Regional hospital solid waste assessment using the evidential reasoning approach

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Regional hospital solid waste assessment using the evidential reasoning approach

Armaghan Abed-Elmdoust a,⁎, Reza Kerachian b,1

a School of Civil Engineering, College of Engineering, University of Tehran, Tehran, Iranb School of Civil Engineering and Center of Excellence for Engineering and Management of Civil Infrastructures, College of Engineering, University of Tehran, Tehran, Iran

H I G H L I G H T S

► We assess the regional hospital solid waste using evidential reasoning (ER) approach.► Different types of uncertainties are considered in our assessment.► We used Dempster–Shafer theory to aggregate multiple hospital solid waste assessment criteria.► Distributed assessment for each regional hospital is provided by the proposed methodology.► Application of the proposed framework will help pointing out the most polluting hospital.

a b s t r a c ta r t i c l e i n f o

Article history:Received 3 April 2012Received in revised form 13 September 2012Accepted 23 September 2012Available online xxxx

Keywords:Hospital solid waste assessmentMultiple criteria decision analysisEvidential reasoning (ER)Uncertainty modelingUtility

Hospital solid waste assessment is regularly characterized by a large number of known criteria that are bothqualitative and quantitative in nature. The qualitative criteria can only be assessed by human judgments,which predictably engage a variety of uncertainties such as fuzziness and ignorance. Therefore, hospitalsolid waste assessments need to be analyzed and modeled using approaches that can handle uncertainties.The evidential reasoning (ER) approach can be utilized for such an analysis. In this paper, perhaps for thefirst time, the ER approach is applied to regional hospital solid waste assessment. The assessment criteriaare characterized by a set of assessment grades assumed to be commonly exclusive and communally exhaus-tive. All assessment information, incomplete or complete, qualitative or quantitative, and imprecise or pre-cise, are modeled using a cohesive belief structure. The ER approach will be used to aggregate multiplehospital solid waste assessment criteria, resulting in distributed assessment for each alternative. The pro-posed methodology is applied for regional hospital solid waste assessment in the province of Khuzestan, Iran.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

Due to the fact of industrialization and population growth, hospi-tal solid waste disposal, which includes an extensive scope of conta-gious hazardous pollutants, has turned out to be one of the mostimportant environmental issues. A limited number of studies relatedto the hospital solid waste management have been made, in particu-lar for the improvement of existing schemes for hospital wasteassessment.

Liberti et al. (1996) proposed a model to present optimal operat-ing policies for a general waste management system involving charac-terization, handling (collection, storage, transportation), and burningthe hospital wastes created by a large sanitary area. Awad et al.(2004) did some statistical analyses to develop prediction models for

the quantity of waste produced at two private and public hospitals lo-cated in Jordan. In their models, number of beds and patients, andtypes of hospitals were recognized as significant criteria. Multiple re-gressions were also used to estimate the generated waste quantity.

Morrissey and Browne (2004) had a review on various types ofmodels that are used in the area of hospital, municipal, and industrialwaste management and pointed out some principal weaknesses ofthese models. According to their work, most of the models in the lit-erature are decision support models being divided into three classesbased on: life cycle assessment, cost–benefit analysis, and multi-criteria decision making. Vego et al. (2008) modeled the efficacy ofdeveloping a waste management system in the coastal part of Croatia.Two multi-criteria decision-making (MCDM) methods, GAIA andPROMETHEE, were used for analysis and assessment of options. Theproblem was investigated according to numerous social, economic,and ecological criteria sets that were recognized as related to thedecision-making procedure. The GAIA and PROMETHEE methodswere shown to be efficient tools for investigating the considered prob-lem. Such an attitude delivered new awareness to waste management

Science of the Total Environment 441 (2012) 67–76

⁎ Corresponding author. Fax: +98 21 66403808.E-mail addresses: [email protected], [email protected]

(A. Abed-Elmdoust), [email protected] (R. Kerachian).1 Tel.: +98 21 61112176; fax: +98 21 66403808.

0048-9697/$ – see front matter © 2012 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.scitotenv.2012.09.050

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planning (WMP) at the strategic level, and provided an aim for rethink-ing about the current documents of strategic waste management inCroatia.

Ulukan and Kop (2009) compared several collection methodsusing fuzzy TOPSIS method. To study the solid waste recovery, theytook into consideration the social, financial, and also environmentalcriteria. The innovation of their study was that the decision makingprocedure was enhanced by using the environmental impact data.They assessed the environmental special effects via life cycle assess-ment approach.

Zamali et al. (2009) focused on the expansion of a new MCDMmethod with giving emphasis to the several natures of the input datain the assessment procedure to select the bestway for disposingmunic-ipal solid wastes (MSW). Through using both fuzzy ideal solution tech-nique and the analytic hierarchy process (AHP), the usage of dilationconcept was fully hired in their methodology. The results revealedthat their methodology is effective in dealing with the uncertainty ofthe primary data and simplifies an organized decision making.

De Feo and De Gisi (2010) verified the efficiency of applying a newcriteria weighting tool for ranking a list of municipal solid waste man-agement sites using AHP. In order to study both the social and techni-cal criteria; the usage of the “priority scale” was proposed to simplygather non-conflicting criteria preferences by the decision-makers.The proposed technique was used to the site selection of a compostingplant in a region suffering from a severe MSW emergency.

