLS

1

tmtLluaddfiWPsgtpha

0d

Resources, Conservation and Recycling 56 (2011) 7–21

Contents lists available at SciVerse ScienceDirect

Resources, Conservation and Recycling

journa l homepage: www.e lsev ier .com/ locate / resconrec

n AHP-based fuzzy interval TOPSIS assessment for sustainable expansion of theolid waste management system in Setúbal Peninsula, Portugal

na Piresa,∗, Ni-Bin Changb, Graca Martinhoa

Departamento de Ciências e Engenharia do Ambiente, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, 2829-516 Caparica, PortugalDepartment of Civil, Environmental, and Construction Engineering, University of Central Florida, 4000 Central Florida Blvd., Orlando, FL 32816, USA

r t i c l e i n f o

rticle history:eceived 23 February 2011eceived in revised form 10 August 2011ccepted 14 August 2011

eywords:aste management

ncertaintyulti-criteria decision making

a b s t r a c t

Recent challenges in solid waste management in Europe are intimately tied to the fulfillment of theprescribed targets of recycling and organic waste recovery in response to the requirements of Euro-pean Directives. Challenges with characterizing and propagating uncertainty, and validating predictionspermeate decision making. In order to retrieve the societal ramifications in decision making, this studyintegrates the analytic hierarchy process (AHP) and the technique for order performance by similarityto ideal solution (TOPSIS) for alternative screening and ranking to help decision makers in a Portuguesewaste management system. To underscore the role of uncertainty in decision making for alternativeranking, a fuzzy interval multi-attribute decision analysis was carried out to aid in environmental policy

ife cycle assessmentustainable decisions

decisions. While AHP was used to determine the essential weighting factors, screening and ranking wascarried out by TOPSIS under uncertainty expressed by using an interval-valued fuzzy (IVF) method. Suchan AHP-based IVF-TOPSIS approach driven by a set of weighting factors associated with the selected crite-ria has been proven useful for final ranking via an iterative procedure. The practical implementation wasassessed by a case study in Setúbal Peninsula, Portugal for the selection of the best waste management

tain e

practices under an uncer

. Introduction

In Portugal, it is vital to ensure the full compliance withhe targets required by the European Directives for solid waste

anagement, such as the Packaging and Packaging Waste Direc-ive 2004/12/EC (Council and European Parliament, 2004) andandfill Directive 1999/31/EC (Council, 1999). Facing such chal-enges, Portugal needs to comply with packaging recycling targetsntil 2011. For organic waste, the targets established for 2009nd 2013 aiming to divert 50% and 65% of organic waste pro-uced based on the 1985 generation basis, respectively, have beenelayed until 2013 and 2020. In addition to complying with Land-ll and Packaging Directives, a new challenge arose from the Newaste Framework Directive 2008/98/EC (Council and European

arliament, 2008) in which it is imperative that waste managementystems provided by Member States should take into account theeneral environmental protection principles with regard to precau-ion and sustainability, technical feasibility and economic viability,

rotection of resources as well as the overall environmental, humanealth, social, and economic impacts. In other words, waste man-gement practices would be related to a series of trade-offs among

∗ Corresponding author. Tel.: +351 212948397; fax: +351 212948554.E-mail address: alp11931@fct.unl.pt (A. Pires).

921-3449/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.resconrec.2011.08.004

nvironment, which is geared toward the target fulfillment in the future.© 2011 Elsevier B.V. All rights reserved.

different stakeholders having different objectives, making the oper-ation more difficult to decision makers to reach a cordial decision.These trade-offs therefore involve considering relevant technical,economic, environmental, and social criteria that may be delin-eated by either quantitative or qualitative ways or both. Suchchallenges facing in the decision making arena have to be welladdressed by a more scientifically credible approach to reach asustainable solution.

Within this context, several sources of uncertainties can beaddressed during waste management, which can affect the com-pliance of Directives’ targets and the choice of the best wastemanagement solution. The Directive targets are information (orinnovation) to be spread through as national law or regulations.However, as the science and technology evolve over time we willnever have perfect knowledge after all to ensure the right choicethat makes implementation of the waste management practicesan educational process. No matter which choice to be made, gov-ernment agencies have to translate estimated changes into directimpacts on the affected entities and transform direct impact intochanges in final demand for the waste management of those enti-ties. These waste management entities mainly include Green Dot

System (i.e., it is named Sociedade Ponto Verde in Portugal) andrelevant private sectors which will use those products such as recy-clables, compost, electricity. Some more changes can be inducedby Pay-as-You-Throw (PAYT), which is a successful instrument but

8 A. Pires et al. / Resources, Conservation

h(cmtm1gqwsbdu

mmotTcfs

tctfldf[fim

iotacetoitd

Fig. 1. Information diffusion through waste management stakeholders.

as not yet applied in Portugal. The information diffusion processsee Fig. 1) for social education to promote the PAYT is hard to beharacterized and such unattended consequences or complicationsay affect future election at both regional and local levels. In fact,

he existence of an innovation is seen to cause uncertainty in theinds of potential adopter (Berlyne, 1962; Rogers, 1962; Nimmo,

985) causing a lack of predictability. Challenges arise from that theeneral public receiving the information of PAYT has to respond asuickly as possible in a short period of time to be able to complyith the waste management targets. However, the predicted mea-

ures of how to achieve this goal with a soft computing model mighte implemented in the field for evaluation. Yet metrics for vali-ation and mathematical constructs that are useful for describingncertainties in decision making as a whole are lacking.

Not only the uncertainty of the projections of PAYT imple-entation but also uncertainties from model parameters, type ofodels, inherent process uncertainties, uncertainties due to lack

f knowledge about a specific process or processes, or uncertain-ies embedded in decision making could affect the final outcome.his necessitates creating a new spectrum of uncertainty quantifi-ation (UQ) that has been recognized as a critical element necessaryor continued advancement in handling of waste management andocietal sustainability.

Since information diffusion function is a fuzzy classifying func-ion (Chongfu, 1997) in which fuzzy sets theory can be applied toope with such social and technical complexity to some extent. Thishrust covers a diversity of approaches to deal with uncertaintyrom different disciplines, reflecting differences in the underlyingiterature. The general framework of fuzzy reasoning allows han-ling much of this uncertainty, where fuzzy systems employ type-1uzzy sets, which represent uncertainty by numbers in the range0,1]. When something is uncertain, like a measurement, it is dif-cult to determine its exact value, and of course type-1 fuzzy setsake more sense than using sets (Zadeh, 1975a,b).Because of the uncertain nature of information, indicators used

n waste management analyses to address a unique topologyf uncertainties have to cover unpredictability, structural uncer-ainty, and value/preference uncertainty in decision making, suchs aleatoric and epistemic uncertainties, was investigated holisti-ally in this study using the type-2 fuzzy sets, introduced by Karnikt al. (1999). According to Liang and Mendel (2000), applying theype-2 fuzzy has been regarded as one way to increase the fuzziness

f a relation and, according to Hisdal (1981), “increased fuzzinessn a description means increased ability to handle inexact informa-ion in a locally correct manner”. Our disposition in handling such aecision analysis is to construct suitable interval-valued fuzzy (IVF)

and Recycling 56 (2011) 7–21

sets or type-2 fuzzy sets in this case study so as to characterize andquantify the unique topology of uncertainty encountered in solidwaste management systems.

According to Pohekar and Ramachandran (2004), in a multi-criteria decision making (MCDM) process, a decision-maker isrequired to choose among quantifiable or non-quantifiable andmultiple criteria. The objectives are usually conflicting and there-fore, the solution is highly dependent on the preferences of thedecision-maker leading to the generation of a compromised solu-tion. The multi-attribute decision making (MADM) process that hasbeen capable of helping decision making process by consideringlimited number of criteria, analyzing several alternatives (finite orinfinite) is deemed a good framework. In the group decision mak-ing cases, different groups of decision-makers may be involved insuch a MADM process. Each group brings along different criteriaand points of view, which must be proposed within a mutual under-standing framework. It would be intellectually stimulating if type-2fuzzy sets may be characterized to help such a decision makingprocess.

The aim of this study is to integrate the analytic hierarchy pro-cess (AHP) and the technique for order performance by similarityto ideal solution (TOPSIS) to help decision makers in a Portuguesewaste management system for priority settings. To underscore therole of uncertainty in decision making for alternative ranking, afuzzy interval multi-attribute decision analysis was carried outto aid in environmental policy decisions. While AHP was used todetermine the essential weighting factors, screening and rankingwas carried out by TOPSIS under uncertainty expressed by usingan interval-valued fuzzy (IVF) method. Such a new decision makingprocess eventually led to the screening and ranking of 18 manage-ment alternatives in order to improve the sustainability of solidwaste management in Setúbal region, Portugal. Through the useof a multi-attribute decision analysis under uncertainty, the cho-sen UQ methods help illustrate the sensitivity of various sources ofuncertainty in decision making.

2. Literature review

Several MADM methods have been applied in waste manage-ment, like ELECTRE (Roy, 1973, 1991), PROMETHEE (Brans et al.,1984) and GAIA (Brans and Mareschal, 1994), AHP (Saaty, 1980),TOPSIS (Yoon and Hwang, 1985) and SAW. The summary of pros andcons of those MADM methodologies for solid waste managementwould be helpful for understanding the possible compensatoryeffect in decision making (Table 1). These traditional methodsinclude most likely the whole family of compensatory meth-ods, such as simple additive weight (SAW) (or simple weightedaddition or weighted sum method), weighted product (WP), per-mutation method (PM), AHP, ELimination Et Choix Traduisantla REalité (ELECTRE), TOPSIS, Preference Ranking OrganizationMethod for Enrichment Evaluation (PROMETHEE) – GeometricalAnalysis for Interactive Aid (GAIA), interactive simple additiveweighting (ISAW), LINear programming techniques for Multidi-mensional Analysis of Preference (LINMAP), linear assignmentmethod (LAM), non-metric multi-dimensional scaling with idealpoint and multi-attribute utility theory (MAUT), and more recentSimple Multi-Attribute Rating Technique (SMART). The chosen cri-teria in these previous analyses are comprised of one technicalcriterion, seven environmental impact categories resulting from anindependent life cycle assessment (LCA), three economic criteria,and three social criteria.

