Computer-supported collaborative argumentation and fuzzy similarity measures in multiple criteria decision making

*Corresponding author. Tel.: #41-21-693-2576; fax: #41-21-693-5278.E-mail addresses: [email protected] (N. Karacapilidis), [email protected] (C. Pappis)

Computers & Operations Research 27 (2000) 653}671

Computer-supported collaborative argumentation and fuzzysimilarity measures in multiple criteria decision making

Nikos Karacapilidis!,*, Costas Pappis"

!Department of Computer Science, University of Cyprus, P.O. Box 2055, 1678 Nicosia, Cyprus"Department of Industrial Management, University of Piraeus, 80, Karaoli and Dimitriou str., 18534 Piraeus, Greece

Abstract

Group decision making is usually performed in the presence of con#icting goals and criteria, brought upby spatially dispersed parties with di!erent backgrounds and interests. Recent advances in informationtechnology and computer science may satisfactorily address a variety of related problems, such as commun-ication among the decision makers and e$cient elicitation and representation of the domain knowledge.Furthermore, they may signi"cantly automate the decision making process itself. On the other hand, theinherent uncertainty of the problem advocates the use of approximation models, often coming from the fuzzysets discipline. This paper presents an integrated framework for multiple criteria decision making amonggroups on the World Wide Web. The agents involved use a fully implemented argumentative discoursesystem to pursue their criteria and objectives, the aim being the speci"cation of the desired solution to theproblem. The system organizes the collective knowledge in a discussion graph with truth maintenance andconsistency checking features. Fuzzy similarity measures are then involved in order to assess alternativeexisting solutions with respect to the desired one.

Scope and purpose

We view multiple criteria decision making as a collaborative process, where decision makers have to followa series of communicative actions in order to establish a common belief on the dimensions of the problem.Such dimensions may concern the choice criteria, the existing or desired alternative solutions, or theobjective function, to mention some. This paper presents a framework for multiple criteria decision makingamong groups. Our approach exploits recent advances in information technology and manages to (i) removethe communication impediments among spatially dispersed decision makers, (ii) e$ciently represent thedomain knowledge, (iii) develop e$cient mechanisms to structure and consistently maintain the decisionanalysis, and (iv) automate the multiple criteria decision making process per se. The framework is based ona fully implemented system, namely HERMES, which enhances decision making by supporting argumentative

0305-0548/00/$ - see front matter ( 2000 Elsevier Science Ltd. All rights reserved.PII: S 0 3 0 5 - 0 5 4 8 ( 9 9 ) 0 0 1 1 1 - 2

discourse among decision makers. The system is implemented in Java and runs on the World Wide Web, thusproviding relatively inexpensive access to a broad public. ( 2000 Elsevier Science Ltd. All rights reserved.

Keywords: Multiple criteria decision making; Argumentation; Fuzzy similarity measures; Computer-supportedcooperative work

1. Introduction

Multiple criteria decision making usually raises a lot of intricate debates and negotiations amongparticipants. Con#icts of interest are inevitable and support for achieving consensus and compro-mise is required. Each decision maker may adopt and, consequently, suggest his/her own strategythat ful"lls some goals at a certain level. Opinions may di!er about the relevance or value ofa proposition when deciding an issue. Decision makers may have arguments for supporting oragainst alternative solutions. In addition, they have to confront the existence of insu$cient and toomuch information simultaneously. In other words, for some parts of the problem, relevantinformation which would be useful for making a decision is missing, whereas for others, the timeneeded for the retrieval and comprehension of the existing volume of information is prohibitive.Furthermore, factual knowledge is not always su$cient for making a decision. Value judgements,depending on the role and the goals of each decision maker, are among the critical issues requiringattention. Participants need appropriate means to assert their preferences, which are often ex-pressed in qualitative terms. Finally, decision makers are not necessarily pro"cient in computerscience and information technology; they need appropriate tools in order to easily participate inthe discussion (see also Kreamer and King [1]). This parallels the vision of the DSS communitypioneers, that is, by supporting and not replacing human judgement, the system comes in secondand the users "rst.

Traditional decision making techniques, coming from areas such as mathematical economics,operations research, game theory and statistics, fail to address the above di$culties. Work in thesedisciplines builds on a probabilistic view of uncertainty, where possible actions are evaluatedthrough their expected utility. The use of such crisp values has been extensively critisized; thespeci"cation of the complete sets of probabilities and utilities required renders such approachesimpractical for the majority of decision making tasks that involve common sense knowledge andreasoning [2]. On the other hand, arti"cial intelligence (AI) approaches basically attempt to reducethe burden of numerical information required, while pay much attention to the automation of theprocess itself. The related qualitative decision making techniques use linguistic assessments which,under an appropriate model, are able to convey the vagueness of the existing knowledge. Suchassessments may be related to the importance of a certain alternative or criterion, the preferencedegree of an alternative over another, the degree of acceptability of a decision maker's position, andso on.

This paper presents a framework for multiple criteria decision making among groups on theWorld Wide Web. Our approach exploits recent advances in AI and information technology, theaims being:

f removal of communication impediments among spatially dispersed decision makers;f e$cient elicitation and representation of the domain knowledge;

654 N. Karacapilidis, C. Pappis / Computers & Operations Research 27 (2000) 653}671

1For a comparative analysis of these systems, see Karacapilidis and Papadias [3].

f development of e$cient mechanisms to structure and consistently maintain the decision analy-sis, and

f automation of the multiple criteria decision making process.

