Soft Computing and Web Intelligence for Supporting Consensus ...

Soft Computing manuscript No. (will be inserted by the editor)

Soft Computing and Web Intelligence for Supporting Consensus Reaching Janusz Kacprzyk · Slawomir Zadro˙zny

Received: date / Accepted: date

Abstract A novel idea and architecture of a group decision support system (GDSS) for reaching consensus in a group of individuals (agents) is proposed. The core of the system is the preferences modeling and consensus assessment module which is based on fuzzy logic. However the focus is on providing the members of the group with an information- and knowledge-rich environment, and tools to make an effective and efficient use of such an environment. This should help the agent gain proper opinions about the issues and opinions and/or attitudes of other agents, articulate proper testimonies, actively contribute to the discussion, and finally make sound and informed decisions that can help constructively run the consensus reaching process. For this purpose modern Web-based technologies are employed and tightly integrated with the core of the system. Keywords consensus · group decision making · fuzzy logic · preferences · ontology · information retrieval.

1 Introduction Choosing a restaurant for a dinner by a group of friends, on the one extreme, or selecting an investment project most beneficial for the local community, on the other J. Kacprzyk Systems Research Institute, Polish Academy of Sciences, 01-447 Warszawa, Poland Tel.: +48 223810275 Fax: +48 223810103 E-mail: [email protected] S. Zadro˙zny Systems Research Institute, Polish Academy of Sciences, 01-447 Warszawa, Poland Tel.: +48 223810275 Fax: +48 223810103 E-mail: [email protected]

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extreme – though so different in scale and consequences – are two tasks which share some important features. What matters here is the necessity to take into account and respect opinions of all participants, developing a joint solution (decision), to secure the involvement of all participants in its later implementation. Thus it is about making arguments and convincing, looking for truly the best possible decision for all rather than putting a pressure to accept and imposing the will of some majority (or even minority). These features characterize briefly what is known in the literature as consensus decision making [1–4]. In order to stress its dynamic character, reflected in the form of an iterative and interactive process over some time span, we prefer to refer to it as to the consensus reaching process. This process comprises of many tasks like the elaboration of a joint opinion via identifying various aspects of the problem under consideration, exchange of the knowledge of the particular parties involved, search for new information that may be relevant, etc. The main elements of the model of this process that we adopt are explicitly specified preferences of a group of individuals concerning a set of alternatives and a discussion (process) that aims at getting this preferences closer to one another. With the exception of some trivial cases the need for a computer based support is here evident. In the paper we propose a concept of a Web-based system combining human-consistency of the assumed representation of the decision problem, intelligent and knowledge-based support for the information search and decision process monitoring and guidance with the user-friendliness and intuitiveness of the user interface, typical for Web-based implementations. In section 2 we briefly identify the related research areas. Section 3 describes the core of the proposed system, i.e., the preference representation and the consensus measuring methods. Section 4 shows an overall structure of the proposed system, with a special emphasis on the role of ontologies in its functioning.

2 Relevant concepts and related research lines Concerning the theoretical foundations, very relevant for our purposes is the research on decision making under bipolar information. In our approach we model the discussion as the process of submitting the pro and con arguments. However we perceive this primarily as an opportunity to create a context for a further discussion rather than as a way of an “automatic” or “semi-automatic” determination of the group or individual decision. Nonetheless, even with such a limited aim getting an insight into the arguments and their interplay may be very valuable. Thus the work represented by papers by Amgoud et al. [5] and Bonnefon et al. [6], providing a formal framework for the decision making based on pro and con arguments, though in a different context and perspective, is here very relevant. The consensus reaching support system may be seen in a broader perspective as a tool to exploit collective intelligence in the quest for a solution of the problem under consideration. Surely the question posed at the MIT Center for Collective Intelligence Web site [7] “How can people and computers be connected so that – collectively – they act more intelligently than any individuals, groups, or computers have ever done before?” is very relevant for our discussion. The solutions proposed for their Climate Collaboratorium with the use of the Internet forum and goals to be achieved are definitely in-line with our efforts and are in their spirit very similar to our approach.

