Computer-supported collaborative argumentation ... - Semantic Scholar

Computers & Operations Research 27 (2000) 653}671

Computer-supported collaborative argumentation and fuzzy similarity 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 up by spatially dispersed parties with di!erent backgrounds and interests. Recent advances in information technology and computer science may satisfactorily address a variety of related problems, such as communication among the decision makers and e$cient elicitation and representation of the domain knowledge. Furthermore, they may signi"cantly automate the decision making process itself. On the other hand, the inherent uncertainty of the problem advocates the use of approximation models, often coming from the fuzzy sets discipline. This paper presents an integrated framework for multiple criteria decision making among groups on the World Wide Web. The agents involved use a fully implemented argumentative discourse system to pursue their criteria and objectives, the aim being the speci"cation of the desired solution to the problem. The system organizes the collective knowledge in a discussion graph with truth maintenance and consistency checking features. Fuzzy similarity measures are then involved in order to assess alternative existing solutions with respect to the desired one. Scope and purpose We view multiple criteria decision making as a collaborative process, where decision makers have to follow a series of communicative actions in order to establish a common belief on the dimensions of the problem. Such dimensions may concern the choice criteria, the existing or desired alternative solutions, or the objective function, to mention some. This paper presents a framework for multiple criteria decision making among groups. Our approach exploits recent advances in information technology and manages to (i) remove the communication impediments among spatially dispersed decision makers, (ii) e$ciently represent the domain knowledge, (iii) develop e$cient mechanisms to structure and consistently maintain the decision analysis, and (iv) automate the multiple criteria decision making process per se. The framework is based on a fully implemented system, namely HERMES, which enhances decision making by supporting argumentative

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

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

discourse among decision makers. The system is implemented in Java and runs on the World Wide Web, thus providing relatively inexpensive access to a broad public. ( 2000 Elsevier Science Ltd. All rights reserved. Keywords: Multiple criteria decision making; Argumentation; Fuzzy similarity measures; Computer-supported cooperative work

1. Introduction Multiple criteria decision making usually raises a lot of intricate debates and negotiations among participants. Con#icts of interest are inevitable and support for achieving consensus and compromise is required. Each decision maker may adopt and, consequently, suggest his/her own strategy that ful"lls some goals at a certain level. Opinions may di!er about the relevance or value of a proposition when deciding an issue. Decision makers may have arguments for supporting or against alternative solutions. In addition, they have to confront the existence of insu$cient and too much information simultaneously. In other words, for some parts of the problem, relevant information which would be useful for making a decision is missing, whereas for others, the time needed for the retrieval and comprehension of the existing volume of information is prohibitive. Furthermore, factual knowledge is not always su$cient for making a decision. Value judgements, depending on the role and the goals of each decision maker, are among the critical issues requiring attention. Participants need appropriate means to assert their preferences, which are often expressed in qualitative terms. Finally, decision makers are not necessarily pro"cient in computer science and information technology; they need appropriate tools in order to easily participate in the discussion (see also Kreamer and King [1]). This parallels the vision of the DSS community pioneers, that is, by supporting and not replacing human judgement, the system comes in second and 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$culties. Work in these disciplines builds on a probabilistic view of uncertainty, where possible actions are evaluated through their expected utility. The use of such crisp values has been extensively critisized; the speci"cation of the complete sets of probabilities and utilities required renders such approaches impractical for the majority of decision making tasks that involve common sense knowledge and reasoning [2]. On the other hand, arti"cial intelligence (AI) approaches basically attempt to reduce the burden of numerical information required, while pay much attention to the automation of the process itself. The related qualitative decision making techniques use linguistic assessments which, under an appropriate model, are able to convey the vagueness of the existing knowledge. Such assessments may be related to the importance of a certain alternative or criterion, the preference degree of an alternative over another, the degree of acceptability of a decision maker's position, and so on. This paper presents a framework for multiple criteria decision making among groups on the World Wide Web. Our approach exploits recent advances in AI and information technology, the aims being: f removal of communication impediments among spatially dispersed decision makers; f e$cient elicitation and representation of the domain knowledge;