Du et al. (2011) set up a hybrid model of analytical hierarchy pro-cess and fuzzy comprehensive evaluation for a municipal solid wastemanagement option selection. Dalian Development Area of China waschosen as their case study to validate the practicality of their modelfor municipal solid waste management option selection.

Kumar and Hassan (2012) used AHP for selecting an appropriatelandfill site for disposal of SWM. Various criteria such as distancefrom residential places, existence of water-bodies and forests, trans-port connectivity, groundwater table level and geology were consid-ered in the AHP-based decision making.

Arthur P. Dempster introduced the evidence theory in the 1960s.Later, this theory was refined and extended by Glen Shafer in the1970s. Hence, this theory is known as the Dempster–Shafer theory(or the D–S theory) of evidence. The D–S theory is interrelated to theBayesian probability theory. That is, they both dealwith subjective beliefs.On the other hand, according to Shafer (1976), the Bayesian probabilitytheory is included in the evidence theory as a special case. The largest dif-ference being in that the latter is able to deal with ignorance, while theformer is not and its subjective beliefs have to obey the probability rules.

To date, the D–S theory has found extensive applications in manyareas such as expert systems, artificial intelligence (AI), pattern recogni-tion, knowledge anddatabase discovery, information fusion, risk assess-ment, multiple attribute decision analysis (MADA), etc. (Denoeux andZouhal, 2001; Hullermeier, 2001; Beynon, 2005a; Davis and Hall,2003; Xu et al., 2006; Soundappan et al., 2004; Cobb and Shenon, 2003).

In this paper, a new framework is proposed for hospital solid wasteassessment. Different criteria can be employed for the evaluation of thepollution caused by the existing hospital solid wastes and the efficacyof the existing management schemes. For ranking the hospitals and de-termining the share of each in the whole hospital solid waste pollutionload, a multiple criteria decision making technique, namely evidentialreasoning (ER) approach, is used. The suggestedmethodology is assessedusing data from 40 hospitals in the province of Khuzestan inwhich, mostof the hospital solid wastes are disposed, stored, or burnt in open spaces.In some cases, these solidwastes are disposed in domesticwaste landfills,which can cause considerable environmental and healthiness problems.

2. The Dempster–Shafer theory of evidence

Let θ={H1,…,HN} be a set of propositions or hypotheses. This set ofhypotheses is called the frame of discernment. The basic probability

assignment (bpa) of this set is a mass function m :2θ→[0,1] satisfyingthe following constraints:

∑Apθ

m Að Þ ¼ 1andm ϕð Þ ¼ 0; ð1Þ

where A is any subset of θ,ϕ is an empty set, and 2θ={ϕ,{H1},…{HN},{H1,H2},…,{H1,HN},…,θ} is the power set of θ that contains all subsets of θ.m(A) is the belief (also called probability mass) allocated to A and ishow sturdily the evidence supports A. All the allocated probabilities sumto unity and there is no belief in the empty set (ϕ). The allocated probabil-ity to θ, i.e.m(θ), would be the degree of ignorance.

Each subset Apθ such that m(A)>0 is a central element of m. Allthe related central elements are jointly named as the body ofevidence.

Associated with each bpa is the plausibility measure, Pl, and thebelief measure, Bel, which are calculated by using the following equa-tions, respectively:

Pl Að Þ ¼ ∑A∩B≠ϕ

m Bð Þ; ð2Þ

Bel Að Þ ¼ ∑BpA

m Bð Þ; ð3Þ

where A and B are subsets of θ. Pl(A) is the potential support to A, i.e. thewhole quantity of belief thatmay possibly be allocated toA; Bel(A) is theprecise support to A. i.e. the belief of the hypothesis A being factual.[Bel(A),Pl(A)] represent the interval support to A i.e. the lower andupper bounds of the probability allocated to A being factual. Thesetwo functions can be related by the equation:

Pl Að Þ ¼ 1−Bel �A� �

; ð4Þ

where Ā is the complement of A. The distinction between Pl and Bel of aset A is called the assessment ignorance of the set A (Shafer, 1976).

The Dempster's rule of combination is the heart of the evidencetheory by which the evidence from diverse foundations is aggregatedor combined. The rule presumes that the data sources are not depen-dent and employs the orthogonal sum to aggregate various beliefconstructions:

m ¼ m1⊕m2⊕…⊕mK ; ð5Þ

where ⊕ denotes the combination operator. For two belief structuresm1 and m2, the Dempster's rule of combination would be written asfollows: (Wang et al., 2006)

m1⊕m2½ � Cð Þ ¼0; C ¼ ϕ;

∑A∩B¼C

m1 Að Þm2 Bð Þ1− ∑

A∩B¼ϕm1 Að Þm2 Bð Þ ; C≠ϕ;

8>><>>:

ð6Þ

where A and B are both central fundamentals and [m1⊕m2](C) is amass function (bpa). The denominator, 1− ∑

A∩B¼ϕm1 Að Þm2 Bð Þ is the

normalization factor, ∑A∩B¼ϕ

m1 Að Þm2 Bð Þ is named as the degree of con-

flict, which measures the conflict between the portions of evidence(George and Pal, 1996).