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A very important aspect of the system proposed in this paper is its support for a discussion in the group. A longterm goal is here to “understand” the discussion and to automatically build profiles of the experts, notably with respect to their preferences concerning options. This calls for appropriate models of the discussion and falls in the domain of the theory of argumentation, cf. e.g. [8–10]. The first step in this direction is via imposing some structure on the discussion. The idea of documenting and supporting discussion using some automatic means has a long history [8, 11]. An interesting line of research concerns here an automatic generation of arguments on the basis of agent preferences. For example, Carenini and Moore [12] consider a problem of generating argumentation assuming the user’s preferences modeled in the framework of the multi-attribute utility theory. Their work, belonging to the natural language generation (NLG) domain, is readily applicable for our purposes. Each participant of the group is provided with a template of the argument – based on his or her profile. At the early stages of the discussion such a profile is usually coarse and suggested templates are abstract. An interaction with the system helps build up and enrich the profile and at the later stages suggested templates are getting more precise and complete. Such a structuring of the discussion makes possible its automatic analysis, both for the purposes of the on-going session as well as for the later analysis useful for the internal knowledge management in the organization, in particular, for supporting similar decision making sessions in the future. On the other hand a very important, somehow inverse, problem concerns the analysis of unstructured records of the discussions. Such records may be available in the form of, e.g., the electronic discussion fora logs, news groups archives, etc., both, on the intranet and Internet. Then, in the process of opinion mining [13], known also as the sentiment analysis, the opinions – possibly also the arguments – and their statistics concerning the issues in question may be automatically learnt. This may be extremely helpful for running the discussions on related topics. This is very important because the approaches, methods, algorithms, implementations, etc. developed should be portable and easily reusable to reduce costs and efforts. Opinion mining may be seen as a measure against the information overload. Another useful tool for this purpose is text summarization [14] and information extraction [15]. The former makes it possible to skim through a collection of textual documents potentially relevant for the decision problem under consideration. Automatically generated summaries help the user get quickly acquainted with the content of documents and study in-depth only those most relevant. On the other hand, information extraction makes it possible to extract a specific information that is relevant for a particular decision making problem. For example, the prices of some equipment may be automatically collected from the Internet in order to compare them with those currently considered. A closely related concept of a recommendation system (or recommender), notably of collaborative filtering [16, 17], plays a role in our approach. First of all this paradigm is applied in its “native mode” to enhance the search experience of the group members when looking for some additional sources of information. Furthermore the same paradigm may be used when suggesting changes in the preferences of the group members. All the above mentioned research areas contribute to the proposed architecture of the consensus reaching support system. However the main role play here a few concepts of the theory of decision making which are discussed in the next section.

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3 The core of the system – preferences and consensus modeling 3.1 The basic setting The primary goal of the system we propose here is to support a group of individuals (experts, decision makers, agents, . . . ) in reaching consensus concerning their preferences as to the set of alternatives (options). Thus we assume a discussion as a very important component of the group decision making process which makes it possible to confront the preferences of the individuals, to argue for them and eventually trigger their modifications and/or changes. In our previous work [3, 18–22] we concentrated on the representation of preferences, their acquisition, aggregation and finally on some guidance for the group as to the possible, most fruitful ways of the discussion continuation. Now our main goal is to envisage an information- and knowledge-rich environment within which the discussion in the group will proceed. In what follows we briefly remind the key points of our previous works. Some new elements are introduced which make the representation of preferences more intuitive for an individual and more in line with the modeling principles of argumentation theory. Then, an architecture of the proposed system is presented and discussed in Section 4. Formally, we consider the following setting for the core group decision making process. There is a set of N ≥ 2 alternatives, S = {s1 , . . . , sN }, and a set of M ≥ 2 individuals, E = {e1 , . . . , eM }. This model may be further extended considering, e.g., relevance degrees of the alternatives and the importance weights of the individuals. In the simplest case each individual em ∈ E expresses his or her preferences in the form of an individual fuzzy preference relation Rm in S × S. Thus Rm is a fuzzy set in S × S and its membership function µRm may be given such an interpretation that µRm (si , sj ) > 0.5 denotes the preference degree of an alternative si over an alternative sj and it is understood that the higher is this degree the stronger is this preference. Inversely, µRm (si , sj ) < 0.5 denotes the preference degree of an alternative sj over an alternative si and it is understood that the lower is this degree the stronger is this preference. Finally, µRm (si , sj ) = 0.5 denotes the indifference between alternatives si and sj . In fact we will usually assume the reciprocity of the relation Rm , i.e., that µRm (si , sj ) + µRm (sj , si ) = 1

(1)

holds. Thus, the membership function µRm (si , sj ) has to be specified only for i < j. Usually the degrees of preferences are assumed to be expressed as the numbers from the interval [0, 1]. However some more general approaches are possible where, e.g., the degrees are just elements of an ordered set. In particular, these elements may be assigned some linguistic labels such as ‘strong’ (preference), ‘medium’ (preference) etc. – for more information see, e.g., [4, 23, 24, 20] Here we propose two extensions to the previous setting: – a different view of the alternatives that is more suitable for the discussion, and – a more sophisticated representation of the individual preferences.

3.2 A hierarchical representation of the alternatives In our previous foundational approach an alternative is treated as an atomic entity (in the later work [20] we consider a set of criteria to characterize the alternatives).