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f development of e$cient mechanisms to structure and consistently maintain the decision analysis, and f automation of the multiple criteria decision making process. The framework is based on a fully implemented system, namely HERMES, which enhances decision making by supporting argumentative discourse among decision makers [3]. The system is implemented in Java applets and runs on the Web, thus providing relatively inexpensive access to a broad public. It can be used for distributed, asynchronous or synchronous collaboration, allowing decision makers to surpass the requirements of being in the same place and working at the same time. Unlike other approaches towards the development of web-based conferencing [4] and argumentation support systems [5}10], HERMES does not merely provide threaded discussion forums, where users' assertions are passively linked.1 On the contrary, it focuses on aiding decision makers to reach a decision, not only by e$ciently structuring the discussion, but also by providing appropriate reasoning mechanisms for it. It is an active system, that constantly checks for inconsistencies and updates the discourse status, thus stimulating discussion among participants. In the following section, we discuss how argumentation and decision making interrelate in our approach. Section 3 describes features of HERMES, and presents the argumentation elements, proof standards, and discourse acts involved. Section 4 deals with knowledge elicitation and approximation 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 of a prede"ned set of alternatives and criteria, and provide methods to quantify and aggregate subjective 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 criteria decision making as a collaborative process, where decision makers have to follow a series of communicative 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, or the objective function, to mention some. Issues of knowledge elicitation and representation are inherent in these environments and an appropriate machinery is needed (see, for instance, Klein and Methlie [12] and Vincke [13]). The framework discussed in this paper resorts to an argumentative discourse approach. Research on argumentative discourse has been performed from di!erent viewpoints. As comprehensively described in van Eemeren et al. [14], most approaches follow two main methodologies, namely, formal and informal logic. According to the formal perspective, arguments are de-contextualized sets of sentences or symbols viewed in terms of their syntactic or semantic 1 For a comparative analysis of these systems, see Karacapilidis and Papadias [3].

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relationships. On the other hand, informal logic views arguments as pragmatic, i.e., their meaning is a function of their purposive context. From the AI point of view, most researchers have focused on formal models of argumentation based on various logics. For instance, Brewka [15] reconstructed Rescher's theory of formal disputation [16], Gordon's work [17] was based on Ge!ner and Pearl's concepts of conditional entailment [18], while Fox and his colleagues, in the context of the legal domain, 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 to select one of them, while the second includes those where an ideal case is decided upon "rst, and the subsequent 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 be determined by the participants, and a decision (objective) function must be composed, which combines criteria to decide between alternatives. HERMES can be used in any of the categories discussed above. This paper deals with cases that belong to the second one, and suggests a framework for multiple criteria decision making that comprises 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, and f 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 what information is important and what simplifying assumptions should be made. Furthermore, the domain knowledge typically requires additional explanation and justi"cation. While standard techniques are available for eliciting probability and utility models, the overall task is typically tedious and time consuming. According to our approach, elicitation of knowledge is takes place in an 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 sample constructed discourse about the desired `speeda of a car (similar discourses may be performed for other choice criteria, such as `pricea, `service provideda, etc.). The discourse takes place among three decision makers dm-1, dm-2 and dm-3, who bring up the necessary argumentation to express

2 An extensive discussion on the use of alternative logics in argumentative discourse can be found in Prakken [20]. 3 HERMES 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 system only during the "rst two phases discussed above.


