《电子商务 E-business》阅读文献：Multi-Criteria Recommender Systems

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2 Gediminas Adomavicius, Nikos Manouselis, YoungOk Kwon or real numbers within a certain range [4]. It is assumed that this function is not known for the whole Users x Items space but is specified only on some subset of it. Therefore, in the context of recommendation, we want for each user u E Users to be able to(a) estimate(or approximate)the utility function R(u, i) for item iEItems for which R(u, i) is not yet known, and(b)choose one or a set of items i that will maximize R(u, i),i.e vu∈ Users,i= argeliers In most recommender systems, the utility function usually considers a single- criterion value, e.g., an overall evaluation or rating of an item by a user. In recent work, this assumption has been considered as limited [2, 4, 481, because the suit- ability of the recommended item for a particular user may depend on more than one utility-related aspect that the user takes into consideration when making the choice Particularly in systems where recommendations are based on the opinion of others, the incorporation of multiple criteria that can affect the users'opinions may lead to more accurate recommendations Thus, the additional information provided by multi-criteria ratings could help to improve the quality of recommendations because it would be able to represent more complex preferences of each user. As an illustration, consider the following example. In a traditional single-rating movie recommender system, user u provides a single rating for movie i that the user has seen, denoted by R(u, i). Specifically, suppose that the recommender system predicts the rating of the movie that the user has not seen based on the movie ratings of other users with similar preferences, who are commonly referred to as"neighbors"[72]. Therefore, the ability to correctly determine the users that are most similar to the target user is crucial in order to have accurate predictions or recommendations. For example, if two users u and w have seen three movies in common, and both of them rated their overall satisfaction from each of the three movies as 6 out of 10, the two users are considered as neighbors and the ratings of unseen movies for user u are predicted using the ratings of user In contrast, in a multi-criteria rating setting, users can provide ratings on multi- ple attributes of an item. For example, a two-criterion movie recommender system allows users to specify their preferences on two attributes of a movie(e.g, story and visual effects). A user may like the story, but dislike the visual effects of a movie e.g,R(u, i)=(9, 3). If we simply use two ratings with the same weight in making application might correspond to a variety of situations in multi-rating applicate. 14 recommendations, rating their overall satisfaction as 6 out of 10 in the single-rati (9, 3),(6, 6),(4, 8), etc. Therefore, although the ratings of the overall satisfaction are stated as 6, two users may show different rating patterns on each criterion of an Item, e.g,user ratings(9, 3),(9, 3),(9, 3), and user u gives ratings (, 9),(3, 9),(3, 9)to the same three movies. This additional information on each user's preferences would help to model users' preferences more accurately, and new recommendation techniques need to be developed to take advantage of this addi- tional information. The importance of studying multi-criteria recommender systems

2 Gediminas Adomavicius, Nikos Manouselis, YoungOk Kwon or real numbers within a certain range [4]. It is assumed that this function is not known for the whole Users×Items space but is specified only on some subset of it. Therefore, in the context of recommendation, we want for each user u ∈ Users to be able to (a) estimate (or approximate) the utility function R(u,i) for item i ∈ Items for which R(u,i) is not yet known, and (b) choose one or a set of items i that will maximize R(u,i), i.e., ∀u ∈ Users,i = arg max i∈Items R(u,i) (1) In most recommender systems, the utility function usually considers a singlecriterion value, e.g., an overall evaluation or rating of an item by a user. In recent work, this assumption has been considered as limited [2, 4, 48], because the suitability of the recommended item for a particular user may depend on more than one utility-related aspect that the user takes into consideration when making the choice. Particularly in systems where recommendations are based on the opinion of others, the incorporation of multiple criteria that can affect the users’ opinions may lead to more accurate recommendations. Thus, the additional information provided by multi-criteria ratings could help to improve the quality of recommendations because it would be able to represent more complex preferences of each user. As an illustration, consider the following example. In a traditional single-rating movie recommender system, user u provides a single rating for movie i that the user has seen, denoted by R(u,i). Specifically, suppose that the recommender system predicts the rating of the movie that the user has not seen based on the movie ratings of other users with similar preferences, who are commonly referred to as “neighbors” [72]. Therefore, the ability to correctly determine the users that are most similar to the target user is crucial in order to have accurate predictions or recommendations. For example, if two users u and u ′ have seen three movies in common, and both of them rated their overall satisfaction from each of the three movies as 6 out of 10, the two users are considered as neighbors and the ratings of unseen movies for user u are predicted using the ratings of user u ′ . In contrast, in a multi-criteria rating setting, users can provide ratings on multiple attributes of an item. For example, a two-criterion movie recommender system allows users to specify their preferences on two attributes of a movie (e.g., story and visual effects). A user may like the story, but dislike the visual effects of a movie, e.g., R(u,i) = (9, 3). If we simply use two ratings with the same weight in making recommendations, rating their overall satisfaction as 6 out of 10 in the single-rating application might correspond to a variety of situations in multi-rating application: (9, 3), (6, 6), (4, 8), etc. Therefore, although the ratings of the overall satisfaction are stated as 6, two users may show different rating patterns on each criterion of an item, e.g., user u gives ratings (9, 3), (9, 3), (9, 3), and user u ′ gives ratings (3, 9), (3, 9), (3, 9) to the same three movies. This additional information on each user’s preferences would help to model users’ preferences more accurately, and new recommendation techniques need to be developed to take advantage of this additional information. The importance of studying multi-criteria recommender systems