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Now we adopt the modeling approach postulated by some authors [13] in the domain of the opinion mining (a somehow similar approach, albeit formally specified in the framework of the multi-attribute utility theory, is proposed in [12]). Thus an alternative si ∈ S is assumed to represent an object, composed of a set of components and a set of attributes. Each component may be further composed of components and posses its own set of attributes. Thus an alternative has a hierarchical structure and maybe expressed as a pair: s : (Ts , As ) (2) where Ts is a hierarchy of components and As is a set of values of the attributes. Let us consider the following example which will be used throughout the paper. The decision problem consists in choosing a car for a taxi corporation. The set S is then composed of various models of cars available on the market, or in a more realistic scenario, of offers submitted by a number of car dealers. A car offer may be seen as composed of two main parts: the car itself and details of the deal. The former in turn is composed of specifications of the engine and the body, and may be characterized as a whole by such attributes as the weight, width, color, etc. The details of the deal may be further decomposed into the financial part and the servicing conditions offered, and so on. Of course, a specific decomposition of an object (alternative) into components will depend on the decision problem under consideration. All the aspects that are relevant for the decision making problem should be taken into account and appropriately reflected in a model of the alternative. In the proposed approach we assume that the structure of the alternatives will be represented as a part of the domain ontology - see Section 4.2.2 for the details and for an excerpt of the OWL ontology which illustrates the above example of the decomposition of an alternative. Such a structured view of an alternative is very useful for the justification of the individual preferences; cf. Section 4.2.1.

3.3 Extended fuzzy preference relations A distinguishing feature of the consensus reaching process is the central role of a discussion. In the framework of our system we propose a set of tools to support it. In particular we adopt some basic modeling principles elaborated in the framework of argumentation theory as described in a more detailed way in Section 4.2.1. This may be very briefly summarized as that it boils down to the justification of individual preferences taking the form of the pro and con arguments articulated by the individuals. On a more abstract level it may be seen as an example of bipolar information, which recently has become a subject of an intensive research. Among the approaches to the modeling of bipolarity an important role plays the theory of so-called Atanassov’s intuitionistic fuzzy sets [25], which will be in the sequel, for brevity, referred to as IF-sets. A concept of an IF-set X is similar to that of a fuzzy set, but instead of just a membership function µX also a non-membership function νX is introduced. The rationale behind that is such that for a given element x the whole complement of its membership, i.e., 1 − µX (x) does not necessarily have to be interpreted as the nonmembership degree. Thus both degrees are treated as independent to some extent, but the following consistency condition is imposed: µX (x) + νX (x) ≤ 1

(3)

6 IF In our approach we propose to use an IF preference relation Rm to represent the individual em preferences instead of the ‘regular’ fuzzy preference relation. Thus along with the membership function µRm IF (si , sj ), which preserves its previous meaning, the non-membership function νRm IF (si , sj ) is defined. The latter may be interpreted as the degree to which the alternative si is not preferred to the alternative sj . Simplifying things, and assuming a counterpart of the reciprocity condition (1), this in turn may be interpreted as the intensity of the preference of sj over si . Such an interpretation imposes the obvious consistency condition:

µRm IF (si , sj ) = νRIF (sj , si ) m

(4)

This representation is more flexible than the one with the ‘regular’ fuzzy preference relation as an individual has more freedom (constrained by the consistency condition (3)) in expressing his or her preference for a pair of alternatives si and sj . In what follows we will often omit the superscript IF in µRm IF . For more details on the IF preference relations and their use in group decision making and consensus reaching, cf. Szmidt and Kacprzyk [26–29]. The use of IF preference relation may be motivated by the following scenario. Let us assume that an individual has in mind a set of criteria C while comparing the m+ alternatives. Let us denote by Cij the number of criteria better satisfied (in the m= opinion of individual em ) by alternative si than by alternative sj , and by Cij – the number of criteria equally well satisfied by alternative si and by alternative sj . This IF naturally gives rise to an IF preference relation Rm , specified in the following way: µRm IF (si , sj ) = νRm IF (si , sj ) =

m+ Cij

K m+ Cji

K

(5) (6)

where K is the total number of criteria, i.e. K=card(C). Obviously, the actual values of both the membership and non-membership functions may be defined in a slightly different way (e.g., taking also into account the weights of the criteria). Anyway, the IF preference relations make it possible to represent the fact that there may be criteria indicating the outranking of one of the compared alternatives, but there may also be criteria inconclusive in this respect and this should be taken into account in an appropriate way. A further rationale for the use of the IF preference relations will be given in Section 4.2. One can also refer to abstention in the voting context as a convenient rationale for introducing an IF representation as mentioned in Dubois et al. [30]. Formulas (5)-(6) provide a semantics for the degrees assigned to statements about preferences concerning particular pairs of alternatives. In order to extend this semantics to a more complex statements, with accordance to the definitions of logical connectives in IF logic, an approach similar to the acceptability semantics proposed by Paris [31] may be employed.

3.4 Consensus measuring and supporting the consensus reaching process In our previous work [32, 3, 18] we focused on the issue of obtaining consensus among the individuals as to their preferences concerning the alternatives, expressed via individual fuzzy preference relations. The starting point of this research was an observation

