Use of Belief Function in Brownfield Infrastructure Redevelopment Decision Making

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USE OF BELIEF FUNCTION IN BROWNFIELDINFRASTRUCTURE REDEVELOPMENT

DECISION MAKING

By Nii O. Attoh-Okine,1 P.E., and Juel Gibbons2

ABSTRACT: The decision making in brownfield infrastructure necessitates theconsideration of a multiplicity of complex, interrelated issues. However, technicalissues, liability issues, financial issues, community concerns, and future land-useconcerns are used to construct a hierarchical network for redevelopment decision-making. Finally, the Dempster-Shafer theory of combination is used to combineindependent evidence from various issues to determine the overall uncertainty inredevelopment decision making.

INTRODUCTION AND BACKGROUND

Brownfields are vacant, abandoned, or underutilized commercial and in-dustrial sites and facilities where real or perceived environmental contami-nation is an obstacle to redevelopment. These sites lie somewhere betweensignificantly contaminated sites (superfund sites) and pristine ‘‘Greenfields’’(used land parcels of farmlands outside urban borders). An estimated 130,000to 400,000 such sites exist, according to the U.S. General Accounting Office(Maldonado 1996). Over the last two decades, federal, state, and local en-vironmental regulations, designed to protect public health and natural re-sources, have unintentionally hampered the redevelopment of contaminatedsites. However, the 1990s came with the realization that brownfields rede-velopment makes sense both economically and environmentally. Several fed-eral initiatives have made available more conducive environments for rede-veloping brownfield sites; several states and municipalities have developed,or are in the process of developing, brownfields programs to manage theirinventory of sites. Several benefits are anticipated from returning these sitesto productive uses. These include the creation of new jobs and tax revenues,the protection of human health and environmental resources, the renewal andreuse of existing civil infrastructure, the protection of greenfields, and thecontrol of urban sprawl. While the benefits are numerous, so are the obstaclesassociated with the redevelopment of brownfields. Redevelopment issues typ-ically embrace legal liability concerns, financial, technical, and economicconstraints, competing redevelopment objectives, and uncertainties arisingfrom inadequate site information. These issues may have different levels ofimportance in different localities. Nonetheless, across the board, the processof redeveloping brownfields is similar, and the issues relating to brownfieldsredevelopment remain numerous, with complex relationships.

Reasoning from uncertain, incomplete, and sometimes inaccurate infor-mation is necessary whenever systems like the brownfields redevelopmentprocess and associated issues are to interact in an intelligent way. Typically,

1PhD, Dept. of Civ. and Envir. Engrg., Univ. of Delaware, Newark, DE 19716.E-mail: [email protected]

2Dept. of Civ. and Envir. Engrg., Univ. of Missouri, Rolla, MO 65409.Note. Discussion open until February 1, 2002. To extend the closing date one

month, a written request must be filed with the ASCE Manager of Journals. Themanuscript for this paper was submitted for review and possible publication on June21, 2000; revised May 24, 2001. This paper is part of the Journal of Urban Planningand Development, Vol. 127, No. 3, September, 2001. qASCE, ISSN 0733-9488/01/0003-0126–0143/$8.00 1 $.50 per page. Paper No. 21983.

126 / JOURNAL OF URBAN PLANNING AND DEVELOPMENT / SEPTEMBER 2001

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decision making in brownfields redevelopment embraces several issues, aswell as multiple interests, players, and objectives. Not only does brownfieldsredevelopment have to deal with multiple issues and stakeholders, but theredevelopment process may also be fraught with uncertainty. Environmentaland redevelopment information on abandoned sites is often unavailable. Incases where some information is found, it is likely to be highly deficient forthe purposes of thoroughly evaluating viable redevelopment alternatives andselecting the optimal redevelopment scenario. In addition, there have beenvarying degrees of uncertainty associated with extent and types of issuesassociated with brownfields sites.

Given many players in brownfields redevelopment and their potentiallyconflicting objectives, decisions will have to be clearly defensible and easilycommunicated to all parties. In this complex environment, the comprehensiveneeds in brownfields decision making and uncertainties involved in the de-cision-making process could adequately be captured and expressed using be-lief functions, otherwise known as Dempster-Shafer theory.

Attoh-Okine (1998) proposed the use of Bayesian influence diagrams, atype of directed acyclic graph (DAG), as a potential solution for addressinguncertainties in the brownfield redevelopment process. Influence diagramsprovide a graph-theoretic framework for modeling the probabilistic depen-dence of information between uncertain variables, decision options, and util-ity functions in complex decision systems. Influence diagrams also offer animportant complement to more traditional representations, such as decisiontrees and tabular listings of joint probability distribution and outcomes foreach action. DAGs express outcomes in terms of combination of primitiveevents. In addition, the graphical structure of these models captures the de-pendency structure among events, enabling the decision maker to exploitconditional independence to reduce specification and computation.