ender Systems has been highlighted as a separate strand in the recommender systems literature [2,4, 48], and recently several recommender systems(as we present later in this chapter) have been adopting multiple criteria ratings, instead of traditional single criterion ratings. Thus, the aim of this chapter is to provide an overview of systems that use multiple criteria to support recommendation(referred to as multi-criter recommender systems, with a particular emphasis on multi-criteria rating ones The remainder of this chapter is organized as follows. First, we overview the generic recommendation problem under the prism of multi-criteria decision making (MCDM), and demonstrate the potential of applying MCDM methods to facilitate recommendation in multi-criteria settings. Second, we focus on the particular type of multi-criteria recommender systems that use multi-criteria ratings, referred to multi-criteria rating recommenders because, while it has not been extensivel researched, this type of systems has significant potential for better recommendation performance. We survey the state of the art algorithms for this type of recommender systems. Finally, research challenges and future research directions in multi-criteria recommender systems are discussed 2 Recommendation as a Multi-Criteria Decision Making Problem In order to introduce multiple criteria in the generic recommendation problem,one of the classic MCDM methodologies can be followed. To facilitate the discussion on how MCDM methods and techniques can be used when developing a recommender system, we followed the steps and notations proposed by Bernard roy (one of the 1960s pioneers in MCDM methods) in the generic modeling methodology for de- cision making problems [78]. The discussion could also follow some other generic MCDM modeling methodologies[24, 34, 96, 98], since the scope of this section is to provide some initial insight into issues that recommender systems researchers should consider when designing a multi-criteria recommender Roys[78] methodology includes four steps when analyzing a decision making I. Defining the object of decision. That is, defining the set of alternatives(items) upon which the decision has to be made and the rationale of the recommendation decision 2. Defining a consistent family of criteria. That is, identifying and specifying a set of functions that declare the preferences of the decision maker(targeted user) upon the various alternatives. These should cover all the parameters affecting the recommendation decision and be exhaustive and non -redundant 3. Developing a global preference model. That is, defining the function that synthe- sizes the partial preferences upon each criterion into a model that specifies the total preference of a decision maker regarding a candidate alternative

Multi-Criteria Recommender Systems 3 has been highlighted as a separate strand in the recommender systems literature [2, 4, 48], and recently several recommender systems (as we present later in this chapter) have been adopting multiple criteria ratings, instead of traditional singlecriterion ratings. Thus, the aim of this chapter is to provide an overview of systems that use multiple criteria to support recommendation (referred to as multi-criteria recommender systems), with a particular emphasis on multi-criteria rating ones. The remainder of this chapter is organized as follows. First, we overview the generic recommendation problem under the prism of multi-criteria decision making (MCDM), and demonstrate the potential of applying MCDM methods to facilitate recommendation in multi-criteria settings. Second, we focus on the particular type of multi-criteria recommender systems that use multi-criteria ratings, referred to as multi-criteria rating recommenders because, while it has not been extensively researched, this type of systems has significant potential for better recommendation performance. We survey the state of the art algorithms for this type of recommender systems. Finally, research challenges and future research directions in multi-criteria recommender systems are discussed. 2 Recommendation as a Multi-Criteria Decision Making Problem In order to introduce multiple criteria in the generic recommendation problem, one of the classic MCDM methodologies can be followed. To facilitate the discussion on how MCDM methods and techniques can be used when developing a recommender system, we followed the steps and notations proposed by Bernard Roy (one of the 1960s pioneers in MCDM methods) in the generic modeling methodology for decision making problems [78]. The discussion could also follow some other generic MCDM modeling methodologies [24, 34, 96, 98], since the scope of this section is to provide some initial insight into issues that recommender systems researchers should consider when designing a multi-criteria recommender. Roy’s [78] methodology includes four steps when analyzing a decision making problem: 1. Defining the object of decision. That is, defining the set of alternatives (items) upon which the decision has to be made and the rationale of the recommendation decision. 2. Defining a consistent family of criteria. That is, identifying and specifying a set of functions that declare the preferences of the decision maker (targeted user) upon the various alternatives. These should cover all the parameters affecting the recommendation decision and be exhaustive and non-redundant. 3. Developing a global preference model. That is, defining the function that synthesizes the partial preferences upon each criterion into a model that specifies the total preference of a decision maker regarding a candidate alternative