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that the traditional understanding of the consensus as an unanimous agreement is not applicable for this scenario: one cannot expect the total agreement regarding preferences on all pairs of alternatives under consideration. Moreover, such a total agreement is usually not needed. Thus we introduced a new definition of the consensus, based on the concept of the fuzzy (soft) majority. A natural manifestations of such a “soft” majority are the so-called linguistic quantifiers as, e.g., “most”, “almost all”, “much more than a half”, etc. Such linguistic quantifiers can be, fortunately enough, dealt with by fuzzy-logic-based calculi of linguistically quantified statements as proposed by Zadeh [33]. The new degree of consensus proposed in our previous work can be equal to 1, which stands for full consensus, when, e.g., “most of the important individuals agree as to almost all relevant alternatives”. The emphasized elements of this definition of consensus are modeled using fuzzy logic concepts; for details see, e.g., [3]. The relevance of alternatives is assumed to be given as a fuzzy set B defined in the set of alternatives S such that µB (si ) ∈ [0, 1] is a degree of relevance of alternative si , from 0 for fully irrelevant to 1 for fully relevant, through all intermediate values. The relevance bij of a pair of alternatives, (si , sj ) ∈ S × S, may be defined, as bB ij =

1 [µ (si ) + µB (sj )] 2 B

(7)

B B which is clearly the most straightforward option; evidently, bB ij = bji , and bii do not matter; for each i, j. And analogously, the importance of individuals, I, is defined as a fuzzy set in the set of individuals E such that µI (em ) ∈ [0, 1] is a degree of importance of individual em , from 0 for fully unimportant to 1 for fully important, through all intermediate values. Then, the importance bImn of a pair of individuals, (em , en ) ∈ E × E, may be defined in various ways, e.g., analogously as (7), i.e.

bImn =

1 [µ (em ) + µI (en )] 2 I

(8)

Then the degree of consensus is derived on several levels: 1. first, for each pair of individuals (em , en ) and each pair of alternatives (si , sj ) a degree of agreement vij (m, n) is derived; it is, in general, computed as a function Aggrm of two arguments (µRm (si , sj ), µRn (si , sj )) and can take different forms provided that Aggrm(x, x) = 1 and Aggrm(0, 1) = Aggrm(1, 0) = 0 and the monotonicity of Aggrm(x, y) with respect to | x − y | is preserved; it may be exemplified by: vij (m, n) = Aggrm(µRm (si , sj ), µRn (si , sj )) =  1 if µRm (si , sj ) = µRn (si , sj ) = 0 otherwise

(9)

B 2. second, for each pair of individuals (em , en ) a degree of agreement vQ (m, n) as to 1 their preferences between Q1 (a linguistic quantifier as, e.g., “most”, “almost all”, “much more than 50%”, . . . ) pairs of relevant alternatives is derived as: B vQ (m, n) 1

PN −1 Pn = µQ1 (

i=1

B j=i+1 [vij (m, n) ∧ bij ] ) PN −1 PN B i=1 j=i+1 bij

(10)

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3. third, these degrees are aggregated to obtain a degree of agreement con(Q1 , Q2 , I, B) of Q2 (a linguistic quantifier similar to Q1 ) pairs of important individuals as to their preferences between Q1 pairs of relevant alternatives, and this is meant to be the degree of consensus sought: con(Q1 , Q2 , I, B) =

2 M (M − 1)

PM −1 PM m=1

B I n=m+1 [vQ1 (m, n) ∧ bm,n ] PM −1 PM I n=m+1 bm,n m=1

(11)

If we replace the fuzzy preference relations by the IF preference relations then, basically, it is enough to adjust step 1. given above. Now the agreement between the preferences of a pair of individuals (em , en ) with respect to a pair of alternatives (si , sj ) becomes a function of four arguments: vij (m, n) = Aggrm(µRm IF (si , sj ), νRIF (si , sj ), µRIF (si , sj ), νRIF (si , sj )) m n n

(12)

Some monotonicity and marginal conditions, similar to those indicated for the case of the fuzzy preference relation, should be imposed on the form of the function Aggrm. The use of the hierarchical representation of the alternatives (cf. Section 3.2) does not necessarily require change in the way the consensus is measured. Namely, as it is mentioned in Section 4.2, the preferences are basically still expressed with respect to the pairs of alternatives treated as atomic entities. However another approach, taking into account a more complicated, hierarchical structure of the alternatives is possible. For example, the individuals comparing a pair of alternatives may be requested to express their preferences with respect to all their components and attributes values; cf. (2). Then the system may proceed in the spirit of the approach proposed in [12] in the context of the multi-attribute utility theory. Finally, depending on the nature of the decision problem in question, the individual preferences may be seen as a step to arrive at a solution of the decision making problem. Namely, if the goal of the decision making process is the selection of the best alternative then it is not that much important if the individuals differ in their preferences concerning the alternatives which definitely not qualify as the best according to some choice rationality assumed. Thus, generally one may consider some (fuzzy) choice sets [22] induced by particular individual fuzzy preference relations and check their consistency. This gives another measure of consensus in the group. The use of these consensus measures gives the general assessment of the current agreement in the group. What is needed now is an advice on how to proceed with the discussion in order to get closer to consensus in case it has not been reached yet. The very general approach is based in identifying these elements (alternatives, individuals) which make the corresponding consensus measures low. We have proposed some solutions in this respect in our previous work [18, 34]. Also other researchers proposed a number of interesting discussion guidance approaches, notably HerreraViedma et al. [35, 23]. A general scheme of the consensus reaching process, as it was meant in our previous work and is a starting point of this work, is presented in Fig. 1. Research on the consensus reaching process carried out along the lines sketched above and documented in our (and other researchers’) previous papers does not take into account neither the “information environment” in which the process is proceeding nor the needs for a more active support for the structuring of discussion in the group. The aim of this paper is to complete our previous work in this respect.