The nature of the brownfield infrastructure redevelopment process is suchthat a method to address uncertainty needs to have the following properties:

• The method should be able to handle incomplete or conflicting evidence.It is well understood that many databases and information sources forbrownfield infrastructure are quite incomplete.

• The method should be able to incorporate updates or corrections in ev-idence. As new federal, state, and local incentives and techniques forassessing brownfield sites emerge, updates in hypotheses relevant tobrownfield infrastructure redevelopment should be readily assessed.

• The nested or hierarchical nature of hypotheses for the brownfields re-development process should be addressed. Hypotheses for the brown-fields infrastructure redevelopment process can typically be broken downinto subhypotheses.

• The method should be able to generate alternative solutions.• The method should take advantage of all available information.

The present stage of the brownfields infrastructure redevelopment process—incomplete data and information, and changing data, in addition to thechanging nature of federal, state, local, financial, and real estate laws—makesuse of the belief functions framework as an appropriate tool in brownfielddecision-making. This occurs because the factors involved in brownfield in-frastructure are constantly changing. Furthermore, uncertainties and subjec-tive judgments are also present when a decision must specify an optimalalternative.

JOURNAL OF URBAN PLANNING AND DEVELOPMENT / SEPTEMBER 2001 / 127

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Fundamental to the belief function is the representation of uncertain knowl-edge in the form of basic probability assignments in which probabilities canbe assigned to directly form subsets of states of nature. The direct conse-quence of this kind of assignment is that, although the actual probability ofany individual subset of nature may not be specified, its minimum and max-imum values will be specified (Caselton and Wuben 1992).

Given pieces of independent evidence, general inferences may be madeabout what each piece implies. The Dempster-Shafer theory of evidence rea-soning allows one to combine evidence in a consistent and probabilistic man-ner. The theory can be applied to obtain a more complete assessment of whatthe entire body of evidence implies when taken as a whole—for example,in assessing site remediation given several pieces of evidence, including thepresence or absence of hazardous material. Each piece of evidence alone maybe used to lend credibility or ‘‘belief’’ to a particular hypothesis. It is, how-ever, helpful to know what each piece of evidence implies, relative to the setof all possible outcomes.

The purpose of this article is to demonstrate how the belief function frame-work can be used in brownfield infrastructure redevelopment decision pro-cesses.

THE BROWNFIELDS REDEVELOPMENT PROCESS

Most brownfields programs follow a generic four-step process for rede-veloping brownfields sites:

1. Site identification2. Site assessment3. Site remediation4. Site redevelopment

Site IdentificationA number of sites that have been designated as brownfields possess the

stigma of being contaminated, rather than having any actual site contami-nation. While the USEPA has estimated about 450,000 brownfields sites na-tionwide (Angelo 1995), many of these sites may not be contaminated at allbut are merely perceived to be so (Maldonado 1996). Thus, the first step inany brownfields redevelopment initiative is to identify contaminated brown-fields and develop an inventory of these sites. This stage usually involves aPhase I site assessment, in which environmental consultants are engaged toprovide an analysis of government and other historical records, perform sitereconnaissance studies, and interview owners, occupants, and others associ-ated with the site, in order to determine if there is evidence of contamination.

The legal liability framework for contaminated sites strongly influenceswhether or not site identification will be pursued by parties interested inbrownfields redevelopment. Uncertainty over the extent and types of legalliabilities attached to contaminated sites acts as a barrier to site remediationand redevelopment.

Site AssessmentIf the Phase I assessment reveals evidence of contamination, a Phase II

level assessment may then be conducted. This includes actual sampling ofthe soil and groundwater and results in the determination of the actual typeand extent of site contamination. This phase also involves the determination


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of appropriate cleanup standards, the identification of feasible site remedia-tion technologies for cleaning up the contamination, and an estimation of siteremediation costs. The determination of a feasible plan and level of cleanupis based on a host of criteria, including toxicity, exposure pathways and as-sociated risk, surrounding land uses, economic considerations, and future landuse. The decision to proceed with site assessment involves some levels oflegal liability and financial assurances, as well as favorable socioeconomicfactors. In cases where a number of sites are to be redeveloped, an attemptmay be made to prioritize the redevelopment of sites in an order that makesthe best use of otherwise limited resources.

Site RemediationSite remediation involves the actual remediation of the site to clean up

levels established in the previous phase. This phase brings into play all fivebasic issues relevant to brownfields redevelopment; specifically, feasible tech-nical methods and tools, legal liability assurances, financial incentives, com-munity concerns, and promising redevelopment prospects will strongly factorinto the decision to remediate the site. The targeted cleanup levels will belargely determined by the acceptable laws for site cleanup in a particularlocality and the anticipated future land use of the site.