Developed by Roy (1973), outranking techniques do not assumethat a single best alternative can be identified, when comparing theperformance of two or more alternatives at a time to identify theextent to which a preference for one over the other can be asserted

A. Pires et al. / Resources, Conservation and Recycling 56 (2011) 7–21 9

Table 1Comparison of MADM methodologies applied to SWM.

MADM methods Description Advantages Disadvantages

SAW • Value based method • Easy to use and well understandable • Normalization is required to solvemultidimensional problems

• Use of measurement of the utility ofan alternative (Cheng et al., 2003)

• Applicable when exact and totalinformation is collected• Well-proven technique• Good performance when comparedwith more sophisticated methods(Chang and Yeh, 2001; Zanakis et al.,1998)

AHP • Use of value based, compensatory,and pairwise comparison approach

• Applicable when exact and totalinformation is collected

• Due to aggregation, compensationbetween good scores on some criteriaand bad scores on other criteria canoccur (Macharis et al., 2004)

• Use of Hierarchical structure topresent complex decision problem

• Decision problem can be fragmentedinto its smallest elements, makingevidence of each criterion applied(Macharis et al., 2004)

• Implementation is quite inconvenientdue to complexity (Tahriri et al., 2008)

• Applicable for either single ormultiple problems, since itincorporates qualitative andquantitative criteria.

• Complex computation is required(Chou et al., 2008)

• Generation of inconsistency index toassure decision makers (Pohekar andRamachandran, 2004)

• Time-consuming

TOPSIS • Use of value based compensatorymethod

• Easy to implement understandableprinciple

• Normalization is required to solvemultidimensional problems

• Measures the distances of thealternatives from the ideal solution

• Applicable when exact and totalinformation is collected

• Selection of the one closest to theideal solution (Cheng et al., 2002)

• Consideration of both the positiveand negative ideal solutions• Provision of a well-structuredanalytical framework for alternativesranking (Geng et al., 2010)• Use of fuzzy number to deal withuncertainty problems

ELECTRE • Use of outranking method • Applicable even when there ismissing information

• Time consuming without usingspecific software due to complexcomputational procedure (Cheng et al.,2002)

• Use of pairwise comparison,compensatory

• Applicable even when there areincomparable alternatives

• May or may not reach the preferredalternative

• Use of indirect method that ranksalternatives by means of pairwisecomparison (Cheng et al., 2002)

• Applicable even when incorporationof uncertainties is required

• Applicable for quantitative andqualitative attributes

PROMETHEE-GAIA

• Use of outranking method, pairwisecomparison, and compensatorymethod

• Applicable even when there ismissing information

•Time consuming without usingspecific software

• Use of positive and negativepreference flows for each alternative inthe valued outranking

• When using many criteria, it becomesdifficult for decision maker to obtain aclear view of the problem (Machariset al., 2004)

• Applicable even when simple andefficient information is needed(Queiruga et al., 2008)

(tp(iieatmadm

• Generation of ranking in relation todecision weights

Linkov et al., 2006). The overall target of outranking models ishe detailed description and structuring of the decision-makingrocess rather than the determination of one optimal solutionLinkov et al., 2006). ELECTRE, PROMETHEE and GAIA are outrank-ng methods, which may even assist the decision maker in cases ofncomplete information (Queiruga et al., 2008). Besides strict pref-rence and indifference, weak preference and incomparability oflternatives are also allowed (Brans and Mareschal, 1994). In addi-ion, SAW, AHP and TOPSIS can be considered value measurement

ethods. The intention of such methods is to construct a means ofassociating a real number with each alternative, in order to pro-uce a preference order on the alternatives consistent with decisionaker value judgments (Belton and Stewart, 2002). In other words,

to the several criteria applied are given weights, which translate theimportance of the criteria to decision makers.

With the existing features and potential applications with dif-ferent purposes and domains, MADM methods may be applied fora variety of waste management issues. According to Cheng et al.(2002), waste management problems can be adequately addressedusing SAW, TOPSIS and ELECTRE. SAW that has widely used in manyfields is an easy tool for use by the decision makers (Cheng et al.,2002). TOPSIS have shown to be logic, and easily programmable

in computational procedure (Önüt and Soner, 2008). However,both SAW and TOPSIS need the prior normalization to allow acorrect integration of criteria and adequate comparison amongalternatives.

10 A. Pires et al. / Resources, Conservation and Recycling 56 (2011) 7–21

te ma

tbbgiigboapetamotfpAaruA(me

r

•

•

•

Fig. 2. Setúbal Peninsula was

Norese (2006) justified the application of ELECTRE III methodhat has a decision group support for waste management systemased on: (1) a method which can prevent decision-maker fromeing asked questions that are too intricate, (2) it can be used inroup decision-making (Hokkanen and Salminen, 1997), and (3)ts multi-criteria model integrates different types of informationn a transparent way and is easily elaborated and understood. Ineneral, ELECTRE method is capable of handling discrete criteria ofoth a quantitative and a qualitative nature and provides completerdering of alternatives (Rousis et al., 2008). PROMETHEE and GAIAlso present success in waste management. PROMETHEE is a non-arametric outranking method for a finite set of alternatives (Branst al., 1984). GAIA is a visualization method, which complementshe PROMETHEE ranking method (Vego et al., 2008). PROMETHEE islso reclaimed to have simplicity, clarity, efficiency, and low infor-ation requirements (Queiruga et al., 2008). The same as the other

utranking methods, PROMETHEE does not require merging cri-eria when they are too heterogeneous. AHP is an ideal methodor ranking alternatives when multiple criteria and sub-criteria areresent in the decision making process (Tahriri et al., 2008). TheHP decomposes decision problems into a hierarchical structure,nd uses both qualitative and quantitative information to deriveatio scales between decision elements at each hierarchical levelsing pairwise comparisons (Bello-Dambatta et al., 2009). WhileHP is one of the preferred methods for multi-criteria assessment

e.g. expert choice), little application is know on waste manage-ent problems (Contreras et al., 2008), being important to be

xplored.The choice for TOPSIS at this case study is justified by several

easons:

It is a common applied method not only in solid waste manage-ment, but also at other areas, like economy and environment,manufacturing, tourist analysis, water resource management,transportation, project manager, inventory planning, and airlineservice evaluation, and cases mentioned by Dai et al. (2010).Within this context, reverse logistics have been applied (Kannanet al., 2009);

A simple method which can be developed in a spreadsheet (Kimet al., 1997);TOPSIS intends to find a compromise solution (Garcia-Cascalesand Lamata, 2010), since it may identify the best solution that

nagement existing structure.

has the one more close to the positive ideal solution and farthestfrom negative ideal solution.

• TOPSIS compromise solution is quite similar to what happensduring decision making process in waste management: most ofthe time, the best solution is not reached since the criteria arenot in agreement, some must be maximized (like revenues fromselling recyclables) and others minimized (like investment andoperation costs); what can be a good option from cost perspec-tive can bring considerable environmental and social issues (likea landfill near a habitation area).

For the weight criteria step, AHP is quite well-proven to beapplied for this purpose, which ensures the application at thiscase. Also, due to the considerable number of criteria evaluatedby decision makers, is important to measure the consistency of theevaluation, and AHP allows it.

3. Case study

Setúbal peninsula is located in the district of Setúbal with anarea of 1522 km2 and has 714 589 inhabitants (AMARSUL, 2009).The area is divided in nine municipalities, as shown in Fig. 2. Witha regionalization basis, the AMARSUL is the company owned by thelocal municipalities, which has been responsible for managing theMSW since 1997. This SWM system is composed of nine recyclingcenters, two material recovery facilities (MRFs), two landfills, onetransfer station, and one aerobic mechanical biological treatment(MBT).

Nowadays, the AMARSUL promotes the separation ofpaper/cardboard, glass and light packaging (plastics, metalsand composite packaging) waste by means of curbside recyclingsystems. Each type of waste is collected separately in three specificcontainers, and then directly sent to the MRF for recycling, materialrecovery, and reuse. The remaining waste fractions in householdsare then collected through a door-to-door and/or bin collectionscheme, which is normally destined for final disposal at landfills.In the case of Sesimbra municipality, the waste stream is first sentto the transfer station, and then followed by the final disposal at

sanitary landfills. Yet the residual waste after waste separation andrecycling collected from Setúbal municipality is transported to anaerobic MBT plant where the “stabilized residue” can be producedas fertilizer to be applied as agriculture soil-amendment materials.

A. Pires et al. / Resources, Conservation and Recycling 56 (2011) 7–21 11

Start

New interval iteraction?

End

Final ranking with final interval

Crisp data: LCI/LCA results, economic data

Membership function for IVF (fuzzification)

Weighting criteria by stakeholders

Abiotic depletion

Acidification

Eutrophication

Global warming

Human toxicity

Photochemical oxidation

Economic efficiency

Gross energy requirement

Investment

Operational cost

Operational revenues

Fee

Odor

Landfill space saving

IVF normalization matrix

IVF weighting normalized matrix

Distance from ideal solutions (+ and -)

Assigning interval of relative closeness

AHP procedure

Fuzzy TOPSIS procedure

Interval definition for IVF matrix

Ranking

Yes

No

thod

cWLdeamIw(baba

4

4

atIrfdt

Fig. 3. Flowchart of the proposed me

Within this MSW system, there is a recent need to make somehanges in order to comply with the Packaging and Packaging

aste Directive (Council and European Parliament, 2004) andandfill Directive (Council, 1999). The National Plan for MSW (i.e.,esignated as PERSU II) decided to pursue the construction of sev-ral more MBT units. An anaerobic digestion (AD) MBT unit, withmechanical treatment to separate recyclables and high calorificaterial to produce refuse derived fuel (RDF), is under planning.

t is expected that this unit will work with two separate lines, inhich one is related to the biodegradable municipal solid wastes

BMW) and the other is for the residual waste streams. The RDF maye combusted in an incinerator to generate electricity. The existingerobic MBT plant will be maintained as usual. It is expected thatoth MRF plants with manual sorting will be replaced with twoutomatic sorting units.