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Setting the agenda

Discussion

Preference expression

Group preference

Degree of agreement Yes Consensus ?

End of the session

No Feedback information for individuals

Fig. 1 The overall structure of the consensus reaching support system: a starting point

4 An overall structure of the system Let us start with a clarification of the adopted terminology and by reminding the previously introduced notation; cf. Section 3. We consider a group of individuals E dealing with a decision problem. A set S of the alternatives (decisions) is assumed and the goal is to arrive at an agreement (consensus) as to the preferences concerning the pairs of these alternatives. The time frame in which the preferences have to be agreed upon will be referred to as a session. This is a fairly abstract definition of the problem which may fit many different practical scenarios. We do not explicitly assume that the session takes place during one physical meeting of the individuals. On the other hand for some of the proposed measures such a meeting may be the most favorable arrangement. Anyway, what we are looking for is a computer-based system, which makes arriving at the consensus easier. The overall structure of the system is depicted in Fig. 2. Thus, its core is still composed of the preference elicitation and consensus measurement modules. However, the striking difference with respect to Fig. 1, is the fact that the discussion in the group is not anymore treated as a black box and, moreover, that the external information sources are now treated as part of the system. Now we will describe the subsequent boxes shown in Fig. 2. We will focus on the actions undertaken as well as input and output related to each box. Particular actions will be discussed in the context of specific boxes but it will be done so just for the sake of clarity. Some of the actions will be possibly continuously undertaken during the whole session.

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Setting the agenda domOnt ontology

Internet and intranet

consOnt ontology

Discussion

si sj? Collaborative filtering

YES

NO

Arg1

Arg1

Arg2

Arg2 Arg3

Databases

Arg4

NLG

…...

IF preference relations …………...

Consensus?

Yes

End of the session

No Feedback information for individuals

Fig. 2 The structure of the new proposed system

4.1 Setting the agenda This is the first stage of the consensus reaching process which boils down to the definition of the decision making problem. This definition may be improved during the course of the session but we will relate this task mainly to the first stage. It may be worthwhile to organize the first, separate meeting devoted to this purpose as the adopted

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definition may require gathering more data, e.g., in order to completely characterize the alternatives. For example, referring to our example in Section 3.2, the group may decide to consider some features of the cars which were not specified in the currently submitted car offers. It may also be reasonable to organize such a meeting before a tender for the car offers is prepared. This however depends on the intricacies of the decision making process in a given organization. The proposed model of the system is a bit more abstract and should cover many different practical scenarios. The main output of this step is the set of alternatives S. There are also other important elements as, e.g., determining the objectives of the decision process, which at the moment will not be formalized in the framework of the proposed system. An alternative is assumed to have a hierarchical structure which is discussed in section 3.2 and defined on the abstract level in the consOnt ontology; cf. p. 4.2.1. A substantiation of this structure forms a core part of the domain ontology, which will be referred to as domOnt in what follows. An example of such an ontology is shown in Fig. 3 and it is described in more detail in Section 4.2.2. The process of the construction of such an ontology provides a great opportunity for the clarification of particular aspects of the decision problem at hand. In fact agreeing on the meaning and structure of the alternatives components may make an essential contribution also to the consensus of the group with respect to their preferences, and at least makes the discussion of the preferences more focused and effective.

Fig. 3 An example of the domOnt ontology. Only classes are shown. Classes whose names are dimmed are imported from the consOnt ontology; cf. Section 4.2.1

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The domOnt ontology does not have to be limited to the representation of structure of the alternative. Some additional concepts and properties may be added and, in general, this ontology should be seen as a part of the more comprehensive domain ontology. In fact the construction of the ontology requires consensus of its own: consensus on the particular components and attributes, or more generally, on the concepts and properties. In the literature there are some known approaches to the support of the consensual construction of ontologies; cf., e.g., [36], which will be adapted in the framework of our system during its further development.

4.2 The discussion 4.2.1 A model of the discussion The discussion is meant as a way to clarify and unify the preferences of the individuals as to the pairs of the alternatives. A general scheme of the discussion is represented by the consOnt ontology shown in Fig. 4. It borrows common components from many approaches proposed in the framework of argumentation theory which in turn in their majority are based on the IBIS model [8]. The main classes1 of this ontology have the following interpretation: Alternative denotes the class (set) of the alternative decisions under consideration, i.e., the set S introduced in Section 3.1. An alternative may be related with the following subsequent classes: – via the property hasAttribute with the class AltAttribute representing the attributes of the alternatives and their components, – via the property hasComponent with the class AltComponent representing the components of an alternative and their subcomponents. Thus this part of the ontology represents a hierarchical structure of the alternatives, described in Section 3.2. Individuals denotes the class (set) of the individuals participating in the decision making, i.e., the set E introduced in Section 3.1. The individuals are supposed to submit some arguments concerning their preferences with respect to the pairs of alternatives. In particular, the individuals may be authors of arguments (via property isAuthorOf) or may just support arguments submitted by other individuals (via property endorses). Preference is a class of preferences with respect to a pair of alternatives. An instance of this class is linked with properties firstAlternative and secondAlternative to alternatives and is assumed to express the preference for the former alternative over the latter. Argument is a class representing arguments submitted by the particular individuals to justify or challenge the preference for one alternative over another. There are two subclasses representing the pro and con arguments, respectively. The arguments have an internal structure which is described in section 4.2.3. 1 Referring to the ontologies we adopt the terminology used by the OWL language specification (http://www.w3.org/TR/owl-ref/).