The framework is based on a fully implemented system, namely HERMES, which enhances decisionmaking by supporting argumentative discourse among decision makers [3]. The system is imple-mented in Java applets and runs on the Web, thus providing relatively inexpensive access toa broad public. It can be used for distributed, asynchronous or synchronous collaboration,allowing decision makers to surpass the requirements of being in the same place and working at thesame time.

Unlike other approaches towards the development of web-based conferencing [4] and argumen-tation support systems [5}10], HERMES does not merely provide threaded discussion forums, whereusers' assertions are passively linked.1 On the contrary, it focuses on aiding decision makers toreach a decision, not only by e$ciently structuring the discussion, but also by providing appropri-ate reasoning mechanisms for it. It is an active system, that constantly checks for inconsistenciesand updates the discourse status, thus stimulating discussion among participants.

In the following section, we discuss how argumentation and decision making interrelate in ourapproach. Section 3 describes features of HERMES, and presents the argumentation elements, proofstandards, and discourse acts involved. Section 4 deals with knowledge elicitation and approxima-tion issues; appropriate fuzzy similarity measures are used to assess alternative existing solutions.Section 5 reports on a preliminary evaluation of the system and highlights future work directions,while Section 6 concludes the paper.

2. Argumentation and decision making

Classical approaches to multiple criteria decision making are built on the assumption ofa prede"ned set of alternatives and criteria, and provide methods to quantify and aggregatesubjective opinions (consider, for instance, the analytic hierarchy process [11]). Everyday practices,however, make it obvious that there is a lot of room for debate here. We view multiple criteriadecision making as a collaborative process, where decision makers have to follow a series ofcommunicative actions in order to establish a common belief in the dimensions of the problem.Such dimensions may concern the choice criteria, the existing or desired alternative solutions, orthe objective function, to mention some. Issues of knowledge elicitation and representation areinherent in these environments and an appropriate machinery is needed (see, for instance, Kleinand Methlie [12] and Vincke [13]). The framework discussed in this paper resorts to an argumen-tative discourse approach.

Research on argumentative discourse has been performed from di!erent viewpoints. As compre-hensively described in van Eemeren et al. [14], most approaches follow two main methodologies,namely, formal and informal logic. According to the formal perspective, arguments arede-contextualized sets of sentences or symbols viewed in terms of their syntactic or semantic

N. Karacapilidis, C. Pappis / Computers & Operations Research 27 (2000) 653}671 655

2An extensive discussion on the use of alternative logics in argumentative discourse can be found in Prakken [20].3HERMES also works e$ciently for cases in which all existing alternatives and choice criteria are clearly prede"ned or

jointly considered during the same discourse [21}23]; however, the approach described in this paper resorts to the systemonly during the "rst two phases discussed above.

relationships. On the other hand, informal logic views arguments as pragmatic, i.e., their meaning isa function of their purposive context. From the AI point of view, most researchers have focused onformal models of argumentation based on various logics. For instance, Brewka [15] reconstructedRescher's theory of formal disputation [16], Gordon's work [17] was based on Ge!ner and Pearl'sconcepts of conditional entailment [18], while Fox and his colleagues, in the context of the legaldomain, have based their work on a non-standard logic [19].2

Generally speaking, approaches to decision making can be classi"ed into two large categories:the "rst includes cases where a set of alternative solutions is determined a priori and the task is toselect one of them, while the second includes those where an ideal case is decided upon "rst, and thesubsequent task is to "nd a real case that best approximates the ideal one. In both approaches,however, there are a number of common elements. More speci"cally, an overall goal is speci"ed,a set of alternatives is selected (this set may not be exhaustive), a collection of choice criteria must bedetermined by the participants, and a decision (objective) function must be composed, whichcombines criteria to decide between alternatives.

HERMES can be used in any of the categories discussed above. This paper deals with cases thatbelong to the second one, and suggests a framework for multiple criteria decision making thatcomprises the following phases:

f elicitation of users' knowledge aiming at specifying the ideal (desired) solution to the problem,together with representation of the related objectives/criteria by approximation models;

f argumentation on the objectives/criteria brought up and "nal speci"cation of the ideal case, andf application of similarity measures in order to decide which of the existing solutions is closer to

the ideal one.

The "rst two phases may take place recursively, until agreement on the ideal case is reached.Elicitation in decision analysis has traditionally required the skill of an expert to identify whatinformation is important and what simplifying assumptions should be made. Furthermore, thedomain knowledge typically requires additional explanation and justi"cation. While standardtechniques are available for eliciting probability and utility models, the overall task is typicallytedious and time consuming. According to our approach, elicitation of knowledge is takes place inan interactive way, among the decision makers involved, using the HERMES argumentation system.3

3. Using HERMES

To present the features of our argumentation-based framework, we use in this section a sampleconstructed discourse about the desired `speeda of a car (similar discourses may be performed forother choice criteria, such as `pricea, `service provideda, etc.). The discourse takes place amongthree decision makers dm-1, dm-2 and dm-3, who bring up the necessary argumentation to express


Fig. 1. An instance of a HERMES discussion forum.

their interests and perspectives. Fig. 1 illustrates an instance of the corresponding HERMES dis-cussion forum. As shown, our approach constructs a discussion graph with a hierarchical structure.

3.1. Argumentation elements

The argumentation framework of HERMES has its roots in the informal IBIS model of argumenta-tion [24] (QuestMap [5] and gIBIS [6] have also adopted concepts from this model). HERMES

supports as argumentation elements issues, alternatives, positions, and preferences.Issues correspond to decisions to be made, or goals to be achieved (e.g., issue-2: `what about the

speed of the car?a). They are brought up by the decision makers and are open to dispute (the root ofa HERMES discussion forum is always an issue). Issues consist of a set of alternatives that correspond


to potential choices or courses of action (e.g., alternative-4: `we should buy a fast enough cara, andalternative-5: Ì would prefer a rather slow cara belong to issue-2, and have been proposed by dm-1and dm-2, respectively). Issues can be inside other issues in cases where some alternatives need to begrouped together.