. Methodology

.1. AHP-based interval-valued fuzzy TOPSIS

The proposed method for the evaluation of waste treatmentlternatives consists of two basic stages: (1) AHP computationso know criteria weights, and (2) evaluation of alternatives withVF TOPSIS, where the best results may be expressed as an interval

ather than an exact ideal solution. In the first stage, criteria definedor the assessment of the alternatives have been integrated in aecision hierarchy. AHP model is structured such that the objec-ive, criteria, and waste management alternatives are on the first,

for waste management alternatives.

second, and third level, respectively. A weighting factor associ-ated with each of the criteria can be derived by AHP throughouta hierarchy process. Pairwise comparison matrices are formed todetermine the criteria weights. Computing the geometric mean ofthe values obtained from individual evaluation can lead to the iden-tification of the final pairwise comparison matrix. The weights ofthe criteria are calculated based on this final comparison matrix.

With the aid of the derived weighting factors, ranking of wastemanagement alternatives can be determined by IVF TOPSIS methodin the second stage. Based on the iterative process (Fig. 3), differentintervals are defined with respect to the distance between linguisticvariables that uniquely reflect the possible sources of uncertainty.In such an iterative procedure, it is expected that repeated calcu-lations for testing several intervals that are intimately linked withthe major sources of uncertainty. Beginning with an initial guess inregard to which range might be possible to reflect the fluctuationsexpressed by the interval, and might disturb the determination of aspecific solution more close to the ideal solution. A schematic dia-gram of the proposed method can be seen in Fig. 3. Iteration mightbe terminated when all types of uncertainty can be fully taken intoaccount.

4.1.1. Analytical hierarchy processAccording to Saaty and Vargas (2001), the AHP is a basic

approach in decision making. It is designed to cope with both therational and the intuitive sources of uncertainty to select the bestout of a number of alternatives evaluated with respect to sev-eral criteria. In this process, the decision maker carries out simple

12 A. Pires et al. / Resources, Conservation

pii(

1

••

•

••

artoaeo(

srsffmowm

idbCoi1

cttw

4

ct

+ + + + +

Fig. 4. Interval-valued triangular fuzzy number (Ashtiani et al., 2009).

airwise comparisons which are then used to develop overall prior-ties for ranking the alternatives. The AHP allows for inconsistencyn the judgments and provides a means to improve consistencySaaty and Vargas, 2001).

The AHP is developed based on the following five steps (Saaty,980):

Define the problem, and determine the objective;Development of the hierarchy from the top (the objective froma general view point) through the intermediate levels (attributesand sub-attributes on which subsequent levels depends) to thelowest level (the list of alternatives);Employ a simple pair-wised comparison matrices for each of thelower levels;Undertake a consistency test; andEstimate relative weights of the components of each level.

For designing the pairwise comparison matrix, the decision hier-rchies can be organized based on a suite of criteria listed in theight portion of Fig. 3. The top level in such an AHP analysis ishe selected goals, followed by some sustainable criteria. The goalsf concern include environment, economic, social and technicalspects. The third level is comprised of the breakdown criteriaxpanded from these sustainable criteria. The relative importancef the criteria is rated by the nine-point scale proposed by Saaty1980) (Table 2).

The AHP decomposes decision problems into a hierarchicaltructure through the pairwise comparison. Such comparisons areecorded in a comparative matrix A, which must be both transitiveuch that if, i > j and j > k then i > k, where i, j and k are alternatives;or all j < k < i and reciprocal, aij = 1/a�. Priorities are then computedrom the comparison matrix by normalizing each column of the

atrix, to derive the normalized primary right eigen vector, the pri-rity vector, by A × w = �max × w, where A is the comparison matrix;is the principal eigen vector; �max is the maximal eigen value ofatrix A (Saaty, 2004).The AHP provides a method of calculating a decision-makers

nconsistency, the consistency index (CI) which is used toetermine whether decisions violate the transitivity rule, andy how much (Bello-Dambatta et al., 2009). CI is defined byI = (�max − n)/(n − 1), where �max as above, n is dimension. Basedn CI is possible to calculate consistency ratio, CR = CI/RI, where RIs the random index, being, at this case, for matrix order 14, RI is.57 (Lin and Yang, 1996).

The number 0.1 is the accepted upper limit for CR. If the finalonsistency ratio exceeds this value, the evaluation procedure haso be repeated to improve consistency. The measurement of consis-ency can be used to evaluate the consistency of decision makers asell as the consistency of overall hierarchy (Wang and Yang, 2007).

.1.2. Interval-valued fuzzy TOPSISTOPSIS developed by Yoon and Hwang (1985) based upon the

oncept that the chosen alternative should have the shortest dis-ance from the ideal solution and the farthest from the negative

and Recycling 56 (2011) 7–21

-ideal solution. A utility value D(i) for each alternative i is obtainedby calculating the relative distance for i to the ideal solution, whichcan be described as follows (Jahanshahloo et al., 2006):

Step 1. Calculate the normalized decision matrix. The normal-ized value nij is calculated as

nij = xij√∑mj=1x2

ij

, j = 1, . . . , m, i = 1, . . . , n. (1)

Step 2. Calculate the weighted normalized decision matrix. Theweighted normalized value vij is calculated as

vij = winij, j = 1, . . . , m, i = 1, . . . , n, (2)

where wi is the weight of the ith attribute or criterion, and∑ni=1wi = 1.Step 3. Determine the positive ideal and negative ideal solutions.

A+ ={

v+1 , ..., v+

n

}=

{(max

jvij|i ∈ I

),

(min

jvij|i ∈ J

)},

A− ={

v−1 , ..., v−

n

}=

{(min

jvij|i ∈ I

),

(max

jvij|i ∈ J

)},

(3)

where I is associated with benefit criteria, and J is associated withcost criteria.

Step 4. Calculate the separation measures, using the n-dimensional Euclidean distance. The separation of each alternativefrom the ideal solution and for the negative ideal solution are givenas, respectively,

d+j

={

n∑i=1

(vij − v+i

)

2}1/2

d−j

={

n∑i=1

(vij − v−i

)

2}1/2 , j = 1, . . . , m. (4)

Step 5. Calculate the relative closeness to the ideal solution. Therelative closeness of the alternative Aj with respect to A+ is definedas

Rj =d−

j

d+j

+ d−j

, j = 1, . . . , m. (5)

Since d−j

≥ 0 and d+j

≥ 0, then Rj ∈ [0,1].Step 6. Rank the preference decreasing order.To apply interval-valued fuzzy numbers in TOPSIS, is neces-

sary to explain a little more in what consists IVF. According toTürksen (2006), in IVF, upper and lower bounds of membership areidentified and the spread of membership, distribution is ignoredwith the assumption that membership values between upper andlower values are uniformly distributed or scattered with member-ship value of “1” on the �(�(.)) axis. Thus, the upper and lowerbounds of interval-valued type 2 (or IVF) fuzziness specify the rangeof uncertainty about the membership values. A representation ofa triangular IVF graphically is in Fig. 4, being an IVF defined asx = [(x1, x′

1); x2; (x′3, x3)]

The developed AHP based IVF TOPSIS method has been based onthe proposed method developed by Ashtiani et al. (2009).

Step 1. Given x = [(aij, a′ij); bij; (c′

ij, cij)], the normalized perfor-

mance rating as an extension of Chen (2000) can be calculatedas:

rij =[(

aij,

a′ij

);

bij ;

(c′

ij,

cij

)], i = 1, . . . , n, j ∈ ˝b

cj

cj

cj

cj

cj

rij =[(

a−j

c′ij

,a−

j

cij

);

a−j

bij;

(a−

j

aij,

a−j

a′ij

)], i = 1, . . . , n, j ∈ ˝c

(6)

A. Pires et al. / Resources, Conservation and Recycling 56 (2011) 7–21 13

Table 2The AHP pairwise comparison scale (Saaty, 1980).

Intensity of weight Definition Explanation

1 Equal importance Contribute equally to the objectives3 Weak/moderate importance of one over another Slightly favor one objective over another5 Essential or strong importance Strongly favor one objective over another7 Very strong or demonstrated importance An objective is favored very strongly over another; dominance demonstrated

in practice9 Absolute importance Evidence favoring one objective over another is of the highest possible order of

rd

V

wmt

TA

*′

2,4,6,8 Intermediate values between the two adjacentscale values

C+j

= Max cij, j ∈ ˝b

a−j

= Min a′ij, j ∈ ˝c

Hence, the normalized matrix R = [rij]n×mcan be obtained.

Step 2. By considering the different importance of each crite-ion obtained from AHP method, the weighted normalized fuzzyecision matrix is constructed as:

˜ = [vij]n×m, where vij = [(gij, g′

ij); hij; (l′ij, lij)]. (7)

Step 3. Ideal and negative ideal solution can be defined as:

A+ = [(1, 1); 1; (1, 1), j ∈ ˝b]

A− = [(0, 0); 0; (0, 0), j ∈ ˝c](8)

Step 4. Normalized Euclidean distance can be calculated:

D−(N, M) =

√√√√13

3∑i=1

[(N−

xi− M−

yi)2

]

D+(N, M) =

√√√√13

3∑i=1

[(N+

xi− M+

yi)2

] (9)

here D−(N, M) and D+(N, M) the primary and secondary distanteasure, respectively. Thereby, distance of each alternative from

he ideal alternative [D+i1, D+

i2] can be currently calculated, where:

D+i1 =

m∑√13

[(gij − 1)2 + (hij − 1)2 + (lij − 1)2]

j=1

D+i2 =

m∑j=1

√13

[(g′ij − 1)2 + (hij − 1)2 + (l′ij − 1)2]

(10)

able 3lternatives proposed for the AMARSUL waste management system.