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Fig. 4 The consOnt ontology defining main concepts of the consensus reaching process (some properties are hidden for clarity of the picture)

4.2.2 A domain ontology The most important structures underlying the support of the discussion are the ontologies consOnt and domOnt. The former has been described in the previous section 4.2.1. Now we will briefly describe the latter. A very simple example of the domOnt ontology for our car offer selection decision problem (cf. Section 3.2) is shown in Fig. 3. As mentioned earlier (cf. Section 4.1) the main part of this ontology is devoted to the substantiation of the structure of the alternatives. The domOnt ontology imports (in the sense of the OWL language) the consOnt ontology. The latter already contains the following basic classes representing the alternatives on the abstract level: Alternative, AltComponent and AltAttribute. In the exemplification of the domOnt ontology, shown in Fig. 3, the specific class of alternatives CarOffer is defined which is subsumed by the class Alternative. Similarly, for instance, the subclasses Car, CarBody, Engine and Financing are subsumed by the class AltComponent, while the classes Power and FuelConsumption are subsumed by the class AltAttribute. The separation of the domain ontology (domOnt) and the ontology describing the adopted consensus reaching process model (consOnt) provides the necessary flexibility. However, in case of the domOnt ontology it requires some extra efforts in order to properly represent the intended semantics. For example, it is not immediately visible in Fig. 3 that the class CarOffer, on the one hand, and the classes Car and Financing

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are somehow related. This link is expressed by the following definition (in the sense of the OWL-Plugin for the Protege software [37]; ) of the CarOffer class: Alternative AND (hasComponent SOME Car) AND (hasComponent SOME Financing) AND hasComponent EXACTLY 2 Similar definitions are used for other classes, including Car, CarBody and Engine. In the latter case we need to relate this class with the class Power, representing this time an attribute of the alternative’s component rather than a component. 4.2.3 The generation of arguments In our previous model (cf. Fig. 1) the discussion in the group was treated as a black box. It was assumed to be stimulated by the discrepancy of the preferences of the individuals and to result in the changes of these preferences. In the current approach we want to grasp and exploit actual arguments used during the discussion. Thus the arguments have to be represented in a machine-readable form. Getting such a representation is not a trivial task. The two following extreme approaches may be adopted. The first one assumes the discussion to be carried out “as usual”, i.e., mostly using a spoken natural language, blackboard, etc., and is recorded using cameras and microphones; cf. e.g. [38, 39]. Then, the most ambitious approach is to automatically obtain a semantic representation of the discussion. Thus there is virtually no additional burden put on the individuals attending the session but the later transformation step is a real challenge. In the second extreme case the individuals participate in the discussion using highly formalized written messages. This approach makes the machine-readable representation immediately available but imposes essential constraints on the discussion. We follow this second approach accepting that part of the discussion will have an informal character and will not be reflected in the representation used by the system. On the other hand the aim is to provide the individuals with a fairly simple user interface making it possible to express their arguments in the twofold form, readable for both the humans and the machine. The above mentioned interface is depicted in Fig. 2 as “NLG”, as what is accomplished here is an example of the natural language generation (NLG) task. The proposed system supports the generation of arguments in the form of natural language expressions called comparatives [40, 41]. In [40] they are defined as: “Comparative constructions are used to express explicit orderings between two objects with respect to the degree or amount to which they possess some gradable property.” We use a practical characterization of this constructions, similar to the one proposed in [41], and define it as follows. A comparative is composed of: – a feature with respect to which the comparison is expressed; by a feature a component or an attribute of an alternative is meant, e.g., “power of an engine”; cf. Section 3.2 and Fig. 3, – a word expressing the relation (comparison), e.g., “much greater than”, Correspondingly the comparatives are represented in the consOnt ontology by the class Comparative, linked:

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– via the property refersToFeature with the classes AltComponent and AltAttribute, – via the property usesWord with the class RelationWord. The instances of the Argument class are assumed to be characterized by instances of the following classes, via appropriate properties: – Preference via the property concerns, indicating that the argument supports (in case it belongs to the subclass Pro) or challenges (in case it belongs to the subclass Con) the preference expressed by the given instance of the Preference class, – Comparative via the property usesComparative, representing the internal structure of the argument, as described above, – Individual, as described in p. 4.2.1, pointing out an individual being the author of the argument or supporting it, – Document via the property supportedByDoc, pointing out a document (or an excerpt of thereof) supporting the claims of the argument; cf. Section 4.5 for more details. It is worth noticing that an argument may be composed of several comparatives. For example, the higher power of an engine alone may be an argument not strong enough for preferring one car against another, but coupled, e.g., with a lower fuel consumption may form a convincing argument. Thus the generation of arguments is based on the domOnt and the consOnt ontologies. Submitting an argument may be seen as creating an instance of the class Argument in the domOnt ontology. It is illustrated using the Protege system2 interface in Fig. 5. Thanks to that a machine-readable representation of the arguments is immediately available. It is then translated to a more human-readable form using, e.g., the approaches discussed in [42, 43].