Positions are asserted in order to support the selection of a speci"c course of action (alternative),or avert the agents' interest from it by expressing some objection. For instance, position-7: `sucha car will save us some time in our daily trips to worka has been asserted to support alternative-4,while position-10: ìt will certainly have a rather heavy gas consumptiona to express some objectionof dm-3 to the same alternative. Positions may also refer to some other position in order to provideadditional information about it, e.g., position-9: à recent report supports exactly the oppositea(arguing against position-8), and position-37: `remember what was the case with our last cara(arguing in favor of position-10). A position always refers to a single other position or alternative,while an alternative is always in a single issue.

In decision making environments, one has usually to de"ne priorities among actions and weighdi!erent beliefs. Unfortunately, well-de"ned utility and probability functions regarding propertiesor attributes of alternatives (used in traditional approaches), as well as complete ordering of theseproperties are usually absent. In argumentation studies, subjects like priority relationships andpreference orders between arguments have been mostly handled through quantitative approaches[25,26]. In HERMES, preferences provide a qualitative way to weigh reasons for and against theselection of a certain course of action. Such preferences are tuples of the form [position, relation,position], where relation can be `more (less) important thana or òf equal importance toa. Due to theirform, we have alternatively used the term constraint to refer to them. This is not to be confused withcases where a criterion is compared to a numeric value; constraints in our framework alwayscompare two positions (in the rest of the paper, and in order to be coherent with our implementa-tion, we mostly use this second term).

Constraints may give various levels of importance to alternatives. Like the other argumentationelements, they are subject to discussion; therefore, they may be `linkeda with positions supportingor challenging them. In Fig. 1, constraint-12: `less time on the road on a daily basis vs. rather heavygas consumptiona expresses the preference relation `position-7 is less important than position-10a,while constraint-13: `less time on the road on a daily basis vs. extra safety due to less speeda therelation `position-8 is more important than position-7a.

Two types of preferences can be expressed by the system: (i) Local, when a constraint refers toa position, or another constraint. In this case, the positions that constitute the constraint must referto the same element (i.e., have the same father). In the example shown in Fig. 1, a preferenceexpressed by the constraint `position-11 is equally important to position-37a would fall in this type.Note that a constraint of the form `position-10 is less important than position-14a is not permitted(the consistuent positions of the constraint do not refer to the same father). (ii) Non-local, whena constraint refers to an issue. In this case, its consistuent positions must refer to alternatives (notnecessarily the same one) of this very issue (e.g., constraint-12 and constraint-13).

3.2. Proof standards

Alternatives, positions and constraints have an activation label indicating their current status (itcan be active or inactive). This label is calculated according to the argumentation underneath and


the type of evidence speci"ed for them. In general, di!erent elements of the argumentation, even inthe same debate, do not necessarily need the same type of evidence. Quoting the well-used legaldomain example, the arguments required to indict someone need not be as convincing as thoseneeded to convict him [27]. Therefore, a generic argumentation system requires di!erent proofstandards (work on AI and Law uses the term burdens of proof). In the sequel, we describe the onesimplemented in our system (the names have the same interpretation as in the legal domain). We donot claim that the list is exhaustive; other standards, that match speci"c application needs, can beeasily incorporated into the system (integration of alternative standards is currently in progress).

De5nition 1 (scintilla of evidence (SoE)). According to this proof standard, a position piis active, if

at least one active position argues in favor of it:

active(pi)Q&p

j(active(p

j)'in}favor(p

j, p

i)).

De5nition 2 (beyond reasonable doubt (BRD)). According to BRD, a position piis active if there are

no active positions that speak against it:

active(pi)Q2&p

j(active(p

j)'against(p

j, p

i)).

Activation in HERMES is a recursive procedure; a change of the activation label of an element(alternative, position or constraint) is propagated upwards. When an alternative is a!ected duringthe discussion, the issue it belongs to should be updated since a new choice may be made. Thisbrings us to the last proof standard, namely preponderance of evidence (PoE), used for the selectionof the best alternative (however, it can also be used for activation/inactivation of positions).In the case of PoE, each position has a weight"(max}weight ] min}weight)/2, while analternative has weight"min}weight. Max}weight and min}weight are initialized tosome pre-de"ned values (in the following, we assume that initially min}weight"0 andmax}weight"10; this may be changed by preference constraints). The score of an element e

iis

used to compute its activation label (score is calculated on the #y). If an element does not have anyarguments, its score is equal to its weight; otherwise, the score is calculated from the weights of theactive positions that refer to it

score(ei)" +

in}favor(pj ,ej )\active(pj )

weight(pj)! +

against(pj ,ej )\active(pj )

weight(pk).

De5nition 3 (preponderance of evidence (PoE)). According to this standard, a position is activewhen the active positions that support it outweigh those that speak against it

active(pi)Q score(p

j)*0.

Concerning alternatives, PoE will produce positive activation label for ai

when there are noalternatives with larger score in the same issue:

active(ai)Q ∀a

jin}issue(a

i),(score(a

j))score(a

i)).