The Dempster's rule of combination is shown to be bothassociative ((m1⊕m2)⊕m3=m1⊕ (m2⊕m3)) and commutative(m1⊕m2=m2⊕m1) (Shafer, 1976). These two properties indicatethat evidence can be aggregated in any order. Hence, in the caseof various belief constructions, the aggregation of evidence can bedone in a pairwise way.

Note that the basic appliance of the D–S theory and the aggrega-tion rule can result in illogical termination in the aggregation of vari-ous portions of evidence in conflict (Murphy, 2000). This concern is

68 A. Abed-Elmdoust, R. Kerachian / Science of the Total Environment 441 (2012) 67–76


conquered in the ER approach brought in the next section by pro-ducing basic probability assignment through the aggregation ofbelief degrees and by normalizing the aggregated probabilitymasses.

3. Evidential reasoning (ER) approach for hospital solidwaste assessment

The ER approach for hospital solid waste assessment consistschiefly of four key parts, which are the identification of hospitalsolid waste assessment criteria, the ER distributed modeling frame-work for the identified solid waste assessment criteria, the recursiveand analytical ER algorithms for aggregating multiple identified envi-ronmental criteria, and the utility interval based ER ranking methodwhich is designed to compare alternatives analytically. Each partwill be described in detail in this section.

3.1. The identification of hospital solid waste assessment criteria

This is the first step to conduct hospital solid waste assessment. Inthis step, all contributing criteria that will probably be involved needto be investigated and carefully identified. Generally speaking, determi-native criteria can be described in two broad categories: the solid wastegeneration, consisting of hazardous solid wastes and non-hazardoussolid wastes criteria, and the solid waste management, again consistingof hazardous solid wastes and non-hazardous solid wastes criteria. Asshown in Fig. 1, each categorymay include the following typical criteria:

• Solid waste generation (hazardous solid wastes): Pharmaceuticalwastes, sharps wastes, and human tissue wastes.

• Solidwaste generation (non-hazardous solid wastes): Semi-domesticwastes, paper wastes, food wastes, and miscellaneous.

• Solidwastemanagement (hazardous solidwastes): Separation, storage,transportation, and disposal of solid wastes.

• Solid waste management (non-hazardous solid wastes): Separation,storage, transportation, and disposal of solid wastes.

The key concern in this step is to make sure that all needed criteriaare considered. Typically, a primary list of criteria of possible rele-vance to a wished-for project may be first determined throughoutall-embracing literature review. Review of other recent hospitalwaste assessment on similar projects or projects in the same geolog-ical area as the planned project. And then, a selected list of significantcriteria for a certain project can be screened during site visits, engi-neering judgments, interdisciplinary team negotiations, and so on.

Site visits can make available familiarization with an area in ques-tion and allow more efficient review of existing environmental data.Interdisciplinary team discussions can clarify the project impactsand can also enlighten the pertinent criteria which were not includedin any preliminary list. The subsequent three criteria questions can behelpful in screening and identifying criteria; if any of these criteria berelevant to a given criterion, then that criterion must be included(Canter, 1996):

• Is the criterion affected beneficially or adversely by any of the alter-natives under study?

• Will the criterion apply any pressure on project scheduling or asucceeding operational phase of any of the alternatives?

• Is the criterion the particular interest of public or debated containedby the local people?

Objective:Determination of the share of each hospitalin the total solid waste

pollution

Solid waste management

(0.35)

Solid waste generation

(0.65)

Hazardous (0.65)

Non-hazardous

(0.35)

Hazardous (0.75)

Non-hazardous

(0.25)

Separation (0.25)

Storage (0.15)

Transportation (0.15)

Disposal (0.45)

Level 4

Separation (0.3)

Storage (0.15)

Transportation (0.15)

Disposal (0.4)

Pharmaceutical wastes (0.25)

Sharps (0.3)

Human issues (0.45)

Level 3 Level 2 Level 1

Semi-domestic (0.2)

Paper (0.1)

Food wastes (0.3)

Miscellaneous (0.4)

Fig. 1. Hierarchy structure of indicators and their relative weights (numbers in the parentheses) for ranking of hospitals based on their solid waste generation and management.(Adapted from Karamouz et al., 2007).

69A. Abed-Elmdoust, R. Kerachian / Science of the Total Environment 441 (2012) 67–76


3.2. The ER distributed modeling framework for hospital solid wasteassessment — the belief structure

To carry out hospital solid waste assessment, the impacts of therecognized criteria need to be known and assessed. The recognizedhospital assessment criteria can be assessed based on the grades de-fined in Table 1.

H ¼ H1;H2;H3;H4;H5;H6;H7;H8;H9f g

Please note that based on the requirement of real applications, thevariety of assessment grades would change. In other words, theywould be defined more generally or more accurately. In the ER frame-work, each criterion can even have a different set of assessmentgrades; although, these different sets of assessment grades have tobe unified before the operation of the ER algorithm.