ISSUES IN REDEVELOPMENT OF BROWNFIELDS

GeneralBrownfields redevelopment is identified with several benefits (Davis and

Cornwell 1991):

• The sites can be bought cheaply.• They tend to be near downtown business districts and therefore make

sense for a host of support services, e.g., messenger and maintenanceservices, etc.

• Inner-city sites offer a large pool of persons who can offer a moderatelypriced workforce.

All this acts to revitalize inner-city neighborhoods, widen the tax base, protectpublic health and natural resources, ensure the renewal and reuse of civilinfrastructure, and stem urban sprawl. However, there are several obstaclesto be overcome.

Redevelopment issues typically embrace a host of legal liability concerns;these include financial, technical, and socioeconomic constraints, uncertain-ties arising from inadequate site information, and competing redevelopmentobjectives. Collectively, local, state, and federal efforts seek to address thesebrownfields issues and provide the framework for achieving the productivereuse of brownfield sites. While federal- and state-level programs tend tofocus on providing broad incentives (liability, financial, and technical) forbrownfield redevelopment, local initiatives tend to provide the actual strate-gies for brownfields redevelopment. Local brownfields programs are increas-ingly the practical engine for eradicating existing brownfields and preventingtheir future formation.

VCPs (State Voluntary Cleanup Programs) are particularly effective in thatthey attempt to address all five of the redevelopment issues in a holistic way.It must be noted, however, that the precise strategies employed vary widely.VCPs can be broadly categorized in three ways, depending on the level of


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state involvement (Begley 1997). The basis for these classifications is asfollows:

• The state works closely with the developer, in a supervisory capacity,overseening the cleanup process from the initial site investigation to thecompletion of the remedial work. A certificate of completion is issuedupon satisfactory conclusion.

• The state acknowledges the technical expertise provided at a site. Doc-umentation of the site’s work is provided for the state at the end of theproject. At this point the state exercises the option to examine or not toexamine the finished work, and may or may not issue a certificate ofcompletion.

• The state restricts its participation in the project to a review of the com-pleted work and an assessment of the environmental state of the cleanedsite.

According to the Office of Technology Assessment, most VCPs apply one ormore of the following standards in formulating technical guidelines:

1. EPA guidelines for toxic chemicals2. Maximum contaminant level (MCL)3. Water quality criteria4. Site-specific risk assessment5. Background level for contaminants6. State-declared cleanup standards

These guidelines are only examples. Liability protection ranks high on thelist of concerns for potential investors, and the VCPs have responded to thisobstacle. Many states offer some level of liability protection. However, theliability assurances offered by VCPs must be in keeping with current states’laws and can only be used for such activities as recognized by that state.

Technical IssuesTechnical issues in brownfields redevelopment revolve around accurately

assessing the type and extent (or absence) of contamination at a site anddeciding on which cleanup standards and procedures must be followed. Typ-ically, developers are concerned about soil and groundwater contaminationand water conservation and air quality (Emerson 1996). These issues areclosely related to issues of legal liability. Uncertainty about the exact natureof a site’s contamination and the process through which it may be addressedis associated with unknown and potentially high costs for remediation. Thiscreates disincentives for parties who are potentially interested in brownfieldsredevelopment. Also an obstacle to redevelopment is the inability of pro-spective developers to predict future liability that may result from involve-ment at brownfield sites.

Liability IssuesThe legal liability framework that will promote (or retard) brownfields

redevelopment has to be simple and straightforward, able to provide clearlydefined types and levels of liability for potential site developers. While thereare few assurances at the federal or state levels to protect private parties fromfuture liability, the redevelopment of contaminated sites is simply not a viableoption.


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Financial IssuesFinancial issues are particularly complicated at brownfields sites, primarily

because of the following three interrelated factors:

1. Potential risk of legal liability2. Uncertainty regarding the ultimate costs of assessment and remediation3. Depressed or declining neighborhoods surrounding brownfield sites.

The initial investment in site assessment may be prohibitive and, in somecases, only be justified by the economic gains anticipated from future siteredevelopment. However, in depressed areas where several brownfields exist,there is little economic inventive for the redevelopment of contaminated sites.

Community ConcernsBrownfield sites hardly exist in isolation. They are often located in the

heart of depressed or declining urban communities and may be in close prox-imity to retail districts and residential areas. Community concerns are fueledby the desire to protect human and environmental health. Existing contami-nated properties may pose direct threats to human and environmental healthwhere they are located. For this reason, community groups are usually inter-ested in promoting the cleanup and redevelopment of such sites in their neigh-borhoods. However, almost without exception, they demand some assurancesthat the remediation procedure(s) used will protect human health and theenvironment. In several communities as well, certain individuals and privateparties may seek an active role in decision-making for the future use(s) ofspecific sites. For these and other reasons, community members have varyingdegrees of involvement with their neighborhood’s brownfields.