In the discussion instance of Fig. 1, the proof standard is SoE for all positions and PoE foralternatives. Position-8 and position-11 are inactive (their accompanying icons are red; they are


shown in dark grey color here) since position-9 and position-14, respectively, are active and speakagainst them. On the contrary, position-10 is active (the accompanying icon is blue; it appears inlight gray color here) since there is at least one active position that speaks in favor of it (position-7and position-15 are also active since they are leafs of the discussion tree; that is, there is noargumentation underneath them). Active positions are considered àccepteda due to discussionunderneath (e.g., strong supporting arguments, no counter-arguments), while inactive positions aretemporarily `rejecteda (not taken into account).

Similarly, active alternatives correspond to `recommendeda choices, i.e., choices that arethe strongest among the alternatives in their issue. Note that, for the discussion instanceunder consideration, alternative-6 is not supported or objected to by any position, alternative-5 isonly supported by position-15 (position-8 is inactive), while alternative-4 is supported by position-7and objected to by position-10. The mechanisms for the calculation of activation labels ofalternatives always depend on the related constraints and will be discussed in the followingsubsection.

The activation label of constraints is decided by two factors: the discussion underneath (similarto what happens with positions) and the activation label of their consistuent positions. In Fig. 1,constraint-13 is currently inactive because position-8 is also inactive. According to the evolution ofthe discussion, the insertion of position-9 inactivated position-8, which in turn inactivated con-straint-13. Both constraints have BRD as proof standard, therefore constraint-12 is active (no activepositions speak against it). If in the sequel of the discussion, a new position inactivates position-9,this will result in a new activation of both position-8 and constraint-13 (assuming that nothing elserelated to them changes).

3.3. Consistency checking

Apart from an activation label, each constraint has a consistency label which can be consistent orinconsistent. Every time a constraint is inserted in the discussion graph, the system checks if bothpositions of the new constraint exist in another, previously inserted, constraint. In the a$rmativecase, the new constraint is considered either redundant, if it also has the same preference relation, orconyicting, otherwise. A redundant constraint is ignored, while a con#icting one is groupedtogether with the previously inserted constraint in an issue automatically created by the system, therationale being to gather together con#icting constraints and stimulate further argumentation onthem until only one becomes active.

If both positions of the new constraint do not exist in a previously inserted constraint, itsconsistency is checked against previous active and consistent constraints referring to the sameelement (or belonging to the same issue). This process is based on a polynomial (O(N3), N being thenumber of the associated positions) path consistency algorithm [28]. Although path consistency, asmost discourse acts described in the sequel, interacts with the database where the discussion graphis stored (Oracle 7 is used), the algorithm is very e$cient. Even for non-local preferences involvingissues with numerous alternatives and positions linked to them, execution time is negligiblecompared to communication delay.

Active and consistent constraints participate in the weighting scheme (only constraint-12 in theexample of Fig. 1). In order to demonstrate how the algorithm for altering weights works, we usethe example of Fig. 2. There exist "ve positions and four constraints that relate them as illustrated


Fig. 2. The weighting scheme.

in Fig. 2a. The arrowed lines correspond to the `more important than (')a relation (e.g., p1'p

2)

and the dotted line to the èqually important to (")a relation (e.g., p3"p

4). First, path

consistency explicates all `'a relations (Fig. 2b). Then, topological sort [29] is applied twice tocompute the possible maximum and minimum weights for each position (Fig. 2c). The weight isthe average of the new max}weight and min}weight: weight(p

1)"6, weight(p

2)"4.5,

weight(p3)"5, weight(p

4)"5 and weight(p

5)"4.

The basic idea behind the above scheme is that the weight of a position is increased every timethe position is more important than another one (and decreased when it is less important), the aimbeing to extract a total order of alternatives. Since only partial information may be given, thechoice of the initial maximum and minimum weights may a!ect the system's recommendation.Furthermore, this weighting scheme is not the only solution; alternative schemes, based on di!erentalgorithms, are under implementation.

The scores of alternative-4, alternative-5 and alternative-6 in Fig. 1 are !1, 5 and 0 (concerningthe "rst one, position-7 and position-10 have scores 4.5 and 5.5, respectively; the second alternativeis supported by the active position-15 while position-8 is inactive; the last alternative has nopositions `linkeda to it). Therefore, only alternative-5 is active and recommended by the system(once again, this may change in the future upon the assertion of further argumentation).

3.4. Discourse acts

Argumentation in our framework is performed through a variety of discourse acts. These actsmay have di!erent functions and roles in the argumentative discourse. We classify them into twomajor categories: agent acts and internal (system) acts. Agent acts concern user actions andcorrespond to functions directly supported by the user interface. Such functions include theopening of an issue, submission of an alternative, etc. We present below the pseudo-code for a fewrepresentative agent acts:


Fig. 3. The applet window for adding a new alternative.

add}Alternative}to}Issue(alternative alt, issue issN) MIn(alt)"iss; /H alt is attached in iss H/update(iss); N

add}Alternative}to}Alternative(alternative alti, alternative alt

j) M

issj"In(alt

j);

create new issue issi;

In(issi)"iss

j;

In(altj)"In(alt

i)"iss

i;

update(issi); N

The applet window for adding a new alternative to an existing issue is shown in Fig. 3. When analternative alt

iis added to another alt

j(and not directly to the issue iss

jwhere alt

jbelongs), a new

issue issiis automatically created inside iss

j(a similar applet window is used in such a case). Both

altiand alt

jare now put inside the new issue and compared through update(iss

i). Update (iss

j)

will be called from update(issi) and the recommended choice between alt

iand alt

jwill be

compared with the other alternatives of the external (initial) issue. Note that in Fig. 3, users cannotonly give a subject (title) of the new alternative, but also provide more details about their entrythrough the URL pane (including an HTML "le). In this way they can àttacha to their elementslarger pieces of text, images, "gures, sound, etc. Such àttachmentsa can then be consulted by thedecision makers at any time; the lower window of a HERMES discussion forum (see Fig. 1) providesall necessary information for the argumentation item being highlighted each time (this can be doneusing the mouse). Clicking on the Url entry, a new browser window appears showing the contentsof the address provided.