Suppose a hospital solid waste assessment problem has O alterna-tives or options, Oj(j=1,…,K), to choose from and M attributes,Ai(i=1,…,M), to consider. Using the five evaluation grades, the as-sessment of an attribute A1 on an alternative O1, denoted byS(A1(O1)), can be symbolized using the following belief structure:

S A1 O1ð Þð Þ ¼ β1;1;H1 Þ; ðβ2;1;H2 Þ; β3;1;H3 Þ; β4;1;H4 Þ; β5;1;H5

� �� o��n

ð7Þ

where, 0≤βn ;1≤1 n ¼ 1;…;5ð Þ denotes the belief degree that the attri-bute A1 is evaluated to be grade Hn. S(A1(O1)) means that the attri-bute A1 for the option O1 is evaluated to be grade Hn with a degreeof βn,1×100%(n=1,…,5).

There must not beX5n¼1

βn;1 > 1: S(A1(O1)) can be considered as a

complete distributed assessment ifX5n¼1

βn;1 ¼ 1 and an incomplete as-

sessment ifX5n¼1

βn;1b1: In the ER approach, both complete and incom-

plete evaluations can be contained (Yang, 2001).In the ER framework, an MCDM problem with M attributes Ai(i=

1,…,M), K alternatives Oj(j=1,…,K) and N evaluation gradesHn(n=1,…,N) for each attribute is written off as an extended deci-sion matrix S(Ai(Oj)) as its element at the i-th row and j -th columnwhere S(Ai(Oj)) is given as follows:

S Ai Oj

� �� ¼ Hn;βn;i oj

� �� ;n ¼ 1;…;N

n oi ¼ 1;…;M; j ¼ 1;…;K: ð8Þ

All the distributed assessment information included in the beliefdecision matrix would be aggregated in a logical and efficient wayusing the ER algorithms discussed in the next section.

3.3. The recursive and analytical ER algorithms

Different from the existing hospital solid waste assessment ap-proaches such as the well-known weighted-ranking AHP, the ERmethodology presents an efficient procedure of synthesizing the eval-uation information on the recognized criteria. The procedure is basedon the belief decision matrix and also the combination rule of the D–Stheory of evidence. In other words, instead of using the averagescores, the ER approach utilizes an evidential reasoning algorithm toaggregate belief degrees. The evidential reasoning algorithm is devel-oped based on the decision theory and the evidence aggregation ruleof the D–S theory. A recursive ER algorithm for aggregating M attri-butes for an alternative (option) O was presented in the past (Yangand Sen, 1994a, b; Yang and Singh, 1994; Yang, 2001; Yang and Xu,2002a; Yang et al., 2006a, b), which can be used here to aggregateM hospital solid waste assessment criteria.

Hence, grade scaling is not essential for attribute aggregating inthe ER approach and this is one of the differences between ER andthe conventional MCDM approaches, most of which combine aver-age scores. The recursive ER algorithm is introduced in brief asfollows.

Suppose ω1 is the relative weight of the attribute Ai and is normal-

ized so that 0bωib1 andXLi¼1

ωi ¼ 1 where L is the total number of at-

tributes in the same hierarchy level. To make the discussion simpler,only the aggregation of a complete assessment is checked. The expla-nation of the proficiency of the recursive ER algorithm in aggregatingboth complete and incomplete assessments is comprehensive in Yang& Sen 1994 a, b and Yang 2001. Without loss of generalization and forillustration purposes, the ER method for combining just two attributeassessments is presented in this section.

Suppose the first assessment is given in Eq. (7) and the secondS(A2(O1)) is given by

S A2 O1ð Þð Þ ¼ β1;2;H1 Þ; ðβ2;2;H2 Þ; β3;2;H3 Þ; β4;2;H4 Þ; β5;2;H5

� �� o:

��n

ð9Þ

Theproblem is to combine (aggregate) the twoassessments S(A1(O1))and S(A2(O1)) to produce a combined assessment S(A1(O1))⊕S(A2(O1)).Suppose S(A1(O1)) and S(A2(O1)) are both complete. Let

mn;1 ¼ ω1βn;1 n ¼ 1;…;5ð Þ and mH;1 ¼ 1−ω1

X5n¼1

βn;1 ¼ 1−ω1 ð10Þ

mn;2 ¼ ω2βn;2 n ¼ 1;…;5ð Þ and mH;2 ¼ 1−ω2

X5n¼1

βn;2 ¼ 1−ω2 ð11Þ

where each mn,j(j=1,2) is called the basic probability mass and eachmH,j(j=1,2) is the left behind belief for attribute j unassigned to anyof the Hn(n=1,2,3,4,5). n is the number of evaluation grades.

The ER algorithm is applied to combine the basic probabilitymasses to produce the aggregated probability masses, denoted bymn(n=1,…,5) and mH using the following equations:

mn ¼ k mn;1mn;2 þmH;1mn;2 þmn;1mH;2

� �; n ¼ 1;…;5ð Þ ð12Þ

mH ¼ k mH;1mH;2

� �ð13Þ

Table 1Assessment grades used for the description of impacts.