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

their interests and perspectives. Fig. 1 illustrates an instance of the corresponding HERMES discussion 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 argumentation [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 of a HERMES discussion forum is always an issue). Issues consist of a set of alternatives that correspond

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to potential choices or courses of action (e.g., alternative-4: `we should buy a fast enough cara, and alternative-5: Ì would prefer a rather slow cara belong to issue-2, and have been proposed by dm-1 and dm-2, respectively). Issues can be inside other issues in cases where some alternatives need to be grouped 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: `such a 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 objection of dm-3 to the same alternative. Positions may also refer to some other position in order to provide additional 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 weigh di!erent beliefs. Unfortunately, well-de"ned utility and probability functions regarding properties or attributes of alternatives (used in traditional approaches), as well as complete ordering of these properties are usually absent. In argumentation studies, subjects like priority relationships and preference 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 the selection 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 their form, we have alternatively used the term constraint to refer to them. This is not to be confused with cases where a criterion is compared to a numeric value; constraints in our framework always compare two positions (in the rest of the paper, and in order to be coherent with our implementation, we mostly use this second term). Constraints may give various levels of importance to alternatives. Like the other argumentation elements, they are subject to discussion; therefore, they may be `linkeda with positions supporting or challenging them. In Fig. 1, constraint-12: `less time on the road on a daily basis vs. rather heavy gas 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 the relation `position-8 is more important than position-7a. Two types of preferences can be expressed by the system: (i) Local, when a constraint refers to a position, or another constraint. In this case, the positions that constitute the constraint must refer to the same element (i.e., have the same father). In the example shown in Fig. 1, a preference expressed 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, when a constraint refers to an issue. In this case, its consistuent positions must refer to alternatives (not necessarily 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 (it can be active or inactive). This label is calculated according to the argumentation underneath and


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the type of evidence speci"ed for them. In general, di!erent elements of the argumentation, even in the same debate, do not necessarily need the same type of evidence. Quoting the well-used legal domain example, the arguments required to indict someone need not be as convincing as those needed to convict him [27]. Therefore, a generic argumentation system requires di!erent proof standards (work on AI and Law uses the term burdens of proof). In the sequel, we describe the ones implemented in our system (the names have the same interpretation as in the legal domain). We do not claim that the list is exhaustive; other standards, that match speci"c application needs, can be easily 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 p is active, if i at least one active position argues in favor of it: active(p ) Q &p (active(p )'in}favor(p , p )). i j j j i De5nition 2 (beyond reasonable doubt (BRD)). According to BRD, a position p is active if there are i no active positions that speak against it: active(p ) Q 2&p (active(p )'against(p , p )). i j j j 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 during the discussion, the issue it belongs to should be updated since a new choice may be made. This brings us to the last proof standard, namely preponderance of evidence (PoE), used for the selection of 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 an alternative has weight"min}weight. Max}weight and min}weight are initialized to some pre-de"ned values (in the following, we assume that initially min}weight"0 and max}weight"10; this may be changed by preference constraints). The score of an element e is i used to compute its activation label (score is calculated on the #y). If an element does not have any arguments, its score is equal to its weight; otherwise, the score is calculated from the weights of the active positions that refer to it score(e )" + weight(p )! + weight(p ). i j k } in favor(pj ,ej )\ against(pj ,ej )\ active(pj ) active(pj ) De5nition 3 (preponderance of evidence (PoE)). According to this standard, a position is active when the active positions that support it outweigh those that speak against it active(p ) Q score(p )*0. i j Concerning alternatives, PoE will produce positive activation label for a when there are no i alternatives with larger score in the same issue: active(a ) Q ∀a in}issue(a ),(score(a ))score(a )). i j i j i In the discussion instance of Fig. 1, the proof standard is SoE for all positions and PoE for alternatives. Position-8 and position-11 are inactive (their accompanying icons are red; they are