The applet window for adding a new position is shown in Fig. 4. The father element can be analternative, another position, or a constraint. In addition to the Àdd a new alternativea applet


Fig. 4. The applet window for adding a new position.

window, users have to specify here the type of link (argues for or argues against) and the proofstandard they prefer.

Fig. 5 illustrates the applet window for adding a new constraint to an issue. Depending on theargumentation element selected for its insertion, the pair of items pane provides users a menu withall valid pairs, preventing users from making errors in expressing a preference. The relation typemenu includes the preference relations more (less) important than and equally important to. Thepseudo-code for adding a constraint to a position is as follows:

add}Constraint}to}Position(constraint con, position pos) Mif (redundant(con)) return; /H ignore H/refersTo(con)"pos;for all constraints con

jthat refer to pos

if (conyicting(conj, con))

M create new issue iss;In(iss)"con

j;

In(iss)"con;update(iss);return; N

if (contains}inactive(con)) 2 active(con);else M active(con);

if(2 consistent}with}previous(con))2 consistent(con);

else M consistent(con);update(pos);NNN


Fig. 5. The applet window for adding a new constraint.

The concepts of redundant and con#icting constraints have already been discussed above.Contains}inactive(con) checks whether one or both positions that con consists of are inactive,in which case con becomes inactive. The justi"cation is that it does not make sense to argueabout the relevant importance of positions that are rejected (con will be activated automaticallywhen the compared positions get activated* see activate(position pos)). If con does notcontain}inactive, then it is checked for consistency. Only if it is found consistent, the positionthat it refers to is updated, since inconsistent constraints do not participate in the weightingscheme. Other agent acts involve addition of constraints to issues, insertion of supporting andcounter-arguments to positions, constraints and alternatives, etc.

Internal acts are functions performed by the system in order to check consistency, updatethe discussion status and recommend solutions. These functions are called by the agent actsand are hidden from the end user. For instance, consistent}with}previous(con), called byadd}Constraint}to}Position, constructs a graph similar to Fig. 2 and applies path consistency.Other representative internal acts are:

boolean compute}activation(position pos) Mboolean 2 status}changed, old}activation"activation(pos);switch Proof}Standard(pos) M

case Scintilla of Evidence M2 activation(pos);for all positions pos

jthat refer to pos

if (active(posj)'in}favor(pos

j, pos))

M activation(pos);break; N N


case Beyond Reasonable Doubt Mactivation(pos);for all positions pos

jthat refer to pos

if (active(posj)'against(pos

j, pos))

M2 activation(pos);break; N N

case Preponderance of Evidence Mscore(pos)"0;calculate}weights(pos);for all positions pos

jthat refer to pos

if (active(posj)'in}favor(pos

j, pos))

score(pos)#"weight(posj);

else if (active(posj)'against(pos

j, pos))

score(pos)!"weight(posj);

if (score(pos)*0) activation(pos);else 2 activation(pos) N N

if (old}activation!"activation(pos)) status}changed;return status}changed; N

Compute}activation returns status}changed, which is true if the activation label of the positionchanged. Activation is calculated according to the proof standard used. Proof standards area straightforward implementation of the previously given de"nitions. In case of PoE,calculate}weights(pos) calls topological sort to compute the weights of the positions in favor andagainst pos.

update(position pos) Mif (compute}activation(pos)) M

if (active(pos)) activate(pos);else inactivate(pos);

update(RefersTo(pos)); N N /H propagate upwards H/

Update calls compute}activation to check whether activation label has changed. If this is thecase, activate (see below) or inactivate are called and the change is propagated upwards.

activate(position pos) Mpos

j"refersTo(pos);

for all constraints conj

that refer to posj

if 2active(conj)'con

jhas a preference relation on pos)

if (compute}activation(conj)) M

if (consistent}with}previous(conj)

consistent(conj);

else 2consistent(conj);NN

Activation of a position pos involves the retrieval of the constraints where pos appears (theseconstraints must refer to the same position as pos) and a check as to whether they can now become


4For a comprehensive discussion on the application of fuzzy sets theory in the area of human decision making (seeZimmermann [38]), a recent survey pointing out the advances in multiple attribute decision making methods dealingwith fuzzy or ill-de"ned information can be found in Roubens [39]; for a discussion on linguistic decision making models,see Delgado et al. [40].

active and consistent. Inactivation of positions is similar, in the sense that when a positionbecomes inactive, the system searches for the constraints where the position appears and inacti-vates them as well. This may cause some other inconsistent constraints to become consistent, soconsistency check is performed again for the related constraints. A number of additional internalacts were implemented for the activation/inactivation of constraints, update of issues (in which casethere is only PoE), etc. The procedures described in this section, although only a subset of the wholeset of functions performed by the system, give an indication of its dynamic structure. A singleinsertion in the discussion graph may update a large portion of the tree. Every time there isa change, the status of the argumentation elements is recorded in the database that keeps track ofthe discourse.