Assessment grades Description of assessment grades

H1 Significant preferred impactH2 Moderately preferred impactH3 Preferred impactH4 Slightly preferred impactH5 No impactH6 Slightly undesirable impactH7 Undesirable impactH8 Moderately undesirable impactH9 Significant undesirable impact



where

k ¼ 1−X5t¼1

X5

n ¼ 1n≠t

mt;1mn;2

0BBBB@

1CCCCA

−1

: ð14Þ

The aggregated probability masses will then be combined with the3rd assessment in the same manner. The process is gone over until allassessments are combined. The final aggregated probability massesare free of the order in which separate assessments are combined.

If we have just two assessments, the aggregated degrees of beliefβn(n=1,…,5) are produced by:

βn ¼ mn

1−mHn ¼ 1;…;5ð Þ: ð15Þ

The aggregated assessment for the alternative O1 can then be sig-nified as follows:

S O1ð Þ ¼ H1;β1ð Þ; H2;β2ð Þ; H3;β3ð Þ; H4;β4ð Þ; H5;β5ð Þf g: ð16Þ

3.4. The utility interval based ER ranking method

The aggregated distributed assessment S(A(Oj))={(Hn,βn(oj)),n=1,…,N} indicates the total assessment for the option Oj. It presents adistributed view about the assessment of the option. From this distrib-uted assessment view, one can notify which grades the option Oj isassessed to, what belief degrees are allocated to all the grades, andwhat most important impacts on the total the option has. Though, itmay not be easy to use the distributed assessments for ranking theoptions.

For rankingK options in the existence of incomplete assessments, pre-sume the utility of an assessment grade Hn is u(Hn), then the expectedutility of the combined assessment S(A(Oj)) is calculated as follows:

S A Oj

� �� ¼

XNn¼1

βn Oj

� �u Hnð Þ: ð17Þ

For example, having the aggregated assessment for the option O1

as S(O1)={(H1,β1),(H2,β2),(H3,β3),(H4,β4),(H5,β5)}, an average scorefor O1, denoted by u(O1), can be presented by means of the weightedaverage of the scores (utilities) of the assessment grades with the de-grees of belief as weights:

u O1ð Þ ¼X5n¼1

u Hnð Þβn O1ð Þ ð18Þ

where, u(Hn) is the utility of the n-th assessment grade Hn. For exam-ple, the utilities of the assessment grades may be given as follows:

u H1ð Þ ¼ 0:2 Slightly preferredð Þ

u H2ð Þ ¼ 0:45 Preferredð Þ

u H3ð Þ ¼ 0:60 Moderately preferredð Þ

u H4ð Þ ¼ 0:75 Significant preferredð Þ

u H5ð Þ ¼ 1:00 Major preferredð Þ:

4. Case study

The proposed approach is applied for ranking 40 hospitals locatedin the Khuzestan province of Iran. The total hospital solid waste gen-eration in the study area is about 13 tons per day, of which about 27%is hazardous wastes (KDOE, 2003).

In this study, the required basic data, the foremost criteria for thehospital solid waste classification, the methods applied for hospitalwaste management in the Khuzestan province, the main characteris-tics of hospitals in the study area as well as the quantitative and qual-itative characteristics of solid waste of each hospital were extractedfrom existing technical reports prepared by the Khuzestan Depart-ment of Environment (KDOE) in Iran. Interviews have been donewith experts in order to determine the relative importance of criteriaand sub-criteria.

Table 2The distributed assessments of the hospital assessment criteria.

Criteria/hospitals Hospital 1 Hospital 2 Hospital 3 Hospital 4 Hospital 5

Management (0.35)Hazardous solid waste (0.65)Separation (0.25) {(1, 0.75), (2, 0.25)} {(1, 0.5), (2, 0.25), (3, 0.25)} {(1, 0.5), (2, 0.5)} {(1, 0.75), (2, 0.25)} {(3, 0.1), (4, 0.9)}Storage (0.15) {(1, 0.75), (2, 0.25)} {(1, 0.7), (2, 0.3)} {(1, 0.5), (2, 0.5)} {(1, 0.2), (2, 0.8)} {(1, 0.2), (2, 0.8)}Transportation (0.15) {(1, 0.85), (2, 0.15)} {(1, 1.00)} {(1, 0.8), (2, 0.2)} {(1, 0.7), (2, 0.3)} {(2, 0.2), (3, 0.6), (4, 0.2)}Disposal (0.45) {(4, 0.3), (5, 0.7)} {(1, 0.3), (2, 0.4), (3, 0.3)} {(3, 0.5), (4, 0.5)} {(3, 0.3), (4, 0.7)} {(1, 0.5), (2, 0.5)}

Non-hazardous solid waste (0.35)Separation (0.3) {(1, 0.5), (2, 0.5)} {(1, 0.25), (2, 0.75)} {(1, 0.85), (2, 0.15)} {(1, 1.00)} {(4, 0.2), (5, 0.8)}Storage (0.15) {(1, 0.5), (2, 0.5)} {(1, 0.75), (2, 0.25)} {(1, 0.9), (2, 0.1)} {(1, 0.9), (2, 0.1)} {(1, 0.9), (2, 0.1)}Transportation (0.15) {(1, 0.85), (2, 0.15)} {(1, 1.00)} {(1, 0.8), (2, 0.2)} {(1, 0.7), (2, 0.3)} {(2, 0.2), (3, 0.6), (4, 0.2)}Disposal (0.4) {(4, 0.3), (5, 0.7)} {(1, 0.33), (2, 0.33), (3, 0.33)} {(1, 0.15), (2, 0.1), (3, 0.75)} {(4, 0.1), (5, 0.8)} {(4, 0.1), (5, 0.8)}