Options Fraction (%)Alternatives

0/0*/0′ 1/1* 2/2*/2′

MRF 12.4 12.4 12.4Anaerobic digestion BMW 5.4 0 0Anaerobic digestion MBT 28.2 0 33.9Aerobic MBT 13.2 49.7 15.8Landfill with ER 40.8 37.9 37.9

Alternatives considering RDF production plus incineration of high calorific fraction.Alternatives not considering RDF production but incineration of high calorific fraction.

affirmationUsed to represent compromise between the priorities listed above

Similarly, the separation from the negative ideal solution isgiven by [D+

i1, D+i2], where:

D−i1 =

m∑j=1

√13

[(gij − 0)2 + (hij − 0)2 + (lij − 0)2]

D−i2 =

m∑j=1

√13

[(g′ij − 0)2 + (hij − 0)2 + (l′ij − 0)2]

(11)

Those equations are employed to determine the distance fromthe ideal and negative ideal alternatives in interval values.

Step 5. The relative closeness can be calculated as follows:

RC1 = D−i2

D+i2 + D−

i2

, RC2 = D−i1

D+i1 + D−

i1

(12)

The final values of RC∗i

are determined as:

RC∗i = RC1 + RC2

2(13)

5. Results of an empirical study on waste managementalternatives in Setúbal area

To better understand the methodology developed, the casestudy presented will be used to explain the procedure developed,based on Fig. 2.

5.1. Waste management case study

Based on such new regulations that AMARSUL must complywith, these 18 alternatives have been proposed and elaboratedwith respect to the preselected waste management technologies(Table 3). The creation of Table 3 is based on the total amount ofwaste produced in 2008, which is 421 726 tonnes. Based on theaverage waste composition data region wide, the waste stream has31.69% putrescibles, 14.13% paper and cardboard, 11.35% of plas-

tics, 5.83% of glass, 4.14% of composites, 1.82% of metals, 2.07% ofwood, 11.72% of textiles, 15.33% of fine particles, and 1.92% of oth-ers. All the alternatives can help comply with the actual need toreach the targets prescribed in the two new Directives. However,

3/3* 4/4*/4′ 5/5*/5′ 6/6* Base

12.4 12.4 12.4 12.4 4.813.3 0 7.5 28.7 0

0 49.6 38.9 0 032.6 0 0 0 13.841.7 38.0 41.2 58.9 81.4

14 A. Pires et al. / Resources, Conservation and Recycling 56 (2011) 7–21

Table 4Evaluation criteria.

Evaluation criteria Description

Environmental criteriaAbiotic depletion (AD) Extraction of natural non-living resources. It is the difference between resources consumed during waste life cycle and

resources consumption avoided from materials and energy substituted, in kg Sb eq.Acidification (Ac) Referent to acidifying pollutants emitted during waste life cycle. The calculation is the difference between impacts from waste

life cycle less the avoided impact from substituted materials and energy, in kg SO2 eq.Eutrophication (Eut) It is the consequence of high levels of macronutrients, such as nitrogen and phosphorous. It is the difference between

eutrophication substances potential impact during waste life cycle and avoided impacts from substituted materials andenergy, in kg PO4

3− eq.Global warming potential (GWP) Represents the impact of greenhouse gases emissions on the radiative forcing of the atmosphere, inducing climate change. It

is obtained from GHG potential impact from waste life cycle less the GHG impact from substituted materials, kg CO2 eq.Human toxicity (HT) It is the difference from impacts on human health of toxic substances emitted less the avoided impacts from substituted

materials and energy life cycle, in kg p-DCB eq.Photochemical oxidation (PO) Represents the formation of reactive chemical compounds, such as ozone, by action of sunlight on certain primary air

pollutants. The calculation is provided from impact difference between waste life cycle and materials and energy substitutedlife cycles, in kg C2H2 eq.

Gross energy requirement (GER) Amount of commercial energy that is required directly and indirectly by the process of making a good or service. It is thedifference between energy consumed and energy produced, in kJ.

Technical criteriaLandfill space saving (LSS) Ratio between waste not landfilled and total waste generated in a year, in percentage.Economic criteriaInvestment (Inv) Represents the amount to be expended to implement the alternative (in infrastructure, equipment, vehicles, land). In millions

D.Operational costs (OC) Related to the amount to be expended during alternative operation, in material, electricity, maintenance, labor, and to

financial costs like annuity. In D/year.Operational revenues (OR) The amount related to the profit obtained from selling products (energy, recyclables, compost) or with the avoidance of

landfilling products (RDF, recyclables). In D/year.Social criteriaEconomic efficiency (EE) Represents the ratio between the waste fee applied to inhabitants and the net cost of MSW management system, in

nance MSW management system, in D/t.tances emitted during waste life cycle, in m3.

tih

•

•

aaatTstSiFMigdRfA

Table 5Summary of economic criteria calculation sources.

Type of data Sources of data

Infrastructures and equipmentsCollection and transport of MSW

and recyclablesLocal data from collection companies,Piedade and Aguiar (2010), EC (2001),EGF data

MRF unit InCI (2010), Piedade and Aguiar (2010),AMARSUL (2009), EGF data

Aerobic MBT unit AMARSUL (2009), Tsilemou andPanagiotakopoulos (2004, 2005), EGFdata

Anaerobic MBT unit with/withoutBMW line unit

AMARSUL (2009), Tsilemou andPanagiotakopoulos (2004, 2005), EGFdata

Landfill AMARSUL (2009), Tsilemou andPanagiotakopoulos (2004, 2005), EGFdata

ProductsRecyclables SPV (2010)Compost AMARSUL, 2009, EGF data

percentage.Fee It is the amount paid by population to fiOdor It is referent to the impact of odors subs

o reach both Directive targets simultaneously requires a behav-oral change in Portuguese society. The two scenarios to analyzeow targets were reached are:

Baseline scenario: Targets may be reached without systematicinvolvement and evolution, meaning that it can be promoted byseveral external agents such as government, Green Dot Society(Sociedade Ponto Verde), and promotion campaigns that moti-vate a better environmental consciousness. The system may befinanced by using water consumption tax for waste managementto be included in the water billing system;Pay-As-You-Throw (PAYT) scenario: Targets can be reached byimposing an economic instrument – PAYT – to be implementedby various levels of MSW system managers.

Based on this system, Table 3 presents these 18 managementlternatives for assessment plus the present situation designateds the base scenario. These alternatives include waste collectionnd separation of the three packaging materials through bin sys-ems, which handle 12.4% of the content MSW in the study area.his MRF system is responsible for the compliance with the pre-cribed targets in Packaging Waste Directive. Alternative 0 refers tohe predicted change that will take place in the Setúbal peninsulaWM system. The remaining alternatives were designed to exam-ne some special options for complying with the Landfill Directive.or example, Alternative 1 emphasizes the inclusion of aerobicBT; alternative 4 signifies the use of AD MBT; alternative 6 exam-

nes the specific case of using BMW anaerobic digestion line. Ineneral, alternatives 0, 3, and 5 are options for a suite of interme-

iate processing. Separation of high calorific fraction of waste forDF production was also considered in two options being defined

or collecting the high calorific fraction from MRF refuse and fromD MBT separation.

Electricity MEI (2007)

5.2. Crisp data

The sustainability criteria may include different areas of wastemanagement systems (Table 4). Seven stakeholders invited reflectversatile area of expertise and they are decision makers, techni-cians, environmentalists, inhabitants and experts who had beeninvited to respond to inquiries for the retrieval of weighting factors.

The criteria presented were selected considering the require-ments of the new waste management philosophy brought byThematic Strategy on the Prevention and Recycling of Waste(Council and European Parliament, 2008). That justifies the appli-

cation of technical, environmental, economical and social aspects.For the technical aspect was considered the landfill space savingsince this is the major aspect that waste managers may control,

A. Pires et al. / Resources, Conservation and Recycling 56 (2011) 7–21 15

Table 6Evaluation matrix of alternative of waste management system in AMARSUL – environmental criteria.

Alternatives Environmental criteria

AD (kg Sb eq) Acid. (kg SO2 eq) Eutrop. (kg PO43− eq) GWP (kg CO2 eq) HT (kg p-DCB eq) PO (kg C2H2 eq) GER (kJ)