Finally, note that disagreements among decision makers can be expressed through the appropri-ate discourse acts, according to the argumentation framework speci"ed. In the simplest case,a position p

iarguing against another position p

jwill inactivate the latter, assuming that p

jhas SoE

as proof standard. In other cases, disagreements are `representeda through alternatives, which areincluded in the same issue. HERMES also helps decision making when there are contradictionsbetween the members of the group. More speci"cally, consider a discussion instance where twodecision makers dm-1 and dm-2 believe a and 2a, respectively. Such argumentation elements areconsidered to be alternatives of the same issue (similar to if the decision makers would believe a andb); thus, the contradiction will be solved through the mechanisms for deciding an issue, as they havebeen described in this section. Furthermore, contradictions concerning the preferences of thedecision makers are automatically detected and grouped together by the system (see the cases ofconyicting and inconsistent constraints in Section 3.3). The integration of additional mechanisms tosolve such problems, e.g. based on weights àttacheda to each decision maker or various votingschemata, is straightforward.

4. Knowledge elicitation and fuzzy similarity measures

The multitude of goals and arguments, which are often expressed in qualitative or ill-structuredforms, is inherent in multicriteria decision making environments, and advocates the use ofapproximation models [30]. Fuzzy sets theory [31] provides a conceptual framework that mayprove to be useful for dealing with situations characterized by imprecision due to subjective andqualitative evaluations.4

This section describes the "nal phase of the proposed methodology (see Section 2), that is theapplication of similarity measures to a multiple criteria decision making problem. A variety of suchmeasures, together with interesting properties, have been proposed in the literature [30,32}35].The idea here is to use fuzzy sets for a (graphical) representation of the decision makers'assessments and apply similarity measures in order to evaluate the `di!erencea between them.


5Detailed de"nitions and properties of the similarity measures discussed here can be found in Pappis andKaracapilidis [33], and Pappis and Karacapilidis [30].

We refer to the problem of the purchase of a new car. Decision makers are "rst called to specifythe ideal case. Assume that they bring up the criteria of `speeda, `safetya, `pricea, `comforta andìmagea. Instead of using numerical values to express their judgements or preferences towards analternative, they may use linguistic assessments which, under an appropriate representation model,are able to convey the vagueness of the existing knowledge [36]. Similar ideas about a linguisticframework in group decision making have been suggested by Herrera and his colleagues [37].However, they address a single-stage version of the problem, where the selection of an alternativesolution is made only through a prede"ned set of criteria.

To express the various degrees of `speeda, for instance, we assume the term set Mvery fast, fastenough, of medium speed, rather slow, very slowN (such terms have been used in the correspondingdiscussion that has been illustrated in Section 3). The elements of the term set used in our approachare fuzzy numbers (de"ned on the interval [0,1]), which are described by some (prede"ned andagreed upon) membership functions. Since the decision makers' assessments are only approxima-tions, we may use triangular membership functions to express their vagueness.

We "rst outline some basic notations and de"nitions: A fuzzy set A of the universe of discourse;"Mu

iD i"1,2, mN is a set of ordered pairs M(u

i,k

A(u

i)) D i"1,2, mNN, where k

Ais the member-

ship function of A, kA

:;P[0, 1], and kA(u

i) indicates the grade of membership of u

iin A. When

; is a "nite set, then A can also be represented by +mi/1

kA(u

i)/u

i, and the vector of scalars

ao "(a1, a

2,2, a

m) corresponds to A i! a

i"k

A(u

i), ∀i"1,2, m.

The similarity measures used are based on the operations of union and intersection, on themaximum di!erence, and on the di!erences and the sum of grades of membership.5 Moreanalytically, the following grades of similarity between two fuzzy sets A and B have been de"ned

(for two scalars a and b, it is: a'b$%&" min(a,b)), and asb

$%&" max(a, b)):

MA, B

$%&"

+i(a

i'b

i)

+i(a

isb

i),

¸A, B

$%&" 1!maxi(Da

i!b

iD),

SA, B

$%&" 1!

+i(Da

i!b

iD)

+i(a

i#b

i)"1!

+i(a

isb

i!a

i'b

i)

+i(a

i#b

i)

.

A and B are said to be approximately equal (denoted by A&B) i! GSA, B

)e, where GSA, B

is any ofthe M

A, B,¸

A, B, S

A, B, and e, the proximity measure of A and B, is a given small non-negative

number. Assume now that after the knowledge elicitation and argumentation processes previouslydescribed, two existing alternatives, namely car1 and car2, and the ideal solution appear to have the`performance values a shown in Table 1. Note that the values of the ideal case have been indicatedby HERMES, after discussions about all choice criteria, similar to what was illustrated in Section 3 for


Table 1Performance values

Speed Safety Price Comfort

car1 0.5 0.8 0.2 0.5car2 0.9 0.4 0.6 0.7Ideal 0.7 0.9 0.5 0.5

the `speeda criterion. Appropriate fuzzi"cation and defuzzi"cation processes are involved here;however, such issues do not fall in the scope of this paper (for details, see Karacapilidis and Pappis,[3,21]).

The performance values 0 and 1 denote minimum and maximum performance, respectively. Forinstance, as shown in the table above, the ideal case has received a very good performance value for`safetya (0.9) and an average one for `comforta (0.5). Using the "rst similarity measure, it is

Mcar1, ideal

"

0.5#0.8#0.2#0.50.7#0.9#0.5#0.5

"0.77,

Mcar2, ideal

"

0.7#0.4#0.5#0.50.9#0.9#0.6#0.7

"0.68,

Mcar1, car2

"

0.5#0.4#0.2#0.50.9#0.8#0.6#0.7

"0.53.

It is clear that alternative car1 is `closera to the ideal solution, while there is a signi"cant di!erenceamong the two existing alternatives (use of the other two measures does not a!ect the "nal decision,since it is ¸

car1, ideal"0.7 and ¸

car2, ideal"0.5, while S

car1, ideal"0.87 and S

car2, ideal"0.81). There-

fore, alternative car1 is the one indicated by our framework.