Redevelopment ProspectsRedevelopment prospects are the issues that determine the marketability

of brownfields. Site redevelopment prospects refer to the socioeconomic andplanning variables that influence the demand for the site and its potentialprofitability once the contamination and the uncertainty relating to legal lia-bility are removed. Examples of socioeconomic variables are crime, acces-sibility of well-qualified labor to support the future use(s) of brownfields,prevailing levels of congestion, and the quality of social amenities. The land-use and transportation planning environment, on the other hand, revolvesaround zoning laws, land-use regulations, and long-term growth managementlaws that determine development patterns in the locality of the brownfieldsites

Redevelopment prospects are crucial because they are measures of demandfor the property if the problem of contamination and the potential for liabilityare removed. These prospects make it clear that concerns about site contam-ination are only one aspect of the brownfields remediation and redevelopmentprocess, namely the remedial aspect. The other major aspect of brownfieldsredevelopment revolves around the important socioeconomic variables thatdetermine the site’s marketability once remediation is complete. Undoubtedly,the issues to be considered are numerous and interconnected. These issuesmay be better understood with clear graphical models that depict the variousinterrelationships between the issues.

BELIEF FUNCTIONS

Formally, the theory of belief functions concerns itself with belief struc-tures defined as follows:


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Q = {Q , Q , . . . , Q }1 2 n

being a finite set of elements called the ‘‘framework of discernment,’’ oruniverse of discourse. Let m be a measure of the subset of Q such that 0 #m(A) # 1 for each A , Q. Formulation of problems using the theory involvesdefining the set u to contain all possible outcomes or hypotheses about theproblem. Q is commonly referred to as the frame of discernment. An exampleof Q in the context of a brownfield’s condition 5 years from now might beexcellent, good, fair, or poor, where each element in Q represents a particularhypothesis. Next the theory uses the quantity known as the plausibility of agiven hypothesis PL(H). The plausibility is the maximum amount of beliefpossible, given the amount of evidence negating the hypothesis. Specifically,it is obtained by subtracting the basic probability assignment associated withall subsets of the complement of the hypothesis (H). The next basic elementof the Dempster-Shafer theory is the belief function BEL(H). The belief func-tion measures the amount of belief in the hypotheses on the basis of observedevidence. Specifically, it is obtained by combing the basic probability as-signment of H with that of all subsets.

The BEL(H) and PL(H) represents the lower and upper limits of the beliefin the hypothesis, respectively, and form the belief interval.

The interval effectively measures the degree in which further evidencemight increase the belief to H. Larger intervals reflect a greater uncertaintyin the value of BEL(H). In other words, there is a greater opportunity foradditional evidence to further substantiate H. The purpose of the belief func-tion approach in brownfields infrastructure redevelopment is its ability torepresent the more general situation.

When there is only probabilistic information about some of the eventsassociated with a frame of discernment, and about other events very littleinformation, the Dempster-Shafer theory can be helpful. For example, let A= redeveloped brownfield site, and let BEL(A) = 0.3 and PL(A) = 0.9. Thisimplies that I have direct evidence that A is true with a level of support of0.3, but the maximum possible support that could be assigned to A is 0.9. Itsimply means that the decision maker has a 0.6 (0.9–0.3) level of supportunassigned that could be assigned to A if further evidence in its favor iscollected.

The belief function approach involves three related representations for be-lief concerning a topic: the belief function (BEL), the plausibility function(PL), and the basic probability assignment (a generalization of a probabilitymass distribution).

A basic probability assignment is a function m from 2 to the power Q, thepower set of Q to (0, 1), such that

m(f) = 0 (1)

(A) = 1 (2)OA#Q

The quantity m(A), called A’s basic probability number, corresponds to themeasure of the belief that is committed exactly to hypothesis A, in general,and not to the total belief committed to A. Hence, a belief function is designedas BEL, induced by basic probability assignment m by

BEL(A) = m(B)(A, B # Q) (3)OB#A

m(A) = (21) uA 2 B uBEL(B) (4)OB#A


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A-B denotes A ù B and uA 2 B u denotes the cardinality of this set. M-valuescan either be assigned directly by the decision maker on the basis of subjec-tive judgment, or they can be derived from compatibility relationships be-tween a frame with known probabilities and a frame of interest. From (4),

¯BEL(A) 1 BEL(A) # 1 (5)

a nonadditive formalism. This is different from probability theory in which

¯Pr(A) 1 Pr(A) = 1 (6)