A0 −2.2E+05 −1.9E+05 4.9E+03 3.0E+08 3.8E+06 7.7E+04 −1.3E+12A0* −5.4E+05 −3.9E+05 −1.0E+04 1.6E+08 3.1E+06 5.4E+04 −2.6E+12A0′ −5.6E+05 −4.0E+05 −1.1E+04 1.4E+08 3.1E+06 4.6E+04 −2.8E+12A1 −1.7E+05 −2.0E+05 −4.5E+03 2.5E+08 6.2E+06 6.2E+04 −1.4E+12A1* −1.9E+05 −2.1E+05 −5.5E+03 2.4E+08 6.2E+06 6.0E+04 −1.7E+12A2 −1.9E+05 −2.1E+05 −6.1E+02 3.2E+08 4.8E+06 8.2E+04 −1.5E+12A2* −5.7E+05 −4.5E+05 −1.8E+04 1.5E+08 4.0E+06 4.6E+04 −2.7E+12A2′ −5.9E+05 −4.6E+05 −1.9E+04 1.4E+08 4.0E+06 4.4E+04 −2.8E+12A3 −2.1E+05 −1.3E+05 1.4E+04 2.3E+08 3.5E+06 6.0E+04 −1.7E+12A3* −2.3E+05 −1.6E+05 1.3E+04 2.2E+08 3.5E+06 5.8E+04 −1.8E+12A4 −2.4E+05 −2.4E+05 −7.4E+02 3.1E+08 4.0E+06 8.0E+04 −1.8E+12A4* −7.5E+05 −5.5E+05 −2.4E+04 1.0E+08 3.0E+06 4.0E+04 −3.7E+12A4′ −7.8E+05 −5.7E+05 −2.6E+04 8.7E+07 2.9E+06 3.6E+04 −3.8E+12A5 −2.4E+05 −1.9E+05 8.3E+03 3.3E+08 3.0E+06 8.7E+04 −1.7E+12A5* −6.8E+05 −4.6E+05 −1.2E+04 1.2E+08 2.0E+06 4.4E+04 −3.4E+12A5′ −7.0E+05 −4.7E+05 −1.3E+04 1.1E+08 2.0E+06 4.2E+04 −3.5E+12A6 −2.5E+05 −5.7E+04 3.4E+04 2.3E+08 −2.7E+06 6.1E+04 −1.7E+12A6* −2.7E+05 −7.2E+04 3.3E+04 2.1E+08 −2.8E+06 5.9E+04 −1.8E+12P.A0 −2.2E+05 −1.9E+05 4.9E+03 3.0E+08 3.8E+06 7.7E+04 −1.3E+12P.A0* −5.4E+05 −3.9E+05 −1.0E+04 1.6E+08 3.1E+06 5.4E+04 −2.6E+12P.A0′ −5.6E+05 −4.0E+05 −1.1E+04 1.4E+08 3.1E+06 4.6E+04 −2.8E+12P.A1 −1.7E+05 −2.0E+05 −4.5E+03 2.5E+08 6.2E+06 6.2E+04 −1.4E+12P.A1* −1.9E+05 −2.1E+05 −5.5E+03 2.4E+08 6.2E+06 6.0E+04 −1.7E+12P.A2 −1.9E+05 −2.1E+05 −6.1E+02 3.2E+08 4.8E+06 8.2E+04 −1.5E+12P.A2* −5.7E+05 −4.5E+05 −1.8E+04 1.5E+08 4.0E+06 4.6E+04 −2.7E+12P.A2′ −5.9E+05 −4.6E+05 −1.9E+04 1.4E+08 4.0E+06 4.4E+04 −2.8E+12P.A3 −2.1E+05 −1.3E+05 1.4E+04 2.3E+08 3.5E+06 6.0E+04 −1.7E+12P.A3* −2.3E+05 −1.6E+05 1.3E+04 2.2E+08 3.5E+06 5.8E+04 −1.8E+12P.A4 −2.4E+05 −2.4E+05 −7.4E+02 3.1E+08 4.0E+06 8.0E+04 −1.8E+12P.A4* −7.5E+05 −5.5E+05 −2.4E+04 1.0E+08 3.0E+06 4.0E+04 −3.7E+12P.A4′ −7.8E+05 −5.7E+05 −2.6E+04 8.7E+07 2.9E+06 3.6E+04 −3.8E+12P.A5 −2.4E+05 −1.9E+05 8.3E+03 3.3E+08 3.0E+06 8.7E+04 −1.7E+12P.A5* −6.8E+05 −4.6E+05 −1.2E+04 1.2E+08 2.0E+06 4.4E+04 −3.4E+12P.A5′ −7.0E+05 −4.7E+05 −1.3E+04 1.1E+08 2.0E+06 4.2E+04 −3.5E+12P.A6 −2.5E+05 −5.7E+04 3.4E+04 2.3E+08 −2.7E+06 6.1E+04 −1.7E+12

octifiEmprMdsia2aatpclPlcb

iiw

P.A6* −2.7E+05 −7.2E+04 3.3E+04Base −1.4E+05 −3.7E+04 −2.7E+03

r else their non-renewable resource will be exhausted and moreosts will be needed to construct a new landfill. Environmental cri-eria were obtained from LCA made for the alternatives elaboratedn a companion study (Pires et al., 2011). The use of LCA is justi-ed by New Waste Framework Directive 2008/98/EC (Council anduropean Parliament, 2008) in which suggested waste manage-ent plan should conform with the waste hierarchy from waste

revention to waste recycling and reuse, to incineration and energyecovery, and to landfill sequentially. However, when applying it,ember States shall take measures to encourage the options which

eliver the best overall environmental outcome. This may requirepecific waste streams departing from the hierarchy, and justify-ng life-cycle thinking on the overall impacts of the productionnd management of such waste (Council and European Parliament,008). LCA software used was UMBERTO 5.5 in this study to gener-te quantitative information. The environmental impact categoriesssessed were abiotic depletion (AD), acidification, eutrophica-ion, global warming potential (GWP), human toxicity (HT) andhotochemical oxidation (PO). Another important environmentalriterion used was gross energy requirement (GER), also calcu-ated for each alternative based on life cycle inventory data. Sinceortugal is a country without producing fossil fuels, it is wise toook for waste management solutions in which net energy demandan be as low as possible. All the data used to perform the LCA maye seen in a companion study (Pires et al., 2011).

There are three criteria for addressing the economic aspects:nvestment, operational costs and operational revenues. Initialnvestment costs represent the amount needed to implement the

aste management system. Concerning the use and operation of

2.1E+08 −2.8E+06 5.9E+04 −1.8E+129.5E+08 5.8E+06 2.5E+05 −1.3E+12

MSW facilities, to know cost and benefit during its life cycle is alsorelevant to choose which alternative is the best one. To calculateeach costs/benefits category, several entities have been inquiredto provide information and minimize gaps. They are summarizedin Table 5.

Three social criteria were selected, including economic suffi-ciency, fees and odor. Odor was obtained from LCA. Since its impactcan be considered a public health issue, odor issue was thereforeclassified as social criterion. Fees are the price paid by populationto ensure the service of MSW disposal. Yet the Not-In-My-Backyard(NIMBY) syndrome is a specific social impact that makes order issuelinked with siting such new facilities. Fees are dependent with costsand revenues during a specific time framework. The importance ofthis criterion can be justified by the fact that fees are no-popularin Portugal and AMARSUL and municipalities would not favor thisoption. Without regard to the polluter pays principle (PPP), how-ever, the MSW facilities have to be financed by municipalities withother sources. This justifies the use of economic sufficiency cri-teria. Economic sufficiency corresponds to the ratio between theamount paid by municipalities to AMARSUL to manage the wastestream and the total cost required. Overall, some criteria are self-explanatory, but the other may require further elaboration to avoidambiguity and ensure sound understanding among the respon-dents.

All the criteria values for each alternative are presented in

Tables 6 and 7. It should be noticed that economic and social crite-ria for base scenario are overestimated due to the fact that recentbiogas collection to produce electricity in the last few years has notreceived enough biogas. From environmental criteria point of view,

16 A. Pires et al. / Resources, Conservation and Recycling 56 (2011) 7–21

Table 7Evaluation matrix of alternative of waste management system in AMARSUL – economical, social and technical criteria.

Criteria Alternatives Technical Economic Social

Landfill space saving (%) Investment (106 D) Operating. cost (D/y) Operating. revenues (D/y) Econ. efficiency (%) Fee (D/t) Odor (m3)

A0 30 1.3E+02 4.0E+07 1.6E+07 55 69 1.5E+13A0* 43 1.2E+02 3.9E+07 1.7E+07 58 66 1.2E+13A0′ 44 1.2E+02 3.9E+07 1.7E+07 58 65 1.2E+13A1 42 1.0E+02 3.4E+07 1.5E+07 67 53 1.4E+13A1* 43 1.0E+02 3.4E+07 1.5E+07 67 53 1.3E+13A2 23 1.3E+02 4.0E+07 1.7E+07 56 64 1.6E+13A2* 43 1.2E+02 3.9E+07 1.7E+07 57 63 1.2E+13A2′ 44 1.2E+02 3.9E+07 1.7E+07 58 62 1.2E+13A3 43 1.1E+02 3.4E+07 1.7E+07 73 58 1.3E+13A3* 44 1.1E+02 3.4E+07 1.7E+07 73 58 1.2E+13A4 21 1.3E+02 3.9E+07 1.8E+07 61 58 1.6E+13A4* 45 1.2E+02 3.8E+07 1.7E+07 63 57 1.2E+13A4′ 46 1.2E+02 3.8E+07 1.7E+07 64 56 1.1E+13A5 25 1.3E+02 3.8E+07 1.8E+07 63 62 1.6E+13A5* 44 1.2E+02 3.8E+07 1.8E+07 65 60 1.2E+13A5′ 45 1.2E+02 3.7E+07 1.8E+07 66 59 1.2E+13A6 38 1.1E+02 3.3E+07 1.8E+07 87 61 1.2E+13A6* 38 1.1E+02 3.3E+07 1.8E+07 87 61 1.1E+13P.A0 30 1.3E+02 4.0E+07 1.6E+07 100 69 1.5E+13P.A0* 43 1.2E+02 3.9E+07 1.7E+07 100 65 1.2E+13P.A0′ 44 1.3E+02 3.9E+07 1.7E+07 100 65 1.2E+13P.A1 42 1.0E+02 3.4E+07 1.5E+07 100 53 1.4E+13P.A1* 43 1.0E+02 3.4E+07 1.5E+07 100 53 1.3E+13P.A2 23 1.3E+02 4.0E+07 1.7E+07 100 64 1.6E+13P.A2* 43 1.2E+02 3.9E+07 1.7E+07 100 62 1.2E+13P.A2′ 44 1.2E+02 3.9E+07 1.7E+07 100 62 1.2E+13P.A3 43 1.1E+02 3.4E+07 1.7E+07 100 58 1.3E+13P.A3* 44 1.1E+02 3.4E+07 1.7E+07 100 57 1.2E+13P.A4 21 1.3E+02 3.8E+07 1.8E+07 100 57 1.6E+13P.A4* 45 1.2E+02 3.8E+07 1.7E+07 100 56 1.2E+13P.A4′ 46 1.2E+02 3.7E+07 1.7E+07 100 56 1.1E+13P.A5 25 1.3E+02 3.8E+07 1.8E+07 100 62 1.6E+13P.A5* 44 1.2E+02 3.8E+07 1.8E+07 100 59 1.2E+13P.A5′ 45 1.2E+02 3.7E+07 1.8E+07 100 59 1.2E+13

tw

5

silam

TT

Ne

P.A6 38 1.1E+02 3.3E+07P.A6* 38 1.1E+02 3.3E+07Base 13 8.8E+01 2.3E+07

he situation is the same, i.e., the base scenario is also overestimatedith the best possible environmental performance.