5. Discussion

HERMES has been evaluated by a variety of users, such as students of various levels (from highschool up to undergraduate ones), well-experienced AI researchers, medical doctors, and civil andmechanical engineers. Evaluation can be classi"ed into two phases, a formative and a realapplication one. The former has been conducted in two di!erent AI research labs, while the latter ina third lab and a hospital (with the participation of 12 doctors). The average number of users ineach research lab was 9. Furthermore, 16 high school students were involved in the evaluationduring two public demonstrations of the system in the second lab.

During the formative phase, we asked for feedback concerning the usability of the model, thediscourse structure, and the functionality of the user interface. By setting up various pilot


discussions and by applying their individual way of argumentation, users contributed signi"cantlyto what the system looks like today. Features like the permission for opening an issue insideanother one, or the grouping of con#icting constraints in a separate issue, resulted from varioussuggestions at this phase.

The recently started real application phase includes two projects. The "rst concerns an instruc-tional environment for Mechanical Engineering undergraduate students, which use the system tosolve a problem given by their supervisor. Students contemplate alternative solutions and argue onthem linking their argumentation elements with existing electronic documents (supervisor's notes,papers, etc.). The second project is in the context of medical decision making and, more speci"cally,it concerns the appropriateness of certain medical and surgical procedures for patients with variouspeptic anomalies. The objective is the achievement of consensus as to whether a medical treatmentor an operation is appropriate. Doctors use the system to express and validate their proposals andargue on those of others.

In both phases, users worked with individual computers and in di!erent places. Even forinexperienced users, a system introduction of less than an hour was su$cient to get themacquainted with it. Most of the concepts involved were perfectly understood and adopted.A human moderator supervised the argumentation and assisted the users whenever needed. Therole of the supervisor was similar to that of a system's administrator, i.e., to provide access rights,make sure that elements were inserted in the right position in the discussion graph, etc.

In general, we are very satis"ed with the feedback received so far from all the above studies. Themajority of users admitted that HERMES certainly stimulates discussion, organizes it in a compre-hensible way, and aids them in reaching an agreement more quickly. A preliminary evaluation ofthe system, which results from the medical application, indicates a signi"cant reduction in theoverall problem complexity. Such a reduction concerns the representation, monitoring andsolution of the problem. Users have also found the decision making capabilities of the system veryhelpful and recognized its advantages compared to those of existing conferencing systems. Finally,they only had good comments about the user interfaces.

The medical application gave us the idea of extending the system with another component thatwill assist users in constructing their arguments. The hospital keeps detailed records of the patientswhich can be useful in similar future cases. A potential àssistanta component could matchelements and patterns of an on-going discussion with previous ones, and suggest to a userappropriate actions in order to further support his/her beliefs or, if needed, argue against those ofothers. Similar tools have been recently integrated into Belvedere to address students' tasks to "ndand use information about a controversy [41].

6. Conclusions

Work presented here is a part of a larger project that attempts to link argumentation withcollaboration services in the context of Group Decision Making. Such services include a sharedworkspace for the agents involved, and sophisticated navigation, visualization and informationretrieval tools. Other issues include authentication and access rights, concurrency control, and dataconversion and integration (when accessing remote databases or Information Systems). Generallyspeaking, it is very di$cult to completely automate the processes involved in multiple criteria


decision making. Rather, HERMES acts as an assistant and advisor, by facilitating communicationand recommending solutions, but leaving the "nal enforcement of decisions to the agents.

The framework suggested here attempts to address the inherent subjectivity in group decisionmaking environments and the approximation required. The overall model is quite sensitive to theinitial speci"cations of the term sets and the argumentation brought up by the users. However, theprocedure of knowledge elicitation and argumentation with HERMES, together with the use of fuzzylinguistics and similarity measures in order to handle subjective estimates, appears quite promisingas the model becomes more representative of the real situation.

Acknowledgements

The authors would like to thank the anonymous referees for their constructive and helpfulremarks on the previous versions of this paper.

References

[1] Kreamer KL, King JL. Computer-based systems for cooperative work and group decision making. ACMComputing surveys 1988;20(2):115}46.

[2] Tan SW, Pearl J, Qualitative decision theory. Proceedings of the AAAI-94 Conference, AAAI/MIT Press, 1994. p.928}33.

[3] Karacapilidis N, Papadias D. HERMES: supporting argumentative discourse in multi-agent decision making.Proceedings of the 15th National Conference on Arti"cial Intelligence (AAAI-98). Cambridge, MA: AAAI/MITPress, 1998. p. 827}32.

[4] Hurwitz R, Mallery JC. The open meeting: a web-based system for conferencing and collaboration. Proceedings ofthe fourth International WWW Conference, 1995.

[5] Conklin J. Designing organizational memory: preserving intellectual assets in a knowledge economy. GDSSWorking Paper, 1996. Available at: http://www.gdss.com/DOM.htm

[6] Conklin J, Begeman ML. gIBIS: a hypertext tool for team design deliberation. Proceedings of the Hypertext'89Conference. New York:ACM, 1987. p. 247}52.

[7] Fischer G, McCall R, Morch A. JANUS: integrating hypertext with a knowledge-based design environment.Proceedings of the Hypertext'89 Conference, New York: ACM, 1989. p. 105}17.

[8] Smolensky P, Fox B, King, R, Lewis C. Computer-aided reasoned discourse, or how to argue with a computer. In:Guindon R. editor. Cognitive science and its applications for human-computer interaction. Hillsdale, NJ: Erlbaum,1987. p. 109}62.