From (5),

¯BEL(A) # 1 2 BEL(A) (7)

The quantity 1 2 is called the plausibility of A and is denoted by¯BEL(A)PL(A). Intuitively, the plausibility of A is the degree to which A is plausiblein the light of the evidence. A zero plausibility for a hypothesis means thatone is sure that it is false, but zero degree for a proposition means only thatone sees no reason to believe the proposition. The equation

¯BEL(A) 1 BEL(A) = 1 (8)

which is equivalent to

BEL(A) = PL(A) (9)

holds for all subsets of A if and only if BEL’s focal elements are all single-tons. A subset of A of Q is called a focal element of BEL if m(A) is greaterthan zero. The belief-function is appropriate when the evidence being con-sidered does not itself tell us anything about which element of Q is the truth.The following properties hold for BEL and PL:

PL(B) $ BEL(A)

BEL(f) = PL(f) = 0

BEL(Q) = PL(Q) = 1

¯PL(B) = 1 2 BEL(B)

¯BEL(B) = 1 2 PL(B)

¯PL(B) 1 PL(B) $ 1

In the belief function theory, the information about the degree of certaintyfor an element is represented by a belief interval [BEL(A), PL(A)]. The beliefand plausibility functions denote a lower and an upper bound for unknownprobability functions. The lower bound represents the degree to which theevidence supports the preposition; the upper bound represents the degree towhich the evidence fails to refute the proposition to the degree to which itremains plausible.

• If [BEL(A), PL(A)] = [0, 1], then no information concerning A is avail-able.

• If [BEL(A), PL(A)] = [1, 1], then A has been completely confirmed bym-probability assignment.


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FIG. 1. Graphical Representation of Dempster’s Rule (Shafer 1976)

• If [BEL(A), PL(A)] = [0.3, 1], then there is some evidence in favor of,as well as against, A.

• If [BEL(A), PL(A)] = [0.15, 0.75], then the evidence is in favor of, aswell as against, A.

The difference PL(A) 2 BEL(A) provides the measure of uncertainty. If twobasic probability assignments for Q are obtained as a result of two pieces ofindependent information, they can be combined using Dempster’s rule ofcombination to yield a new base probability assignment’s m. This combina-tion can be performed as follows:

m(c) = m (A) ! m (B) = 1/K m (A) ! m (B) (10)1 2 1 2OA ù B = C

where

K = 1 2 m (A)m (B)1 2OA ù B ù C

The second term in K represents the conflict between two items of evidence.If the conflicting term is unity, that is, if the two terms contradict each other,


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FIG. 2. Contradictory Evidence

K is equal to 0; in such a situation, the two items of evidence are not com-binable.

The connection between probabilistic information and belief functionframework is based on the fact that the underlying probability of event A,Pr(A), is related to the belief and plausibility function by BEL(A) # P(A) #PL(A). The Dempster rule of combination satisfies commutativity and asso-ciativity properties.

Fig. 1 can be used to graphically illustrate this process. Since all basicprobability assignments add up to 1.0, a line of unit length can be used torepresent all the basic probability assignments generated by one piece ofevidence. Similarly, a line of unit length is used to represent the belief froma second, independent piece of evidence. Their combination is then repre-sented by a square formed from each piece of evidence. This resulting com-bination is represented by the unit square. The sets (or hypotheses) from thefirst piece of evidence are intersected with sets (or hypotheses) from thesecond piece of evidence to obtain the identity of the resulting set. Thisformula works only if the set intersection does not correspond to the null set.If the intersection results in the null set, the resulting basic probability as-signment for that intersection must be set to zero. The probability mass as-sociated with the null intersection must therefore be accounted for within theunit square by a procedure called normalization. This ensures that the basicprobability assignment resulting from the combination by Dempster’s rulewill also sum to unity. With Dempster’s rule, this normalization occurs byspreading the probability mass from the null intersections over the remainingbasic probability assignments (Butler et al. 1995).

Common Forms of EvidenceThe classification of any item of evidence is, of course, always relative to

the particular inferential situation in which it is used (Schum 1994). Thereare five essential categories:

• Tangible evidence based on objects, documents, measurements, etc.,which can be reexamined over time

• unequivocal testimony (from another person based upon direct obser-vation) obtained second-hand, or by the expression of an inference oropinion

• equivocal testimony (from another person)• missing tangible or testimonial evidence• evidence from authoritative records


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FIG. 4. Corroborative Evidence