Generation (0.65) (kg/day)Hazardous solid waste (0.65)Pharmaceutical waste (0.25) 102 55.4 44 37.5 30Sharps (0.3) 31 27.6 19 22.5 20Human tissues (0.45) 148 92.25 87 100 50

Non-hazardous solid waste (0.35)Semi-domestic (0.2) 394 244 206 147 150Paper (0.1) 53 35 28 22 17Food waste (0.3) 320 452 259 207 10Miscellaneous (0.4) 51 55.35 30 34 25



To perform the regional hospital solid waste assessment, somesteps were listed in the previous section. Some of the fundamentalsteps are described as follows:

• Data gathering: Information and detailed data which are necessaryfor hospital evaluation should be collected by tripping differentunits, sending questionnaires and reconsidering the associated re-ports. Lack of data may be confronted via engineering judgmentand experts' opinion.

• Detection of the pollution sources: biomedical pollution sources de-tection is the first step. Some criteria such as hospital solid wastequality and quantity can be used for categorization of these pollu-tion sources.

• Specification of the evaluation criteria: An all-inclusive set of indi-cators should be chosen for the pollution load evaluation, environ-mental impact recognitions, and solid waste assessment in allhospitals. Indicators can be categorized in two key criteria, namelysolid waste generation and management. Some sub-criteria forthese criteria can be defined. For example for solid waste manage-ment, some sub-criteria such as the separation, storage, packing,transfer and disposal of the diverse types of hospital wastes canbe considered.

• Computing the environmental pollution share of each hospital viasolid waste disposal: Ranking the hospitals based on a hierarchystructure of criteria is imperative for the main pollution sourcesidentification. The hierarchy structure of criteria proposed byKaramouz et al. (2007), presented in Fig. 1, is used for this purpose.

The related weight of the criteria and sub-criteria in each level isdetermined using a pair-wise comparison (see Karamouz et al., 2002and Karamouz et al., 2003 for more details). To add in engineeringjudgments and exploit mixed information with uncertainties, theevidential reasoning approach (ER) has been used to combine thedistributed assessment (belief degrees) of the lower level attributesto higher level attributes gradually. The ER approach is used forranking the hospitals and determining their relative share in totalsolid waste pollution.

5. Results of applying ER for ranking hospitals

A hierarchy structure of criteria is applied for ranking the hospitalsbased on their solid waste generation and their management methods.As shown in Fig. 1, there are two major criteria for evaluating the solidwaste generation and management in the second level of the structure,which are the hazardous and non-hazardous hospital solid wastes. Inthis hierarchy structure, some sub-criteria such as separation, storage,transportation and disposal of different types of hospital solid wastesare considered as sub criteria to the solid waste management criterionin second level of the hierarchy structure. Solid waste generation isevaluated using the amount of hazardous and non-hazardous hospitalwastes. Hazardous hospital wastes contain sharps, pharmaceuticalwastes, and animal and human tissues.

The relative weights of the criteria are computed based on pair-wisecomparisons done by the experts and decision-makers familiarwith thesystem. These comparisons are typically accessible in the form of

Table 3The aggregated distributed assessments for the four alternatives (hospitals).

Hospital code Assessment criterion Degrees of belief assessed to each assessment grade

Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 9

H1-Ahw Solid waste management 0.24 0.07 0.01 0.03 0.14 0.49Solid waste generation 0.93 0.06 0.02

H2-Ahw Solid waste management 0.27 0.12 0.31 0.15 0.15Solid waste generation 0.21 0.36 0.42 0.01

H3-Ahw Solid waste management 0.27 0.10 0.01 0.39 0.18 0.04Solid waste generation 0.21 0.74 0.05

H4-Ahw Solid waste management 0.30 0.09 0.02 0.21 0.31 0.07Solid waste generation 0.54 0.35 0.10 0.00

H5-Kho Solid waste management 0.20 0.21 0.01 0.06 0.03 0.21 0.26Solid waste generation 0.11 0.33 0.54 0.03

0

5

10

15

20

25

30

35

40

45

50

55

60

Shar

e of

hos

pita

ls (

%)

Different regions in the province of Khuzestan (Iran)

Fig. 2. Share of hospitals located in different zones of the Khuzestan province in polluting the environment via solid waste disposal (%).



pair-wise comparison matrices. Decision-makers can hand over a con-sistent weight when only two criteria are concerned; neverthelesswhen there are numerous criteria, the judgments and weighting

about their value in environmental polluting via solid waste disposalare pretty complicated and can consequence in inconsistent evalua-tions. The relative weights used here in this study are derived fromthe pair-wise comparison done by Karamouz et al. (2007). In theirstudy, a group of experts and decision makers, with six environmentaland system engineers whowere skilled in hospital waste management,arranged the pair-wise comparison matrices. The geometric meanmethod (Saaty, 1994) was used to find the group judgment about therelative importance of sub-criteria, which resulted in the weightsshown in Fig. 1. The following matrix shows the group judgments forthe sub-criteria of the non-hazardous solid wastes as an example(Karamouz et al., 2007):