4.3 Expression of the preferences and consensus measurement After the discussion the individuals are requested to express their preferences. As mentioned in Section 3 they are assumed to express them in the form of IF preference relation. An appropriate user interface makes elicitation of the preferences easy. It should be noted that the individuals may use just one membership function, i.e., express a fuzzy preference relation, or even just a regular binary preference relation. They are special cases of an IF preference relation, thus the same elicitation and representation techniques may be applied. This flexibility of the proposed preference representation is very important from the practical point of view. Namely, the user may use as much sophisticated representation (but requiring more data) as he or she finds necessary (and possible). On the other hand he or she may limit the range of entered data to just these pairs of alternatives for which he or she has a clear preference. The remaining pairs will be treated as indifferent, by default. Clearly, the more sophisticated preference representations may pose some difficulties for some users, notably the novice and less experience ones, but they may be very useful in many cases of more complex real-world decision making settings. The consensus degree is computed using the formulas (12) and (10)–(11). The explicit representation of arguments used in the discussion (cf. p. 4.2) provides some rationale for the distinguishing of importance/relevance degrees of the particular individuals and alternatives; cf. Section. 3.1, formulas (7) and (8). Namely the 2

http://protege.stanford.edu

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Fig. 5 Submitting an argument via creating an instance of the Argument class

individuals may be rated according to their activity during the discussion, measured by the number of arguments they submitted (the activity component of importance) and, in particular, by the number of their arguments endorsed by other individuals (the authority component); cf. the endorses property in the consOnt ontology, Fig. 4. Similarly, the relevance of the alternatives may be measured using the number of arguments used to support preferences concerning them. In particular, the intensity of the arguments over the time may be a good indicator of such an importance. For some details of a possible formalization of these notions see, e.g., [44, 45], where a measure of the usefulness of agents and their statements is considered (the context is slightly different but the general idea is readily applicable for our purposes). If a satisfactory consensus has been obtained the session ends and its results are comprised of: – individual preference relations with added informativeness provided by the use of the IF sets theory, – a group preference relation and/or some group choice set derived on request using some known group decision making techniques on the set of individual preference relations [21, 22]; it is worth noting that these techniques may be further developed to take into account all information available, which is concisely represented in the domOnt ontology (provided the preferences itself are represented there, too); – the domOnt ontology which best represents the general view on the very definition of the decision problem

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Otherwise another round of the discussion is arranged, and some hints are generated by the system in order to help run the session effectively and efficiently.

4.4 Feedback information generation In our previous model [3] and some models of other researchers [4, 23, 35] information generated by the system is derived solely on the basis of individual preference relations. Basically, the guiding of the discussion boils down there to the computation of values of a consensus measure and to checking if it grows or diminishes. Now we envisage more options. The system confronts the individual preference relations and the lists of arguments submitted by the individuals during the session. If there is a high discrepancy in preferences concerning a given pair of alternatives s1 and s2 (computed using, e.g., a formula similar to (10), but by aggregating over the pairs of individuals instead of over the pairs of alternatives), then the system may undertake a more or less deep analysis of the arguments. Thanks to the explicit semantics of the arguments some key components and attributes of the alternatives may be identified, which play an important role in the disagreement. Some natural rules for generating recommendations for further discussion concerning a pair of alternatives s1 and s2 may be exemplified by the following: – lack of arguments: if individual em expresses strong preference for one of the alternatives (i.e., µRM (s1 , s2 ) given by this individual is close to 1 while νRM (s1 , s2 ) is close to 0; cf. Section 3.3) and has not submitted any arguments should be invited to do so, – inconsistency: if individual ek clearly prefers s1 to s2 , i.e., µRk (s1 , s2 ) ≥ α > 0.5 while νRk (s1 , s2 ) = 0 and submitted only arguments against the preference of s1 over s2 , then he or she should be invited to revise either the preferences or the arguments; many more different types of preferences apparently inconsistent with the arguments may be identified and used to guide the discussion, – different focus: if the arguments pro focus on a subset of features (components or attributes) of the alternative s1 and the arguments con focus on a disjoint subset of features then encourage the individuals to discuss the relative importance of the features and their interplay. This are just a few examples of the possible rules which illustrate the essentially higher capacity of the proposed new model in terms of generating valuable feedback information. Another form of an automatic feedback information generation refers to the concept of the collaborative filtering and is briefly described below.