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shown in dark grey color here) since position-9 and position-14, respectively, are active and speak against them. On the contrary, position-10 is active (the accompanying icon is blue; it appears in light gray color here) since there is at least one active position that speaks in favor of it (position-7 and position-15 are also active since they are leafs of the discussion tree; that is, there is no argumentation underneath them). Active positions are considered àccepteda due to discussion underneath (e.g., strong supporting arguments, no counter-arguments), while inactive positions are temporarily `rejecteda (not taken into account). Similarly, active alternatives correspond to `recommendeda choices, i.e., choices that are the strongest among the alternatives in their issue. Note that, for the discussion instance under consideration, alternative-6 is not supported or objected to by any position, alternative-5 is only supported by position-15 (position-8 is inactive), while alternative-4 is supported by position-7 and objected to by position-10. The mechanisms for the calculation of activation labels of alternatives always depend on the related constraints and will be discussed in the following subsection. The activation label of constraints is decided by two factors: the discussion underneath (similar to 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 of the discussion, the insertion of position-9 inactivated position-8, which in turn inactivated constraint-13. Both constraints have BRD as proof standard, therefore constraint-12 is active (no active positions 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 else related to them changes). 3.3. Consistency checking Apart from an activation label, each constraint has a consistency label which can be consistent or inconsistent. Every time a constraint is inserted in the discussion graph, the system checks if both positions of the new constraint exist in another, previously inserted, constraint. In the a$rmative case, the new constraint is considered either redundant, if it also has the same preference relation, or conyicting, otherwise. A redundant constraint is ignored, while a con#icting one is grouped together with the previously inserted constraint in an issue automatically created by the system, the rationale being to gather together con#icting constraints and stimulate further argumentation on them until only one becomes active. If both positions of the new constraint do not exist in a previously inserted constraint, its consistency is checked against previous active and consistent constraints referring to the same element (or belonging to the same issue). This process is based on a polynomial (O(N3), N being the number of the associated positions) path consistency algorithm [28]. Although path consistency, as most discourse acts described in the sequel, interacts with the database where the discussion graph is stored (Oracle 7 is used), the algorithm is very e$cient. Even for non-local preferences involving issues with numerous alternatives and positions linked to them, execution time is negligible compared to communication delay. Active and consistent constraints participate in the weighting scheme (only constraint-12 in the example of Fig. 1). In order to demonstrate how the algorithm for altering weights works, we use the example of Fig. 2. There exist "ve positions and four constraints that relate them as illustrated


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Fig. 2. The weighting scheme.

in Fig. 2a. The arrowed lines correspond to the `more important than (')a relation (e.g., p 'p ) 1 2 and the dotted line to the èqually important to (")a relation (e.g., p "p ). First, path 3 4 consistency explicates all `'a relations (Fig. 2b). Then, topological sort [29] is applied twice to compute the possible maximum and minimum weights for each position (Fig. 2c). The weight is the average of the new max}weight and min}weight: weight(p )"6, weight(p )"4.5, 1 2 weight(p )"5, weight(p )"5 and weight(p )"4. 3 4 5 The basic idea behind the above scheme is that the weight of a position is increased every time the position is more important than another one (and decreased when it is less important), the aim being to extract a total order of alternatives. Since only partial information may be given, the choice 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!erent algorithms, are under implementation. The scores of alternative-4, alternative-5 and alternative-6 in Fig. 1 are !1, 5 and 0 (concerning the "rst one, position-7 and position-10 have scores 4.5 and 5.5, respectively; the second alternative is supported by the active position-15 while position-8 is inactive; the last alternative has no positions `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 acts may have di!erent functions and roles in the argumentative discourse. We classify them into two major categories: agent acts and internal (system) acts. Agent acts concern user actions and correspond to functions directly supported by the user interface. Such functions include the opening of an issue, submission of an alternative, etc. We present below the pseudo-code for a few representative agent acts:

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

M

add}Alternative}to}Alternative(alternative alt , alternative alt ) M i j iss "In(alt ); j j create new issue iss ; i In(iss )"iss ; i j In(alt )"In(alt )"iss ; j i i update(iss ); N i The applet window for adding a new alternative to an existing issue is shown in Fig. 3. When an alternative alt is added to another alt (and not directly to the issue iss where alt belongs), a new i j j j issue iss is automatically created inside iss (a similar applet window is used in such a case). Both i j alt and alt are now put inside the new issue and compared through update(iss ). Update (iss ) i j i j will be called from update(iss ) and the recommended choice between alt and alt will be i i j compared with the other alternatives of the external (initial) issue. Note that in Fig. 3, users cannot only give a subject (title) of the new alternative, but also provide more details about their entry through the URL pane (including an HTML "le). In this way they can àttacha to their elements larger pieces of text, images, "gures, sound, etc. Such àttachmentsa can then be consulted by the decision makers at any time; the lower window of a HERMES discussion forum (see Fig. 1) provides all necessary information for the argumentation item being highlighted each time (this can be done using the mouse). Clicking on the Url entry, a new browser window appears showing the contents of the address provided. The applet window for adding a new position is shown in Fig. 4. The father element can be an alternative, another position, or a constraint. In addition to the Àdd a new alternativea applet

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


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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 proof standard they prefer. Fig. 5 illustrates the applet window for adding a new constraint to an issue. Depending on the argumentation element selected for its insertion, the pair of items pane provides users a menu with all valid pairs, preventing users from making errors in expressing a preference. The relation type menu includes the preference relations more (less) important than and equally important to. The pseudo-code for adding a constraint to a position is as follows: add}Constraint}to}Position(constraint con, position pos) if (redundant(con)) return; /H ignore H/ refersTo(con)"pos; for all constraints con that refer to pos j if (conyicting(con , con)) j 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

M

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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 argue about the relevant importance of positions that are rejected (con will be activated automatically when the compared positions get activated * see activate(position pos)). If con does not contain}inactive, then it is checked for consistency. Only if it is found consistent, the position that it refers to is updated, since inconsistent constraints do not participate in the weighting scheme. Other agent acts involve addition of constraints to issues, insertion of supporting and counter-arguments to positions, constraints and alternatives, etc. Internal acts are functions performed by the system in order to check consistency, update the discussion status and recommend solutions. These functions are called by the agent acts and are hidden from the end user. For instance, consistent}with}previous(con), called by add}Constraint}to}Position, constructs a graph similar to Fig. 2 and applies path consistency. Other representative internal acts are: boolean compute}activation(position pos) M boolean 2 status}changed, old}activation"activation(pos); switch Proof}Standard(pos) M case Scintilla of Evidence M 2 activation(pos); for all positions pos that refer to pos j if (active(pos )'in}favor(pos , pos)) j j M activation(pos); break; N N


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case Beyond Reasonable Doubt M activation(pos); for all positions pos that refer to pos j if (active(pos )'against(pos , pos)) j j M2 activation(pos); break; N N case Preponderance of Evidence M score(pos)"0; calculate}weights(pos); for all positions pos that refer to pos j if (active(pos )'in}favor(pos , pos)) j j score(pos)#"weight(pos ); j else if (active(pos )'against(pos , pos)) j j score(pos)!"weight(pos ); j 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 position changed. Activation is calculated according to the proof standard used. Proof standards are a 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 and against pos. update(position pos) M if (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 the case, activate (see below) or inactivate are called and the change is propagated upwards. activate(position pos) M pos "refersTo(pos); j for all constraints con that refer to pos j j if 2active(con )'con has a preference relation on pos) j j if (compute}activation(con )) M j if (consistent}with}previous(con ) j consistent(con ); j else 2consistent(con );NN j Activation of a position pos involves the retrieval of the constraints where pos appears (these constraints must refer to the same position as pos) and a check as to whether they can now become