FIG. 3. Conflicting Evidence

Types of EvidenceThere are two types of evidence—dissonant evidence and harmonious ev-

idence. Dissonant evidence can be either contradictory or conflicting. Howmuch so is revealed by the degree to which an item of evidence points tothe hypothesis one believes it favors over other hypotheses being considered.When one has a body of evidence to consider composed of several items,one may observe that some evidence favors one hypothesis while anotherpiece of evidence favors another hypothesis. In such a case, the evidence isdissonant to some degree. Harmonious evidence is achieved when all evi-dence favors the same hypothesis. Fig. 2 illustrates contradictory evidence.In Fig. 2, for example, an engineer or planner reports the presence of certaintypes of contaminants: that event E occurred, andE*, E*9.1 2

Fig. 3 illustrates an example of conflicting evidence. Suppose an engineeror planner reports the occurrence of a particular contamination that favorshypothesis H. Some time later, another engineer or planner from a differentgovernment agency reports the occurrence of a contamination, G, that favorsHc. The two items of evidence in this case are conflicting in the sense thatthey are at variance as far as their directional properties are concerned.

Fig. 4 shows two cases of corroborative evidence. One form of corrobo-rative evidence exists when two or more sources of brownfields investigationsreport the occurrence of the same type of site problems. Fig. 5 shows har-monious evidence that is convergent. In this case, two or more sources pro-


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FIG. 5. Harmonious Evidence

vide evidence of different events in the brownfields infrastructure redevel-opment process. Such evidence is said to be convergent. In Fig. 5 an engineerreports F*, that a particular event F (maybe contamination) occurred. Anothersource reports G*, that G occurred. The belief is such that both the F and Gevents favor H over H c.

APPLICATION TO BROWNFIELDS INFRASTRUCTUREREDEVELOPMENT

Fig. 6 is a prototype evidential network representing various issues inbrownfield infrastructure redevelopment decision-making. In the example, itis assumed that the overall payoff (economic benefit from redevelopment) ofthe final decision in regard to brownfields infrastructure depends on site re-mediation and site redevelopment. The example does not cover all decision-making processes in brownfield redevelopment. It only demonstrates the stepsand ways of using belief functions in a specific example of brownfield re-development decision making. The site remediation depends on site assess-ment and site identification. Site redevelopment objectives depend on legalissues and projected costs. The direction of the arrows show dependencies.The objectives are represented with rounded rectangles, and the circular nodesrepresent relationships between the objectives that are of interest to the de-cision maker. In the present example, it was assumed that all values of theobjectives are binary and only ‘‘AND’’ tree relationships may exist amongthe objectives. Furthermore, it is assumed that there is only one item ofevidence for each objective. Fig. 7 is an example of an ‘‘AND’’ tree andthree nodes. Thus, there is only one m-value at different objectives. Fig. 7illustrates how the nodes should be handled in Fig. 6. It was assumed thatthe decision has judgment (although subjective) about the level of support.To determine if the level of payoff (economic benefit) is adequate and thelevel of uncertainty is on the basis of mutually exclusive evidence, one mustaggregate all the evidence to the payoff objective node. This is obtained bypropagating the m-values. Since all the objectives are binary, the m-functionis represented by the triple [m(p), m(2p), m(p, 2p)]. For example, if m(p)is equal to 0 and m(p, 2p) is equal to 0.2, then one can represent mp(0.8,0, 0.2).

In the present example, there are 15 nodes and 15 items of evidence. Theitems of evidence in the example are taken from the methods and proceduresfor engineers, planners, and decision makers responsible for making certainassumptions and decisions about the nodes. Table 1 shows the methods and


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FIG. 6. Prototype Evidential Tree for Com

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FIG. 7. ‘‘AND’’ Tree with 3 Nodes

TABLE 1. Potential Sources of Evidence

Evidence number Recommended procedure and method

1 Financial evaluation of previous redevelopment projects2 Feasibility of selection of remediation technology3 Cost effectiveness of total rehabilitation4 Consideration of presence or absence of hazardous material5 Inactivity of property6 Superfund Legislation7 Weighing the effort at comprehensive rejuvenation against finan-

cial input8 Correlation with level of site contamination9 Hazardous ranking system assessment of level of site contamina-

tion10 State agencies database11 EPA documentation12 Prior greenfields development experience13 Best available and cost-effective technology14 Phase I and II site assessment15 Metropolitan land-use planning department documents

procedures. It is assumed that the decision maker has made judgments aboutthe level of support obtained from these procedures and methods for therespective nodes. These values are represented as m-values.

To determine the overall support for each node, as a result of aggregatingall evidence, one propagates m-values at each node and combines the m-value defined at the node. The combination is done by using Dempster’srules of combination. In Fig. 6 propagation to the payoff node can beachieved through the steps shown in Table 2.