.3. Membership function for IVF

The crisp data applied had to be translated into fuzzy member-hip functions at first. Concerning membership functions defined,

n Fig. 5 are presented each membership for each criterion, withinguistic variables very good (VG), good (G), medium (M), poor (P)nd very poor (VP). The memberships are triangular, since it usedost often for representing fuzzy numbers (Ding and Liang, 2005).

able 8he pairwise comparison matrix for criteria.

AD Ac Eut GWP HT PO GER

AD 1.00 0.96 2.94 2.26 0.54 0.27 0.43Ac 1.04 1.00 2.35 2.14 0.47 0.21 0.37Eut 0.34 0.43 1.00 1.55 0.27 0.22 0.40GWP 0.44 0.47 0.64 1.00 0.28 0.19 0.32HT 1.85 2.14 3.65 3.55 1.00 0.64 1.76PO 3.77 4.74 3.73 5.38 1.56 1.00 3.09GER 2.33 2.70 3.36 3.14 0.57 0.32 1.00Inv 0.81 1.30 1.70 2.12 0.72 0.23 0.59OC 0.56 1.26 1.26 2.08 0.40 0.21 0.55OR 0.85 1.59 1.28 2.33 0.47 0.21 0.54EE 1.40 2.40 2.38 2.38 0.50 0.20 0.57Fee 1.57 2.52 2.54 2.64 0.45 0.23 0.52Odor 1.74 3.03 1.85 2.69 0.55 0.19 0.58LSS 1.59 1.71 1.85 2.00 0.62 0.30 0.47

ote: AD – abiotic depletion; Ac – acidification; Eut – eutrophication; GWP – global warnergy requirement; Inv – investment; OC – operational costs; OR – operational revenue

1.8E+07 100 61 1.2E+131.8E+07 100 61 1.1E+131.2E+07 107 31 3.8E+13

A triangular fuzzy number ã can be defined as a triplet (a1, a2, a3),and such representation of membership functions can be realizedby Fig. 4.

⎧⎪⎪⎪⎪⎪⎨0, x < a1x − a1 , a1 ≤ x ≤ a2

�a(x) = ⎪⎪⎪⎪⎪⎩a2 − a1x − a3

a2 − a3, a2 ≤ xa3

0, x > a3

(14)

Inv OC OR EE Fee Odor LSS

1.24 1.78 1.18 0.71 0.64 0.57 0.630.77 0.79 0.63 0.42 0.40 0.33 0.580.63 0.74 0.78 0.42 0.39 0.54 0.540.47 0.48 0.43 0.42 0.38 0.37 0.501.38 2.52 2.14 2.00 2.24 1.83 1.624.34 4.68 4.68 4.88 4.27 5.10 3.291.70 1.83 1.85 1.76 1.92 1.73 2.141.00 1.41 1.47 1.41 0.89 0.71 0.790.71 1.00 0.42 0.33 0.28 0.35 0.770.68 2.38 1.00 0.64 0.33 0.34 0.710.71 3.03 1.57 1.00 0.55 0.40 0.521.12 3.53 2.99 1.82 1.00 1.51 0.731.41 2.82 2.90 2.49 0.66 1.00 1.161.26 1.41 1.40 1.92 1.37 0.86 1.00

ming potential; HT – human toxicity; PO – photochemical oxidation; GER – grosss; EE – economic efficiency; LSS – landfill space saving.

A. Pires et al. / Resources, Conservation and Recycling 56 (2011) 7–21 17

0

0.5

1

-2.0E+05-4.0E+05-6.0E+05-8.0E+05Abiotic depletion (kg Sb eq)

VPPMGVG

0

0.5

1

0.00E+00-2.00E+05-4.00E+05-6.00E+05Acidification (kg SO2 eq)

VPPMGVG

0

0.5

1

3.0E+041.0E+04-1.0E+04-3.0E+04Eutrophication (kg PO4

3- eq)

VPPMGVG

0

0.5

1

1.0E+095.0E+080.0E+00Global warming (kg CO2 eq)

VPPMGVG

0

0.5

1

7.0E+062.0E+06-3.0E+06

Human toxicity (kg p-DCB eq)

VPPMGVG

0

0.5

1

3.0E+052.0E+051.0E+050.0E+00Phot. oxidation (kg C2H2 eq)

VPPMGVG

0

0.5

1

-2.0E+12-4.0E+12Gross energy requirement (kJ)

VPPMGVG

0

0.5

1

1.3E+021.1E+029.0E+017.0E+01Investment (106 €)

VPPMGVG

0

0.5

1

4.0E+073.0E+072.0E+07Operational cost (€/y)

VPPMGVG

0

0.5

1

2.00E+071.50E+071.00E+07

Operational revenues (€/y)

VPPMGVG

0

0.5

1

1.1E+009.0E-017.0E-015.0E-01Economic efficiency (%)

VPPMGVG

0

0.5

1

7.0E+015.5E+014.0E+012.5E+01Fee (€/t)

VPPMGVG

0

0.5

1

3.0E+131.0E+13

VPPMGVG

0

0.5

1

0.500.400.300.200.10

VPPMGVG

unctio

sbAots(Tl−

Odor (m3)

Fig. 5. Membership f

It was intentional that membership does not reached member-hip = 1, since the interval-valued triangular fuzzy number woulde between [0,1]. To illustrate the procedure, the case of alternative0 for criteria abiotic depletion will be explained. The crisp valuef A0 for AD is −21 900 kg Sb eq. Looking at first graphic of Fig. 5,he triangular number will be (−297 500, −130 000, −130 000),ince the number from x-axis cross firstly the linguistic variable

−297 500, −130 000, −130 000) (“Very Poor” linguistic variable).he crisp value of A0* is −542 000 kg Sb eq., corresponding toinguist variable “Good”, with triangular number of (−800 000,632 500, −465 000).

Landfill space saving (%)

ns of the 14 criteria.

5.4. Interval definition for IVF matrix

Based on membership functions, a triangular number have beenreached. To translate the triangular number into interval-valuedfuzzy numbers is necessary to define different uncertainty degrees.Relative degree of possible level of uncertainty was proposed toaddress the independent impact associated with different type of

uncertainty in an iterative process. Uncertainty degree tested wasbased on the interval between linguistic classes, as 5% uncertainty.

To find IVF matrix was needed to construct again the member-ship functions for all criteria, considering that membership will be

18 A. Pires et al. / Resources, Conservation and Recycling 56 (2011) 7–21

Table 9Results obtained with AHP.

Criteria Weights (w) Criteria Weights (w) �max, CI, RI CR

AD 0.040 Inv 0.036 �max = 14.628 CR = 0.03Ac 0.031 OC 0.046 CI = 0.05Eut 0.025 OR 0.058 RI = 1.57GWP 0.111 EE 0.079HT 0.220 Fee 0.080PO 0.098 Odor 0.067GER 0.056 LSS 0.053

Note: AD – abiotic depletion; Ac – acidification; Eut – eutrophication; GWP – global warming potential; HT – human toxicity; PO – photochemical oxidation; GER – grossenergy requirement; Inv – investment; OC – operational costs; OR – operational revenues; EE – economic efficiency; LSS – landfill space saving.

Table 10Distance to ideal solutions and relative closeness from TOPSIS example.

Alternatives D+ D− RC1 RC2 RCi*

[ont(

5

m

TI

A0 13.69 13.69A0* 13.67 13.68

0,1] for the upper value and [0,0.9] as the lower value. In the casef A0, the triangular number of (−297 500, −130 000, −130 000) isow (−305 875, −289 125, −130 000, −130 000, −130 000). For A0*,he triangular number of (−800 000, −632 500, −465 000) is now−808 375, −791 625, −632 500, −473 375, −456 625).

.5. IVF normalization matrix

The normalization procedure is based on the descriptionade at TOPSIS procedure. For the 5% uncertainty degree, IVF

able 11teration procedure and respective rankings.

Uncertainty tested and rankings

5% Rank 50% Rank

0.0619 P.A5* 0.0505 P.A5*0.0618 P.A5′ 0.0504 P.A5′

0.0611 P.A2 0.0494 A5*0.0608 A5* 0.0493 A5′

0.0606 A5′ 0.0468 P.A20.0598 P.A4 0.0460 P.A10.0593 P.A1 0.0456 P.A40.0585 P.A1* 0.0452 P.A1*0.0583 A2 0.0449 A10.0582 A1 0.0442 A20.0574 A4 0.0440 A1*0.0573 A1* 0.0433 A40.0525 P.A4* 0.0432 P.A4*0.0523 P.A4′ 0.0430 P.A4′

0.0511 P.A2* 0.0419 P.A2*0.0511 P.A2′ 0.0419 P.A2′

0.0507 P.A0* 0.0417 P.A0*0.0502 P.A0′ 0.0411 P.A0′

0.0501 P.A0 0.0405 A4*0.0496 A4* 0.0405 A4′

0.0496 A4′ 0.0404 Base0.0494 Base 0.0396 A2*0.0489 P.A3 0.0393 A0*0.0487 A2* 0.0388 A0′

0.0484 P.A3* 0.0388 A2′

0.0483 A0* 0.0376 P.A30.0482 A0 0.0372 P.A3*0.0477 A2′ 0.0362 P.A00.0477 A0′ 0.0358 P.A6*0.0469 A3 0.0357 A30.0468 P.A6* 0.0356 P.A50.0465 A3* 0.0353 A3*0.0464 P.A5 0.0353 A6*0.0463 A6* 0.0349 P.A60.0459 P.A6 0.0345 A60.0454 A6 0.0344 A00.0440 A5 0.0333 A5

0.05 0.05 0.0480.05 0.05 0.048

normalization matrix has been obtained, being used at the nextsteps of the procedure. Only as example, the results for environ-mental criterion abiotic depletion and for options A0 is ((0.38,0.36); 0.16; (0.16, 0.16)) and for A0* is ((1, 0.98); 0.78; (0.59,0.56)).