Gediminas Adomavicius, Nikos Manouselis, YoungOk Kwon 4. Selection of the decision support process. This covers the design and develop- ment of the procedure, methods, or software systems that will support a decision maker when taking a decision about the set of alternatives(items), in accordance to the results of the previous steps We briefly review these steps in separate subsections below, and mention how each of them pertains to recommender systems 2.1 Object of Decision In recommender systems, the object of decision is item i that belongs to the set of all the candidate items. The elements of this set are referred to as alternatives or actions in related literature [30- To express the rationale behind the decision, Roy [78] refers to the notion of the decision"problematics. Four types of decision problematics are identified Choice. which concerns the selection of one or more alternatives that can be considered as more appropriate from all candidate ones Sorting, which refers to the classification of the alternatives into a number of pre-defined categories, Ranking, which involves ranking all the alternatives, from the best one to the worst Description, which concerns the description of each alternative in terms of how it performs upon each criterion All four types of decision problematics can be considered valid for the recom mendation problem Choosing and recommending one or more items as more suitable for a particular user Classifying (or sorting, as Roy defines it)all available items into pre-defined categories according to their suitability, e.g., into"recommended for purchase and"recommended for viewing items Ranking all available items from the most suitable to the least suitable ones for a particular user, and presenting a ranked list of recommendations to the user, Describing how suitable a particular item is for a specific user, based on how it is evaluated upon each criterion. It corresponds to a full analysis of the item perfor mance upon all criteria, illustrating the suitability of an item for the specific user ( that is, in a personalized manner that aims to help the user to make a selection)

4 Gediminas Adomavicius, Nikos Manouselis, YoungOk Kwon 4. Selection of the decision support process. This covers the design and development of the procedure, methods, or software systems that will support a decision maker when taking a decision about the set of alternatives (items), in accordance to the results of the previous steps. We briefly review these steps in separate subsections below, and mention how each of them pertains to recommender systems. 2.1 Object of Decision In recommender systems, the object of decision is item i that belongs to the set of all the candidate items. The elements of this set are referred to as alternatives or actions in related literature [30]. To express the rationale behind the decision, Roy [78] refers to the notion of the decision “problematics.” Four types of decision problematics are identified: • Choice, which concerns the selection of one or more alternatives that can be considered as more appropriate from all candidate ones; • Sorting, which refers to the classification of the alternatives into a number of pre-defined categories; • Ranking, which involves ranking all the alternatives, from the best one to the worst; • Description, which concerns the description of each alternative in terms of how it performs upon each criterion. All four types of decision problematics can be considered valid for the recommendation problem: • Choosing and recommending one or more items as more suitable for a particular user; • Classifying (or sorting, as Roy defines it) all available items into pre-defined categories according to their suitability, e.g., into “recommended for purchase” and “recommended for viewing” items; • Ranking all available items from the most suitable to the least suitable ones for a particular user, and presenting a ranked list of recommendations to the user; • Describing how suitable a particular item is for a specific user, based on how it is evaluated upon each criterion. It corresponds to a full analysis of the item performance upon all criteria, illustrating the suitability of an item for the specific user (that is, in a personalized manner that aims to help the user to make a selection)