Tables 3 to 8 illustrate the propagation and application of the Dempster-Shafer theory of combination. Each table shows how the combination isachieved using the Dempster-Shafer theory. The table only shows how (10)


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TABLE 2. Steps and Operation for Propagation

Steps Operation

Step 1 Propagate TC and FL to CS; this yields ← TC 1 FLm 9CS

Step 2 is combined with mCS to obtainm 9 m 0CS CS

Step 3 with RE to obtainm 0 m-CS CS

Step 4 with mSA →m- m 9CS SA

Step 5 HR with SIL → m 9SI

Step 6 1 mSI →m 9 m 0SI SI

Step 7 GD 1 RI → m 9PC

Step 8 1 mPC →m 9 m 0PC PC

Step 9 m 9 1 m 0 → m 9SA SI SRI

Step 10 m 1 m 0 → m 9LI PC SR2

Step 11 IIIm 9 1 m → mSRI SRI SRI

Step 12 IIm 9 1 m → mSR2 SR2 SR

Step 13 II IIm 1 m → m 9SR2 SRI P

Step 14 m 9 1 m 0 → m 0P P P

TABLE 3. Combination of mSA and mSIa

(mSA ! mSI) → m 9SRI

mSI mSA {SA} (0.7) u (0.3)

{SI} (0.8) f (0.56) {SI} (0.24)u (0.2) {SA} (0.14) u (0.06)

Note: There is one null entry in the table: ∴ K = 0.56; 1 2 K = 1 2 0.56 = 0.44.amSA ! mSI {SI} = 0.24/0.44 = 0.546; mSA ! mSI {SA} = 0.14/0.44 = 0.318; mSA !

mSI {u} = 0.06/0.44 = 0.136; mSA ! mSI is zero for all subsets u.

TABLE 4. Combination of and mSRIam 9SRI

! mSRI) →(m 9 m 0SRI SRI

mSRI m 9SRI {SI} (0.546) {SA} (0.318) u (0.136)

{SRI} (0.65) f (0.355) f (0.207) {SRI} (0.088)u (0.35) {SI} (0.191) {SA} (0.111) u (0.048)

Note: There are two null hypotheses: K = 0.355 1 0.207 = 0.562 and 1 2 K = 1 20.562 = 0.438.

a ! mSRI {SRI} = 0.088/0.438 = 0.201; ! mSRI {SI} = 0.191/0.438 = 0.436;m 9 m 9SRI SRI

! mSRI {SA} = 0.111/0.438 = 0.253; ! mSRI {u} = 0.048/0.438 = 0.110;m 9 m 9SRI SRI

! mSRI is zero for all subsets u.m 9SRI

TABLE 5. Combination of mLI and mPCa

(mLI ! mPC) → m 9SR2

mPC mLI {LI} (0.4) u (0.6)

{PC} (0.8) f (0.32) {PC} (0.48)u (0.2) {LI} (0.08) u (0.12)

Note: There is one null entry in the table: 1 2 K = 1 2 0.32 = 0.68; K = 0.32.amLI ! mPC {PC} = 0.48/0.68 = 0.706; m LI ! mPC {LI} = 0.08/0.68 = 0.118; mLI !

mPC {u} = 0.12/0.68 = 0.176; mLI ! mPC is zero for all subsets u.


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TABLE 6. Combination of and mSR2am 9SR2

! mSR2) →(m 9 m 0SR2 SR2

mSR2 m 9SR2 {LI} (0.118) {PC} (0.0706) u (0.176)

{SR2} (0.6) f (0.0706) f (0.4235) {SR2} (0.1059)u (0.4) {LI} (0.0470) {PC} (0.2824) u (0.0706)

Note: K = 0.0706 1 0.4235 = 0.4941; 1 2 K = 0.5059.a ! mSR2 {LI} = 0.0470/0.5059 = 0.0930; ! mSR2 {PC} = 0.2824/0.5059 =m 9 m 9SR2 SR2

0.5581; ! mSR2 {SR2} = 0.1059/0.5059 = 0.2093; ! mSR2 {u} = 0.0706/0.5059m 9 m 9SR2 SR2

= 0.1396; ! mSR2 is zero for all subsets u.m 9SR2

TABLE 7. Combination of and am 0 m0SR2 SRI

! →(m 0 m 0 ) m 9SR2 SRI P

m 0 m 0SRI SR2 {PC} (0.5581) {SR2} (0.2093) {LI} (0.0930) u (0.1396)

{SRI} (0.201) f (0.1121) f (0.0421) f (0.0187) {SRI} (0.0280){SI} (0.436) f (0.2434) f (0.0913) f (0.0406) u (0.0608){SA} (0.253) f (0.1414) f (0.0530) f (0.0236) {SRI} (0.0354)u (0.110) {PC} (0.0612) {SR2} (0.0229) {LI} (0.0102) u (0.0153)