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active and consistent. Inactivation of positions is similar, in the sense that when a position becomes inactive, the system searches for the constraints where the position appears and inactivates them as well. This may cause some other inconsistent constraints to become consistent, so consistency check is performed again for the related constraints. A number of additional internal acts were implemented for the activation/inactivation of constraints, update of issues (in which case there is only PoE), etc. The procedures described in this section, although only a subset of the whole set of functions performed by the system, give an indication of its dynamic structure. A single insertion in the discussion graph may update a large portion of the tree. Every time there is a change, the status of the argumentation elements is recorded in the database that keeps track of the discourse. Finally, note that disagreements among decision makers can be expressed through the appropriate discourse acts, according to the argumentation framework speci"ed. In the simplest case, a position p arguing against another position p will inactivate the latter, assuming that p has SoE i j j as proof standard. In other cases, disagreements are `representeda through alternatives, which are included in the same issue. HERMES also helps decision making when there are contradictions between the members of the group. More speci"cally, consider a discussion instance where two decision makers dm-1 and dm-2 believe a and 2a, respectively. Such argumentation elements are considered to be alternatives of the same issue (similar to if the decision makers would believe a and b); thus, the contradiction will be solved through the mechanisms for deciding an issue, as they have been described in this section. Furthermore, contradictions concerning the preferences of the decision makers are automatically detected and grouped together by the system (see the cases of conyicting and inconsistent constraints in Section 3.3). The integration of additional mechanisms to solve such problems, e.g. based on weights àttacheda to each decision maker or various voting schemata, is straightforward.

4. Knowledge elicitation and fuzzy similarity measures The multitude of goals and arguments, which are often expressed in qualitative or ill-structured forms, is inherent in multicriteria decision making environments, and advocates the use of approximation models [30]. Fuzzy sets theory [31] provides a conceptual framework that may prove to be useful for dealing with situations characterized by imprecision due to subjective and qualitative evaluations.4 This section describes the "nal phase of the proposed methodology (see Section 2), that is the application of similarity measures to a multiple criteria decision making problem. A variety of such measures, 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. 4 For a comprehensive discussion on the application of fuzzy sets theory in the area of human decision making (see Zimmermann [38]), a recent survey pointing out the advances in multiple attribute decision making methods dealing with 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].


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We refer to the problem of the purchase of a new car. Decision makers are "rst called to specify the ideal case. Assume that they bring up the criteria of `speeda, `safetya, `pricea, `comforta and ìmagea. Instead of using numerical values to express their judgements or preferences towards an alternative, 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 linguistic framework 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 alternative solution 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, fast enough, of medium speed, rather slow, very slowN (such terms have been used in the corresponding discussion that has been illustrated in Section 3). The elements of the term set used in our approach are fuzzy numbers (de"ned on the interval [0,1]), which are described by some (prede"ned and agreed upon) membership functions. Since the decision makers' assessments are only approximations, 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 D i"1,2, mN is a set of ordered pairs M(u , k (u )) D i"1, 2, mNN, where k is the memberi i A i A ship function of A, k : ;P[0, 1], and k (u ) indicates the grade of membership of u in A. When A A i i ; is a "nite set, then A can also be represented by +m k (u )/u , and the vector of scalars i/1 A i i ao "(a , a , 2, a ) corresponds to A i! a "k (u ), ∀i"1, 2, m. 1 2 m i A i The similarity measures used are based on the operations of union and intersection, on the maximum di!erence, and on the di!erences and the sum of grades of membership.5 More analytically, 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)): M

A, B

$%& "

+ (a 'b ) i i i , + (a sb ) i i i

$%& " 1!max (Da !b D), ¸ i i i A, B $%& + (Da !b D) + (a sb !a 'b ) i "1! i i i i i . S " 1! i i A, B + (a #b ) + (a #b ) i i i i i i A and B are said to be approximately equal (denoted by A&B) i! GS )e, where GS is any of A, B A, B the M , ¸ , S , and e, the proximity measure of A and B, is a given small non-negative A, B A, B A, B number. Assume now that after the knowledge elicitation and argumentation processes previously described, 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 indicated by HERMES, after discussions about all choice criteria, similar to what was illustrated in Section 3 for 5 Detailed de"nitions and properties of the similarity measures discussed here can be found in Pappis and Karacapilidis [33], and Pappis and Karacapilidis [30].