S ST T DSeparation Sð ÞStorage STð Þ

Transportation Tð ÞDisposal Dð Þ

1 2 1:5 0:50:5 1 1 0:360:66 1 1 0:32 3:3 2:7 1

2664

3775:

To carry out ER synthesis, the assessment information for all 40 hos-pitals was provided. The assessment information for the five hospitals ispresented in Table 2 in the form of distributed assessments for illustra-tion purposes, where the figures in parentheses for the hospital assess-ment criteria represent their respective relative weights. For example,the distributed assessment {(1, 0.75), (2, 0.25)} in Table 2 which isassigned to the separation of hazardous solid waste management forhospital 1 means that decision makers had uncertainty equal to 0.75and 0.25 about hospital 1 being grade 1 or 2 respectively. Moreover,there can be a degree of ignorance in a hospital solid waste assessmentas in assessing disposal of non-hazardous solid waste in hospital 4which is shown by distributed assessment {(4, 0.1), (5, 0.8)}. In this as-sessment, there would be 0.1% of ignorance, which is assigned to noneof the grades.

When the ER algorithm is applied to combine the evaluation infor-mation for the hospital assessment criteria, separation, storage, trans-portation, and disposal, are combined to produce evaluations forhazardous and non-hazardous solid wastes management, respective-ly. The criteria including the pharmaceutical wastes, sharps, humantissues, and the set of criteria including semi-domestic, paper, foodwastes, and miscellaneous wastes are combined to produce evalua-tions for hazardous and non-hazardous solid waste generations re-spectively. Then hazardous and non-hazardous solid wastes areaggregated to generate assessment for solid waste generation andmanagement. After all, the solid waste generation and management

0.000.501.001.502.002.503.003.504.004.505.005.506.006.507.007.508.008.50

Shar

e of

hos

pita

ls (

%)

Hospital code

Fig. 3. Share of 20 most polluting hospitals in the Khuzestan province in polluting the environment via solid waste disposal (%).

Table 4Ranking of hospitals based on solid waste generation (SWG), solid waste management(SWM) and both criteria of SWG and SWM (numbers 1 and 40 indicate the best andthe worst situations, respectively).

Hospitalcode

Ranking of hospitals

Considering solid wastegeneration (SWG)

Considering solid wastemanagement (SWM)

Considering bothSWG and SWM

H1-Ahw 1 8 1H2-Ahw 2 24 2H3-Ahw 5 28 5H4-Ahw 3 25 3H5-Kho 7 16 6H6-Beh 4 35 4H7-Ahw 6 29 7H8-Ram 8 10 8H9-Aba 12 16 14H10-Ahw 11 18 12H11-Sho 16 2 9H12-Ahw 15 9 10H13-Ahw 10 30 15H14-Ahw 17 6 11H15-Ahw 14 11 13H16-Ahw 25 5 17H17-Ahw 30 3 21H18-Ize 18 19 19H19-Dez 9 37 16H20-Ahw 22 13 18H21-Ahw 19 22 22H22-Ahw 32 4 29H23-Ahw 21 15 20H24-Shu 27 21 26H25-Mas 26 12 24H26-And 28 20 28H27-Ahw 20 23 25H28-Ahw 23 27 27H29-Sou 13 39 23H30-Omi 38 1 31H31-Beh 24 34 30H32-Mas 29 32 32H33-Beh 34 17 33H34-Sha 39 7 34H35-Aba 36 31 37H36-Dez 37 33 38H37-Agh 40 14 36H38-Aba 31 38 35H39-Mah 33 40 40H40-Mah 35 36 39



are aggregated to generate an overall assessment for each alternative(hospital). These results are presented in Table 3.

Fig. 2 shows the shares of different zones in the study area of thetotal pollution load. The top 20 most polluting hospitals, which aredetermined using ER, are also illustrated in Fig. 3. As shown in Fig. 2,Ahvaz region generates the uppermost load of hospital solid waste dis-posal (the share of Ahvaz region in polluting the environment is morethan 50%).

Ranking of hospitals definitely depends on the selected set ofcriteria. As illustrated in Table 4, there are different rankings for allpolluting hospitals by considering just generation of solid wastes, orjust managing of the solid wastes, or both.

In the same context, the share of each hospital in total hazardous solidwaste generation and the share of each considering all existing criteria de-rived from the ER approach are shown in Fig. 4. Moreover, the shares ofhospitals in hazardous and non-hazardous solid waste generation areshown in Fig. 5. As shown in Figs. 4 and 5, the shares of hospitals in pol-luting the environment absolutely depend on the selected set of criteria.

Table 5 exhibits the share of all inspected hospitals allowing for differ-ent relativeweights for solidwastemanagement and generation. As it canbe seen in this table, changing the weights could lead to different results.

6. Summary and conclusion

Different aspects for the pollution assessment of hospitals werediscussed in this paper. Explanation of objectives and recognition ofthe items and components of hospital assessment system were con-sidered and explained in the framework of a case study for the Prov-ince of Khuzestan in Iran.