Note: K = 0.1121 1 0.0421 1 0.0187 1 0.2434 1 0.0913 1 0.0406 1 0.1414 10.0530 1 0.0236 = 0.7762; 1 2 K = 0.2338.

a ! {PC} = 0.0608/0.2388 = 0.2616; ! {SRI} = 0.0280/0.2388 =m 0 m 0 m 0 m 0SR2 SRI SR2 SRI

0.1199; ! {SR2} = 0.0229/0.2388 = 0.0981; ! {LI} = 0.0102/0.2388m 0 m 0 m 0 m 0SR2 SR1 SR2 SRI

= 0.0436; ! {SI} = 0.0608/0.2388 = 0.2602; ! {SA} = 0.0354/m 0 m 0 m 0 m 0SR2 SRI SR2 SRI

0.2388 = 0.1512; is zero form 0 ! m 0 {u} = 0.0153/0.2388 = 0.0654; m 0 ! m 0SR2 SRI SR2 SRI

all subsets u.

can be achieved. Table 8, for example, shows how the previous propagatednodes can be combined with the payoff node to achieve the overall beliefand plausibility function of the prototype network. BEL(P) = 0.1324; PL(P)= 0.8676; [PL(P) 2 BEL(P)] = 0.7352 is a measure of uncertainty based onthe information and evidence supplied. The values can change when moreinformation and data are obtained. This makes the methodology more dy-namic and a form of sensitivity analysis tool in Brownfield infrastructureredevelopment processes.

CONCLUDING REMARKS

The belief function framework can provide a rigorous way of handlinguncertainty. Combining information and data from different stakeholders forrepresenting and reasoning under uncertainty is widely accepted. However,it has not been applied to brownfields infrastructure decision making. Fur-thermore, the belief function framework provides a platform whereby thefinal payoff can be updated whenever there is new information or data onany of the objective variables. Depending on the nature and availability ofdata, different evidential networks can be constructed and analyzed, and cor-responding uncertainty intervals can be determined. The present exampledemonstrates the potential application of belief function in brownfield rede-velopment. The variables contained in the network depend on the informationavailable to decision maker.


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LE 8. Combination of and mPam 9P

! mP) →(m 9 m 0P P

mP m 9P {PC} (0.2 R2} (0.0981) {LI} (0.0436) {SI} (0.2602) {SA} (0.1512) u (0.0654)

{P} (0.7) f (0.183 f (0.0687) f (0.0305) f (0.1822) f (0.1059) P (0.0458)u (0.3) {PC} (0.0 R2} (0.0294) {LI} (0.0131) {SI} (0.0781) {SA} (0.0454) u (0.0197)

Note: K = 0.6542; 1 2a ! mP {PC} = 0.07 RI} = 0.0360/0.3458 = 0.1040; ! mP {SR2} = 0.0294/0.3458 = 0.0851; ! mP {LI}m 9 m 9 m 9P P P

= 0.0131/0.3458 = 0.0378 8 = 0.2258; ! mP {SA} = 0.0454/0.3458 = 0.1312; ! mP {P} = 0.0458/0.3458 =m 9 m 9P P

0.1324; is zero for all subsets u.m 9 ! m {u} = 0P P

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TAB

616) {SRI} (0.1199) {S

1) f (0.0839)785) {SRI} (0.0360) {S

K = 0.3458.85/0.3458 = 0.2270; ! mP {Sm 9P; ! mP {SI} = 0.0781/0.345m 9P.0197/0.3458 = 0.0567; m 9 ! mP P

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ACKNOWLEDGMENT

This project was conducted with funding from Carnegie Mellon University/National ScienceFoundation under Grant number CMU 06975. The writer gratefully acknowledges the supportof Dr. Sue McNeil, Urban Transportation Center, University of Illinois at Chicago.

REFERENCES

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Attoh-Okine, N. O. (1998). ‘‘Potential applications of influence diagrams as a riskassessment tool in brownfield.’’ STP 1338, Superfund Risk Assessment in Soil Con-tamination Studies, ASTM, West Conshohocken, Pa., 148–159.

Begley, R. (1997). ‘‘Resurrecting brownfields.’’ Envir. Sci. and Technol., Vol. 13, 226–230.

Butler, A. C., Sadegi, F., Rao, S., and Leclair, S. R. (1995). ‘‘Computer-aided design/engineering of bearing systems using Dempster-Shafer theory.’’ J. Artificial Intel-ligence Engrg. Des. Anal., and Manufacturing, 9, 1–11.

Caselton, W. F., and Wuben, L. (1992). ‘‘Decision making with imprecise probabili-ties: Dempster-Shafer theory application.’’ Water Resour. Res., 28(12), 3071–3083.

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Use of Belief Function in Brownfield Infrastructure Redevelopment Decision Making

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