5.6. IVF weighting normalized matrix (AHP procedure step)

The weights of the criteria to be used in evaluation pro-cess are calculated by using AHP method. In this phase, the

75% Rank 100% Rank

0.0479 P.A5* 0.0492 P.A10.0478 P.A5′ 0.0484 P.A1*0.0469 A5* 0.0482 A10.0467 A5′ 0.0474 A1*0.0467 P.A1 0.0466 P.A5*0.0459 P.A1* 0.0465 P.A5′

0.0456 A1 0.0456 A5*0.0448 A1* 0.0454 A5′

0.0439 P.A2 0.0452 P.A20.0426 P.A4 0.0440 P.A40.0415 P.A4* 0.0429 A20.0414 A2 0.0426 P.A30.0413 P.A4′ 0.0422 P.A3*0.0404 A4 0.0421 P.A00.0403 P.A2* 0.0419 A40.0403 P.A2′ 0.0410 P.A6*0.0401 P.A0* 0.0410 P.A4*0.0396 P.A0′ 0.0409 A30.0393 P.A3 0.0408 P.A4′

0.0389 A4* 0.0406 A6*0.0389 A4′ 0.0405 A3*0.0388 P.A3* 0.0405 A00.0382 Base 0.0403 P.A60.0380 A2* 0.0399 A60.0378 A0* 0.0399 P.A2*0.0375 A3 0.0399 P.A2′

0.0375 P.A6* 0.0397 P.A0*0.0374 P.A0 0.0392 P.A0′

0.0373 A0′ 0.0386 A4*0.0373 A2′ 0.0386 A4′

0.0371 A3* 0.0377 A2*0.0371 A6* 0.0375 A0*0.0368 P.A6 0.0372 Base0.0363 A6 0.0370 A0′

0.0356 A0 0.0370 A2′

0.0342 P.A5 0.0369 P.A50.0319 A5 0.0347 A5

vation and Recycling 56 (2011) 7–21 19

swmsTc

sCva

5c

Tdl

6

ctsucw

tvvtAtwbi

5iatcivia

7

bmpetmhtssrh

Table 12Iteration procedure and respective rankings with and without weighted criteria.

Uncertainty tested and rankings

5%, weightedcriteria

Rank 5%, without weightedcriteria

Rank

0.0619 P.A5* 0.0578 P.A5*0.0618 P.A5′ 0.0575 P.A5′

0.0611 P.A2 0.0567 A5*0.0608 A5* 0.0564 A5′

0.0606 A5′ 0.0531 P.A4*0.0598 P.A4 0.0528 P.A4′

0.0593 P.A1 0.0517 P.A10.0585 P.A1* 0.0508 P.A2*0.0583 A2 0.0508 P.A2′

0.0582 A1 0.0506 A10.0574 A4 0.0506 P.A1*0.0573 A1* 0.0505 P.A20.0525 P.A4* 0.0497 A4*0.0523 P.A4′ 0.0497 A4′

0.0511 P.A2* 0.0495 P.A0*0.0511 P.A2′ 0.0495 A1*0.0507 P.A0* 0.0493 A2*0.0502 P.A0′ 0.0485 P.A0′

0.0501 P.A0 0.0484 P.A40.0496 A4* 0.0479 A20.0496 A4′ 0.0477 A2′

0.0494 Base 0.0473 A0*0.0489 P.A3 0.0471 P.A00.0487 A2* 0.0463 A0′

0.0484 P.A3* 0.0461 A40.0483 A0* 0.0459 P.A6*0.0482 A0 0.0455 A6*0.0477 A2′ 0.0453 A00.0477 A0′ 0.0452 P.A50.0469 A3 0.0449 P.A60.0468 P.A6* 0.0448 P.A30.0465 A3* 0.0444 A60.0464 P.A5 0.0440 P.A3*0.0463 A6* 0.0432 Base0.0459 P.A6 0.0430 A3

A. Pires et al. / Resources, Conser

takeholders selected are given the task of forming individual pair-ise comparison matrix by using the scale in Table 2. Geometriceans of these values are found to obtain the pairwise compari-

on matrix on which there is a consensus, like is shown in Table 8.he results obtained from the computations based on the pairwiseomparison matrix provided in Table 8, are presented in Table 9.

The HT and GWP are the two relatively important criteria in theelection of waste management solution for the AMARSUL system.onsistency ratio of the pairwise comparison matrix is 0.03 which isalid because it is smaller than < 0.1. So the weights can be retrievednd used in the MADM decision analysis.

.7. Distance from ideal solutions, assigning interval of relativeloseness and ranking

With the weights obtained will be possible to continue theOPSIS procedure. Applying the equations 6 to 13, the results foristance to ideal solution and relative closeness could be calculated,

ike are shown in Table 10 for example purposes.

. Discussion of overall assessment

Being an iterative procedure, is needed the repetition of the cal-ulations shown for the other defined uncertainty degrees to reachhe final results. The iterative process can be stopped once we areure that all types of uncertainty can be included. The degrees ofncertainty tested were based on the interval between linguisticlasses, such as 5%, 50%, 75%, and 100%. The first round presentedill be related to the 5% uncertainty.

When the iteration can be made possible by simply reducinghe interval gradually after the initial selection across all fuzzyariables, it is now possible to observe that only when the inter-al is one time bigger than the linguistic classes is exactly whenhere is a change in ranking (Table 11). The best solution for theMARSUL system would be the implementation of anaerobic diges-

ion MBT and anaerobic digestion plant of biodegradable municipalaste followed by the RDF production, which should be managed

y the PAYT program. As a consequence, A5 is the best option thats related to PAYT program.

In the case in which criteria weights are equally important and% uncertainty is assumed with respect to the same degree of

nformation diffusion among stakeholders in this practice, decisionnalysis would turn out to be different and the options obtained inhis situation are presented in Table 12. The same best alternativean be reached. The change of weights would signify the highermportance of economic consideration though. In this context, it iserified that economic group that is one of the four groups, includ-ng environmental, economic, social and technical group, cannotlter the final option dramatically.

. Final remarks

For this particular case study, the stakeholders have called onased on their considerable professional background in environ-ental, economic, social and technical criteria. Yet the current AHP

rocedure could only account for seven agents, namely one fromach group at minimum. This is deemed insufficient to representhe possible opinions from all stakeholders involved in decision

aking. The response collected from our stakeholders involvedighlight that they felt quite difficult to compare an environmen-al impact against an economic criterion, since both of which have

o much difference in nature, making final scoring difficult. Thishould be taken into consideration when incorporating the LCAesults into the decision making process since some of the stake-olders probably cannot comprehend the implications of LCA and

0.0454 A6 0.0429 A50.0440 A5 0.0422 A3*

consequences of the environmental impacts. A possible way to min-imize such influence could be the enhancement of communicationduring the implementation of the AHP.

Varying degree of uncertainty may be assumed with respect tothe different degree of information diffusion among stakeholdersin this section to signify the sensitivity of fuzzy classes. Changes canbe reported based on the most sensitive retardation of informationdiffusion so that the final option may be altered. A5 is no longerthe best option and the best one becomes alternative A1, which isbased on the implementation of aerobic MBT units, including PAYTprogram.

8. Conclusions

The selection of waste management strategies to improve sus-tainability in the AMARSUL system is a challenging issue whenreaching the targets at national level set by the European Directives.There are many alternatives that can be geared toward reachingsuch goals, but how the policy information can be propagatedfrom government to all stakeholders of the general public andhow the stakeholders respond to this urgency would be uncer-tain. If the new measures like PAYT have to be in place associatedwith 18 alternatives into decision making process to promotethe odds of success, a scientific methodology (i.e., UQ) to assess

waste management alternatives should be available. Through theuse of interval-valued triangular fuzzy numbers to express lin-guistic uncertainty embedded in the decision process, a MADMmodel in this study provides us with an objective screening and

2 rvation

rnBrSwi

tscrtttoa

A

AFade

R

A

A

B

BB

B

B

C

C

C

C

CC

C

C

C

C

D

D

E

E

0 A. Pires et al. / Resources, Conse

anking procedure with respect to environmental, economic, tech-ical and social criteria partially supported by a stand-alone LCA.oth AHP and TOPSIS are seamlessly integrated and applied toetrieve criteria weights for alternative selection. Whereas IVF TOP-IS is employed to determine the priorities of the alternatives, theeights derived from AHP reveal the impacts in a societal context

n decision-making.Overall, the integrated method has been proven adequate in

his case study, since the uncertainty embraced during the deci-ion analysis ensures that a variety of sources of uncertainty can beollectively characterized by the IVF scheme in concert with TOPSISanking. Final success of this thrust in the AMARSUL system is tiedo the handling of recycling programs, and the selection PAYT, andhe choice of the best solution. Overall, future work may be directedo improve the retrieval of the weights through different methodsther than AHP to further address risk communication complexityssociated with uncertainty simultaneously.

cknowledgements

The authors are grateful for support from the Seixal, Palmela,lmada, Montijo and Moita municipalities, Empresa Geral doomento company, Extruplás company, and also to the nationalssociations Plastval, Fileira Metal, Recipac. We acknowledge all theata and reports cited and used in this study. Ana Pires acknowl-dges FCT for her PhD grant (SFRH/BD/27402/2006).

eferences

MARSUL. Relatório e contas 2009. Available from: http://www.amarsul.pt/relatorios e contas.php; 2009 [accessed 15.07.09].

shtiani B, Haghighirad F, Makui A, Ali Montazer G. Extension of fuzzy TOP-SIS method based on interval-valued fuzzy sets. Appl Soft Comput 2009;9:457–61.

ello-Dambatta A, Farmani R, Javadi AA, Evans BM. The analytical hierarchy processfor contaminated land management. Adv Eng Inform 2009;23:433–41.

erlyne DE. Uncertainty, epistemic curiosity. Br J Psychol 1962;53:27–34.elton V, Stewart TJ. Multiple criteria decision analysis: an integrated approach.