In order to compute the impacts of hospital pollutions on the environ-ment in the study area, a MCDM technique, namely the ER method, wasused.

Regional hospital solid waste assessment engages great amount ofhuman judgments and different types of uncertainties, which consider-ably amplify the difficulty and complexity of the assessment process.The support to the solution of such hospital solid waste assessment

0

2

4

6

8

10

12

1 4 7 10 13 16 19 22 25 28 31 34 37 40

Hospitals

Shar

e of

hos

pita

ls (

%)

based on generatinghazardous solid waste

based on all criteria

Fig. 4. Comparing the shares of hospitals in hazardous solid waste generation and their total shares in polluting the environment.

0

2

4

6

8

10

12

1 4 7 10 13 16 19 22 25 28 31 34 37 40Hospitals

Shar

e of

hos

pita

ls (

%)

based on generatinghazardous solid waste

based on generatingnon-hazardous solidwaste

Fig. 5. Comparing the shares of hospitals in generating hazardous and non-hazardous solid wastes.



problems calls for potent methodologies that are proficient in dealingwith uncertainties in a way that is systematic, rational, flexible, reliable,and transparent. The evidential reasoning (ER) approach provides afresh, systematic andflexiblemanner to support hospital solidwaste as-sessment analysis. The novel analytical ER algorithm introduced in thispaper offers an explicit aggregation function, which can be applied inlots of decision making circumstances. In particular, the ER distributedmodeling structure makes it possible to handle a mixture of decisionmakers' judgments, crisp or fuzz, complete or incomplete, using the be-lief structure, which lets evaluators express evaluation information in anatural, flexible, and trustworthy manner. The ER structures offer twoorganized yet precise processes for combining evaluation informationin an analytical fashion. In this paper, a numerical example waspresented to demonstrate the implementation process of the ER ap-proach for hospital solid waste assessment. The results of applicationof the proposed framework in the province of Khuzestan in Iran showedthat Ahwaz, Behbahan, and Abadan are respectively the three mostpolluting regions in the Khuzestan province via their solid wastegeneration and management. The method used in this paper can be ef-fectively applied for developing amaster plan for regional hospital solidwaste management in future studies.

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Table 5Share of hospitals in polluting the environment considering different weights for themain criteria of solid waste management and generation.

Hospitalcode

SWM=0.1SWG=0.9

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Hospitalcode

SWM=0.6SWG=0.4

SWM=0.7SWG=0.3

SWM=0.8SWG=0.2

SWM=0.9SWQ=0.1

H1-Ahw 4.84 4.13 3.67 3.40H2-Ahw 3.25 2.75 2.46 2.30H3-Ahw 2.80 2.44 2.22 2.10H4-Ahw 3.11 2.68 2.42 2.27H5-Kho 2.92 2.80 2.74 2.71H6-Beh 2.50 2.09 1.85 1.73H7-Ahw 2.36 2.13 1.99 1.93H8-Ram 3.09 3.06 3.06 3.08H9-Aba 2.23 2.17 2.14 2.13H10-Ahw 2.49 2.45 2.44 2.44H11-Sho 3.93 4.11 4.21 4.26H12-Ahw 3.08 3.14 3.16 3.16H13-Ahw 2.00 1.89 1.84 1.83H14-Ahw 3.18 3.28 3.32 3.34H15-Ahw 2.83 2.87 2.91 2.94H16-Ahw 3.12 3.28 3.36 3.39H17-Ahw 3.52 3.79 3.94 4.01H18-Ize 2.32 2.34 2.38 2.41H19-Dez 1.69 1.54 1.45 1.41H20-Ahw 2.65 2.74 2.79 2.84H21-Ahw 2.34 2.37 2.38 2.39H22-Ahw 3.33 3.67 3.87 3.97H23-Ahw 2.62 2.70 2.75 2.78H24-Shu 2.33 2.38 2.41 2.42H25-Mas 2.61 2.72 2.80 2.85H26-And 2.23 2.31 2.36 2.40H27-Ahw 2.28 2.32 2.34 2.36H28-Ahw 1.99 2.00 2.02 2.05H29-Sou 1.46 1.31 1.22 1.18H30-Omi 3.69 4.09 4.29 4.36

(continued on next page)

Hospitalcode

SWM=0.6SWG=0.4

SWM=0.7SWG=0.3

SWM=0.8SWG=0.2

SWM=0.9SWQ=0.1

H31-Beh 1.72 1.70 1.70 1.71H32-Mas 1.75 1.77 1.79 1.81H33-Beh 2.15 2.34 2.44 2.48H34-Sha 2.74 3.05 3.21 3.27H35-Aba 1.61 1.74 1.80 1.83H36-Dez 1.51 1.66 1.75 1.80H37-Agh 2.35 2.62 2.76 2.80H38-Aba 1.31 1.33 1.34 1.35H39-Mah 0.78 0.86 0.93 0.99H40-Mah 1.26 1.37 1.45 1.50

SWG: Solid waste generation.SWM: Solid waste management.

Table 5 (continued)



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Regional hospital solid waste assessment using the evidential reasoning approach

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