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N. Karacapilidis, C. Pappis / Computers & Operations Research 27 (2000) 653}671 Table 1 Performance values

car1 car2 Ideal

Speed

Safety

Price

Comfort

0.5 0.9 0.7

0.8 0.4 0.9

0.2 0.6 0.5

0.5 0.7 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. For instance, 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 M

car1, ideal

0.5#0.8#0.2#0.5 " "0.77, 0.7#0.9#0.5#0.5

M

0.7#0.4#0.5#0.5 " "0.68, car2, ideal 0.9#0.9#0.6#0.7

M

0.5#0.4#0.2#0.5 " "0.53. car1, car2 0.9#0.8#0.6#0.7

It is clear that alternative car1 is `closera to the ideal solution, while there is a signi"cant di!erence among the two existing alternatives (use of the other two measures does not a!ect the "nal decision, since it is ¸ "0.7 and ¸ "0.5, while S "0.87 and S "0.81). Therecar1, ideal car2, ideal car1, ideal car2, ideal 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 high school up to undergraduate ones), well-experienced AI researchers, medical doctors, and civil and mechanical engineers. Evaluation can be classi"ed into two phases, a formative and a real application one. The former has been conducted in two di!erent AI research labs, while the latter in a third lab and a hospital (with the participation of 12 doctors). The average number of users in each research lab was 9. Furthermore, 16 high school students were involved in the evaluation during two public demonstrations of the system in the second lab. During the formative phase, we asked for feedback concerning the usability of the model, the discourse structure, and the functionality of the user interface. By setting up various pilot


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discussions and by applying their individual way of argumentation, users contributed signi"cantly to what the system looks like today. Features like the permission for opening an issue inside another one, or the grouping of con#icting constraints in a separate issue, resulted from various suggestions at this phase. The recently started real application phase includes two projects. The "rst concerns an instructional environment for Mechanical Engineering undergraduate students, which use the system to solve a problem given by their supervisor. Students contemplate alternative solutions and argue on them 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 various peptic anomalies. The objective is the achievement of consensus as to whether a medical treatment or an operation is appropriate. Doctors use the system to express and validate their proposals and argue on those of others. In both phases, users worked with individual computers and in di!erent places. Even for inexperienced users, a system introduction of less than an hour was su$cient to get them acquainted with it. Most of the concepts involved were perfectly understood and adopted. A human moderator supervised the argumentation and assisted the users whenever needed. The role 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. The majority of users admitted that HERMES certainly stimulates discussion, organizes it in a comprehensible way, and aids them in reaching an agreement more quickly. A preliminary evaluation of the system, which results from the medical application, indicates a signi"cant reduction in the overall problem complexity. Such a reduction concerns the representation, monitoring and solution of the problem. Users have also found the decision making capabilities of the system very helpful 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 that will assist users in constructing their arguments. The hospital keeps detailed records of the patients which can be useful in similar future cases. A potential àssistanta component could match elements and patterns of an on-going discussion with previous ones, and suggest to a user appropriate actions in order to further support his/her beliefs or, if needed, argue against those of others. Similar tools have been recently integrated into Belvedere to address students' tasks to "nd and use information about a controversy [41].

6. Conclusions Work presented here is a part of a larger project that attempts to link argumentation with collaboration services in the context of Group Decision Making. Such services include a shared workspace for the agents involved, and sophisticated navigation, visualization and information retrieval tools. Other issues include authentication and access rights, concurrency control, and data conversion and integration (when accessing remote databases or Information Systems). Generally speaking, it is very di$cult to completely automate the processes involved in multiple criteria

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decision making. Rather, HERMES acts as an assistant and advisor, by facilitating communication and recommending solutions, but leaving the "nal enforcement of decisions to the agents. The framework suggested here attempts to address the inherent subjectivity in group decision making environments and the approximation required. The overall model is quite sensitive to the initial speci"cations of the term sets and the argumentation brought up by the users. However, the procedure of knowledge elicitation and argumentation with HERMES, together with the use of fuzzy linguistics and similarity measures in order to handle subjective estimates, appears quite promising as the model becomes more representative of the real situation.

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

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