Boston: Kluwer Academic Publications; 2002.rans JP, Mareschal B, Vincke PH. PROMETHEE: a new family of outranking methods

in multicriteria analysis. Oper Res 1984;84:447–90.rans JP, Mareschal B. The PROMCALC & GAIA decision support system for multicri-

teria decision aid. Decis Support Syst 1994;12:297–310.hang Y-H, Yeh C-H. Evaluating airline competitiveness using multiattribute deci-

sion making. Omega 2001;29:405–15.hen CT. Extensions of the TOPSIS for group decision-making under fuzzy environ-

ment. Fuzzy Sets Syst 2000;114:1–9.heng S, Chan CW, Huang GH. Using multiple criteria decision analysis for support-

ing decision of solid waste management. J Environ Sci Health 2002;A37:975–90.heng S, Chan CW, Huang GH. An integrated multi-criteria decision analysis and

inexact mixed integer linear programming approach for solid waste manage-ment. Eng Appl Artif Intell 2003;16:543–54.

hongfu H. Principle of information diffusion. Fuzzy Sets Syst 1997;91:69–90.hou S-Y, Chang Y-H, Shen C-Y. A fuzzy simple additive weighting system under

group decision-making for facility location selection with objective/subjectiveattributes. Eur J Oper Res 2008;189:132–45.

ontreras F, Hanaki K, Aramaki T, Connors S. Application of analytical hierarchy pro-cess to analyze stakeholders preferences for municipal solid waste managementplans, Boston, USA. Resour Conserv Recycl 2008;52:979–91.

ouncil, European Parliament. Directive 2008/98/EC of the European Parliament andof the Council of 19 November 2008 on waste and repealing certain Directives.Off J Eur Commun 2008;L312/3.

ouncil, European Parliament. Directive 2004/12/EC of the European Parliament andof the Council of 11 February 2004 amending Directive 94/62/EC on packagingand packaging waste. Off J Eur Commun 2004;L047.

ouncil. Council Directive 99/31/EC of April 1999 on the landfill of waste. Off J EurCommun 1999;L182/1.

ai J, Qi J, Chi J, Chen S, Yang J, Ju L, et al. Integrated water resource securityevaluation of Beijing based on GRA and TOPSIS. Front Earth Sci China 2010;4:357–62.

ing JF, Liang GS. Using fuzzy MCDM to select partners of strategic alliances for linershipping. Inf Sci 2005;173:197–225.

C. Costs of Municipal Waste Management in the EU, Final Report toDirectorate General Environment. Available from: http://europa.eu.int/comm/environment/waste/studies/eucostwaste management.html; 2001[accessed 03.10.10].

GF. Personal communication. Empresa Geral do Fomento; 2009.

and Recycling 56 (2011) 7–21

Garcia-Cascales MS, Lamata MT. Adaptation of TOPSIS decision making approachfor linguistic variables. In: Vanhoof K, Ruan D, Li T, Wets G, editors. Intelligentdecision making systems – Proceedings of the 4th international ISKE conference.Singapore: World Scientific Publishing Co. Pte. Ltd.; 2010. p. 287–92.

Geng X, Chu X, Zhang Z. A new integrated design concept evaluation approach basedon vague sets. Expert Syst Appl 2010;37:6629–38.

Hisdal E. The IF THEN ELSE statement and interval-valued fuzzy sets of higher type.Int J Man-Mach Stud 1981;15:385–455.

Hokkanen J, Salminen P. Choosing a solid waste management system using multi-criteria decision analysis. Eur J Oper Res 1997;98:19–36.

InCI. Base: contratos públicos online (Database: online public contracts). Avail-able from: http://www.base.gov.pt/Paginas/Default.aspx; 2010 [accessed on03.07.10].

Jahanshahloo GR, Lotfi FH, Izadikhah M. An algorithmic method to extend TOP-SIS for decision-making problems with interval data. Appl Math Comput2006;175:1375–84.

Karnik NN, Mendel JM, Liang Q. Type-2 fuzzy logic systems. IEEE Trans Fuzzy Syst1999;7:643–58.

Kannan G, Pokharel S, Kumar S. A hybrid approach using ISM and fuzzy TOPSISfor the selection of reverse logistics provider. Resour Conserv Recycl 2009;54:28–36.

Kim G, Park CS, Yoon KP. Identifying investment opportunities for advanced manu-facturing systems with comparative-integrated performance measurement. IntJ Prod Econ 1997;50:23–33.

Liang Q, Mendel JM. Interval type-2 fuzzy logic systems: theory and design. IEEETrans Fuzzy Syst 2000;8:535–50.

Lin Z-C, Yang C-B. Evaluation of machine selection by the AHP method. J MaterProcess Technol 1996;57:253–8.

Linkov I, Satterstrom FK, Kiker G, Seager TP, Bridges TS, Gardner KH, et al. Multicri-teria decision analysis: a comprehensive decision approach for management ofcontaminated sediments. Risk Anal 2006;26:61–78.

Macharis C, Springael J, de Brucker K, Verbeke A. PROMETHEE and AHP: the designof operational synergies in multicriteria analysis: strengthening PROMETHEEwith ideas of AHP. Eur J Oper Res 2004;153:307–17.

MEI. Decreto-Lei n. 225/2007, de 31 de Maio. Available from:http://dre.pt/pdf1sdip/2007/05/10500/36303638.pdf; 2010 [accessed on10.07.10].

Nimmo D. Information and political behavior. In: Ruben BD, editor. Information andbehavior. New Jersey: Transaction Publishers; 1985. p. 343–68.

Norese MF. ELECTRE III as a support for participatory decision-making on the local-isation of waste-treatment plants. Land Use Policy 2006;23:76–85.

Önüt S, Soner S. Transshipment site selection using the AHP and TOPSIS approachesunder fuzzy environment. Waste Manage 2008;28:1552–9.

Piedade M, Aguiar P. Opcões de Gestão de Resíduos Urbanos (Urban Waste Manage-ment Options). Lisboa: ERSAR – Guias técnicos 15; 2010.

Pires A, Chang NB, Martinho G. Reliability-based life cycle assessment for futuresolid waste management alternatives in Portugal. Int J Life Cycle Assess2011;16(4):316–37.

Pohekar SD, Ramachandran M. Application of multi-criteria decision making to sus-tainable energy planning-A review. Renew Sust Energy Rev 2004;8:365–81.

Queiruga D, Walther G, González-Benito J, Spengler T. Evaluation of sites for thelocation of WEEE recycling plants in Spain. Waste Manage 2008;28:190–1.

Rogers EM. Diffusion of innovations. New York: Free Press; 1962.Rousis K, Moustakas K, Malamis S. Multi-criteria analysis for the determination

of the best WEEE management scenario in Cyprus. Waste Manage 2008;28:1941–54.

Roy B. How outranking relation helps multiple criteria decision making in topicsin multiple criteria decision making. In: Cochrane J, Zeleny M, editors. Multiplecriteria decision-making. Columbia: University of South Carolina Press; 1973. p.179–201.

Roy B. The outranking approach and the foundations of ELECTRE methods. DecisTheory 1991;31:49–73.

Saaty TL. The analytic hierarchy process. New York: McGraw-Hill; 1980.Saaty TL, Vargas LG. Models, methods, concepts & applications of the analytic hier-

archy process. Massachusets: Kluwer Academic Publishers; 2001.Saaty T. Decision making – the analytic hierarchy and network processes (AHP/ANP).

J Syst Sci Syst Eng 2004;13:1–35.SPV. Sociedade Ponto Verde – Contrapartidas financeiras (Green Dot System – Finan-

cial counterparts). Available from: http://www.pontoverde.pt/; 2010 [accessedon 03.07.10].

Tahriri F, Osman MR, Ali A, Yusuff RM. A review of supplier selection methods inmanufacturing industries. Suranaree J Sci Technol 2008;15:201–8.

Tsilemou K, Panagiotakopoulos D. Estimating costs for solid waste treatment facil-ities. In: Proceedings of ISWA world environmental congress and exhibition;2004.

Tsilemou K, Panagiotakopoulos D. A statistical methodology for generating costfunctions for solid waste treatment facilities. In: Proceedings of the 5th inter-national exhibition and conference in environmental technology (HELECO’05),2005.

Türksen IB. An ontological and epistemological perspective of fuzzy set theory.Netherlands: Elsevier; 2006.

Vego G, Kucar-Dragicevic S, Koprivanac N. Application of multi-criteria decision-making on strategic municipal solid waste management in Dalmatia, Croatia.Waste Manage 2008;28:2192–201.

Wang JJ, Yang DL. Using a hybrid multi-criteria decision aid method for informationsystems outsourcing. Comput Oper Res 2007;34:3691–700.

vation

Y

Z

A. Pires et al. / Resources, Conser

oon K, Hwang C-L. Manufacturing plant location analysis by multiple attributedecision making: part I-single-plant strategy. Int J Prod Res 1985;23:345–59.

adeh LA. The concept of a linguistic variable and its application to approximatereasoning Part I. Inf Sci 1975a;8:199–249.

and Recycling 56 (2011) 7–21 21

Zadeh LA. The concept of a linguistic variable and its application to approximatereasoning Part II. Inf Sci 1975b;8:301–57.

Zanakis SH, Solomon A, Wishart N, Dublish S. Multi-attribute decision making: asimulation comparison of select methods. Eur J Oper Res 1998;107:507–29.