4.5 Information sources and collaborative filtering In our model of the consensus reaching process external information sources play an important role. First of all textual documents available on the Internet or the intranet may be very relevant for the decision problem in question. They can provide information decisive for the individuals preferences. For example opinion that recent models of the Ford cars are overpriced, found on an Internet website considered by given individual to be reliable, may convince that individual to oppose to offers related to this car make.

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Thus in our model we assume that the arguments in the discussion may be supported by the documents or their snippets; cf. Section 4.2.3. In order to make the flow of information more efficient we propose to exploit the technique of the collaborative filtering [16]. Some documents which have been found relevant by other individuals of similar profiles are suggested to the individuals looking for documents. The profile of an individual is here primarily identified with his or her IF preference relation expressed on the set of the alternatives. The equation (10) is used to determine the similarity of two individuals. Actually two strategies may be employed: – either an individual is suggested the documents found relevant by individuals of a similar profile, – or the documents found relevant by individuals of a different profile. The former strategy may help in case the preferences are very dispersed. The access to the identical information may bring closer the preferences of the individuals of a somehow similar profile. The latter strategy may help soften the difference between individuals holding strongly opposing preferences. Moreover the individuals are encouraged to tag the documents (and/or their snippets) which they find relevant for the decision problem under consideration. The tags may indicate the relevance with respect to an alternative, its component or attribute. Thanks to the tagging other individuals may quickly find relevant documents. Moreover such a markup contributes to building extended profiles of individuals that may be used for the collaborative filtering. Such a folksonomy of tags may well complement and help further develop a domain ontology domOnt. Another important source of information are databases gathering data relevant for the decision problem in question. In this case, in addition to the regular tools for database querying, an interesting technique may be the use of the linguistic summaries of data advocated by the authors [46, 47]. They make it possible to characterize a large set of data in a concise way using a natural-language-like expression. For example, let us assume that the individuals have an access to the detailed data on the service history of many cars used recently by given company and its branches. Then a linguistic summary of the type: “Most high cubic capacity cars are very expensive in the maintenance” may convince an individual to prefer cars with medium capacity (if those of low capacity are excluded for some other reasons). Moreover, such a linguistic summary may be used as an argument while expressing the preferences. Formalization of this idea requires a further research.

5 Concluding remarks We have proposed a new concept of the consensus reaching process support system. Its characteristic features are the use of flexible preference representation, explicit knowledge representation component (ontology) used throughout the whole process, and combination of intelligent textual information and database retrieval support. The ultimate goal of our research is the implementation of an advanced Web-based group decision support system with a special emphasis on supporting the consensus reaching process. Here we present some design assumptions which show the novelty of our approach, notably in comparison to earlier similar works, cf., e.g.[3, 23, 18]. We

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show new vistas of employing various Web related techniques in the framework of a group decision making system. We have proposed some novel means: – to integrate the support for the information seeking the rest of the group decision making system, – to formalize the discussion in order to make it automatically interpretable and at the same time convenient for the users to engage in, – to account for the knowledge concerning the domain of the decision problem under consideration and decision making as such, – to evaluate the consensus and to guide the session in such an information richer environment. The novelty of the proposed approach is basically the central role the preference relations and ontologies play in it. It is an open question how it can be combined with more traditional problem representation, structuring [48] and visualization techniques and systems such as Compendium [9], bCisive3 , Araucaria [49] etc. The role of the ontologies envisaged in the paper, as well as still to be explored, in the framework of systems considered here is very broad and comprises: – providing an opportunity to formalize the knowledge of the group regarding the domain of the decision problem and to alleviate the cognitive barriers for reaching the consensus (assuming it is jointly constructed/extended, or at least discussed by the group of individuals). – the support for the argumentation and expression of the preferences by the individuals; both ontologies combined serve as a source of templates for the generation of arguments during the discussion, – providing an opportunity to analyse consensus on several levels of abstraction; for instance it may be the case that there is no consensus as to the choice of a particular car but there is consensus that French cars are preferred (referring to our decision problem example of section 3.2), – the support for the search for additional information (ontology-based information retrieval). What concerns the preferences, the system proposed makes it possible to use both the traditional fuzzy preferences and some new types of extended fuzzy preferences, notably the IF fuzzy preferences that may be viewed as a convenient tool to deal with bipolar type information in the context of preferences. One should clearly bear in mind that the IF fuzzy preferences offer a greater flexibility and a possibility to express more adequately a human opinion on preferences in a more sophisticated real-world setting. However, their semantics and elicitation is clearly more difficult to grasp and perform than in the case of traditional fuzzy preferences. It seems that such a synergistic combination of tools that are characteristic for the area of group decision making and consensus formation, and new tools of modern knowledge engineering and information technology proposed in this paper will provide a new quality. This will help develop an advanced, human-centric and human-consistent computer system for supporting consensus reaching which will use the strength of the human and the computer to solve a relevant problem. 3

http://bcisive.austhink.com/

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Acknowledgment This work was partially supported by the Ministry of Science and Higher Education under Grant N N519 404734. This work was conducted using the Prot´eg´e resource, which is supported by grant LM007885 from the United States National Library of Medicine.

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