[9] Streitz N, Hannemann, J, ThuK ring M. From ideas and arguments to hyperdocuments: Travelling through activityspaces. In Proceedings of the Hypertext'89 Conference. New York: ACM, 1989. p. 343}64.

[10] Suthers D, Weiner A, Connelly J, Paolucci M. Belvedere: engaging students in critical discussion of science andpublic policy issues. Proceedings of the seventh World Conference on AI in Education, 1995. p. 266}73.

[11] Saaty T. The analytic hierarchy process. New York: Mc-Graw Hill, 1980.[12] Klein MR, Methlie LB. Knowledge-based decision support systems with applications in business. 2nd ed.

Chichester: Wiley, 1995.[13] Vincke P. Multicriteria Decision Aids. Chichester: Wiley, 1992.[14] van Eemeren FH, Grootendorst R, Snoeck Henkemans F. Fundamentals of argumentation theory. Mahwah, NJ:

Erblaum, 1996.[15] Brewka G. A reconstruction of Rescher's theory of formal disputation based on default logic. Working Notes of the

AAAI'94 Workshop on Computational Dialectics, 1994. p. 15}27.


[16] Rescher N. Dialectics: a controversy-oriented approach to the theory of knowledge. Albany: State University ofNew York Press, 1977.

[17] Gordon T. The pleadings game: an arti"cial intelligence model of procedural justice. Dordrecht: Kluwer, 1995.[18] Ge!ner H, Pearl J. Conditional entailment: bridging two approaches to default reasoning. Arti"cial Intelligence

1992;53(2}3):209}44.[19] Fox J, Krause P, Elvang-G+ransson M. Argumentation as a general framework for uncertain reasoning. Proceed-

ings of the UAI-93 Conference. San Mateo, CA: Morgan Kaufmann, 1993. p. 428}34.[20] Prakken, H. From logic to dialectics in legal argument. Proceedings of the "fth International Conference on AI and

Law, 1995. p. 165}74.[21] Karacapilidis N, Pappis CP. Combining knowledge elicitation with fuzzy assessments in group decision making.

Proceedings of the IEEE Computational Engineering in Systems Applications Conference (CESA'98) Nabeul-Hammamet, Tunisia, 1998. Vol. 2. p. 345}50.

[22] Karacapilidis N, Papadias D, Gordon T, Voss H. Collaborative environmental planning with GeoMed. EuropeanJournal of Operational Research 1997;102(2):335}46.

[23] Karacapilidis N, Papadias D, Pappis CP. Modeling negotiations in group decision support systems. In: Stewart T,Honert Rvd, editors. Trends in Multicriteria Decision Making: Proceedings of the 13th International Conferenceon Multiple Criteria Decision Making (MCDM'97), Cape Town, South Africa. Lecture notes series. Berlin,Springer, 1998. p. 158}171.

[24] Rittel H, Webber M. Dilemmas in a general theory of planning. Policy Sciences, 1973. p. 155}69.[25] Pinkas G. Propositional non-monotonic reasoning and inconsistency in symmetric neural networks. Proceedings

of the 12th IJCAI Conference, 1991. p. 525}30.[26] Simari GR, Loui RP. A mathematical treatment of defeasible reasoning and its implementation. Arti"cial

Intelligence 1992;53(2}3):125}57.[27] Farley AM, Freeman K. Burden of proof in legal argumentation. Proceedings of the "fth International Conference

on AI and Law, 1995. p. 156}64.[28] Mackworth A, Freuder E. The complexity of some polynomial network consistency algorithms for constraint

satisfaction problems. Arti"cial Intelligence 1985;25:65}74.[29] Knuth DE. Fundamental algorithms. Art of computer programming, vol. 1. Reading, MA: Addison-Wesley, 1973.[30] Pappis P, Karacapilidis N. A comparative assessment of measures of similarity of fuzzy values. Fuzzy Sets and

Systems 1993;56:171}4.[31] Zadeh LA. Fuzzy Sets. Information and Control 1965;8:338}53.[32] Pappis C. Value approximation of fuzzy systems variables. Fuzzy Sets and Systems 1991;39:111}5.[33] Pappis P, Karacapilidis N. Application of a similarity measure of fuzzy sets to fuzzy relational equations. Fuzzy

Sets and Systems 1995;75:135}42.[34] Wang X, De Baets B, Kerre E. A comparative study of similarity measures. Fuzzy Sets and Systems 1995;73:259}68.[35] Zwick R, Carlstein E, Budescu D. Measures of similarity among fuzzy sets: a comparative analysis. International

Journal of Approximate Reasoning 1987;1:221}42.[36] Tong M, Bonissone PP. A linguistic approach to decision making with fuzzy sets. IEEE Transactions on Systems,

Man and Cybernetics 1980;10:716}23.[37] Herrera F, Herrera-Viedma E, Verdegay JL. A rational consensus model in group decision making using linguistic

assessments. Fuzzy Sets and Systems 1997;88(1):31}49.[38] Zimmermann HJ. Fuzzy set theory and its applications, Boston, MA: Kluwer, 1991.[39] Roubens M. Fuzzy sets and decision analysis. Fuzzy Sets and Systems 1997;90:199}206.[40] Delgado M, Verdegay JL, Vila MA. Linguistic decision making models. International Journal of Intelligent

Systems 1992;7:479}92.[41] Toth JA, Suthers D, Weiner A. Providing expert advice in the domain of collaborative scienti"c inquiry.

Proceedings of the eighth World Conference on AI in Education, 1997.


Documents

Computer-supported collaborative argumentation and fuzzy similarity measures in multiple criteria decision making