2. 2 Family of criteria The performance of alternatives in set Items is analyzed upon a set of criteria for each user. in order to model all their characteristics attributes effects. or conse- quences [78, 98]. In recommender systems, the criteria may refer to the multiple features of an item(often the case in content-based recommendations or to the multiple dimensions upon which the item is being evaluated/rate Any criterion c can be represented by function gc(D) that expresses the preferences of one user(therefore is user-specific), in order for the user to be able to decide between two alternatives in and 12, i.e., whether ge(i1)>g(i2), in the case that alternative iI is preferred to alternative i2, or whether g(in)=g(i2), in the case that the two alternatives are considered equivalent (i.e, perfectly substitutable for the particular user on this criterion). To be able to make rational decisions using multiple criteria, it has to be ensured that the whole set of these functions creates a consistent family of criteria [78]. A family of criteria is said to be consistent when it has the following three properties 1. Monotonic: a family of criteria is monotonic only if, for each pair of alternatives iI and i2, for which gct(i1)>gc(i2) for one criterion cI and gd(i1)=gc(2)for every other criterion c* cl, it can be assumed that alternative in is preferred to 12 2. Exhaustive: a family of criteria is exhaustive only if, for each pair of alternative in and i2, for which gc(i1)=gc(i2)upon each criterion c, we can assume that in and i2 are equivalent 3. Non-redundant: a family of criteria is non-redundant only if the removal of any one of the criteria leads to the violation of one of the other two properties In the remainder of this chapter, unless explicitly specified otherwise, we will assume that we have a consistent family of k criteria, i.e., g1, g2,..., gk. The design of a consistent family of criteria for a given recommendation application has been largely ignored in the recommender systems literature and constitutes an interesting and important problem for future research. Four types of criteria are usually found in MCDM [30] Measurable, i.e., a criterion that allows its quantified measurement upon some evaluation scale Ordinal, i.e., a criterion that defines an ordered set of acceptable values that allow its evaluation using a qualitative or a descriptive scale Probabilistic, 1.e, a criterion that uses probability distributions to represent un- certainty in its evaluation; Fuccy, i.e., a criterion whose evaluation is represented in relation to its possibility to belong in one of the intervals of a qualitative or descriptive evaluation scale From a broad perspective, a family of criteria can be used to facilitate the rep resentation of user preferences in recommender systems as well. Therefore, we can

Multi-Criteria Recommender Systems 5 2.2 Family of Criteria The performance of alternatives in set Items is analyzed upon a set of criteria for each user, in order to model all their characteristics, attributes, effects, or consequences [78, 98]. In recommender systems, the criteria may refer to the multiple features of an item (often the case in content-based recommendations) or to the multiple dimensions upon which the item is being evaluated/rated. Any criterion c can be represented by function gc(i) that expresses the preferences of one user (therefore is user-specific), in order for the user to be able to decide between two alternatives i1 and i2, i.e., whether gc(i1) > gc(i2), in the case that alternative i1 is preferred to alternative i2, or whether gc(i1) = gc(i2), in the case that the two alternatives are considered equivalent (i.e., perfectly substitutable for the particular user on this criterion). To be able to make rational decisions using multiple criteria, it has to be ensured that the whole set of these functions creates a consistent family of criteria [78]. A family of criteria is said to be consistent when it has the following three properties: 1. Monotonic: a family of criteria is monotonic only if, for each pair of alternatives i1 and i2, for which gc1 (i1) > gc1 (i2) for one criterion c1 and gc(i1) = gc(i2) for every other criterion c 6= c1, it can be assumed that alternative i1 is preferred to alternative i2. 2. Exhaustive: a family of criteria is exhaustive only if, for each pair of alternatives i1 and i2, for which gc(i1) = gc(i2) upon each criterion c, we can assume that i1 and i2 are equivalent. 3. Non-redundant: a family of criteria is non-redundant only if the removal of any one of the criteria leads to the violation of one of the other two properties. In the remainder of this chapter, unless explicitly specified otherwise, we will assume that we have a consistent family of k criteria, i.e., g1, g2, . . . , gk . The design of a consistent family of criteria for a given recommendation application has been largely ignored in the recommender systems literature and constitutes an interesting and important problem for future research. Four types of criteria are usually found in MCDM [30]: • Measurable, i.e., a criterion that allows its quantified measurement upon some evaluation scale; • Ordinal, i.e., a criterion that defines an ordered set of acceptable values that allow its evaluation using a qualitative or a descriptive scale; • Probabilistic, i.e., a criterion that uses probability distributions to represent uncertainty in its evaluation; • Fuzzy, i.e., a criterion whose evaluation is represented in relation to its possibility to belong in one of the intervals of a qualitative or descriptive evaluation scale. From a broad perspective, a family of criteria can be used to facilitate the representation of user preferences in recommender systems as well. Therefore, we can

6 Gediminas Adomavicius, Nikos Manouselis, YoungOk Kwon assume that all types of criteria could be potentially engaged in multi-criteria rec- ommender systems, although(as shown later) it seems that some types are used in currently developed systems more often than others 2.3 Global Preference Model The development of a global preference model provides a way to aggregate the values of each criterion ge(where c= l,..., k) in order to express the preferences between the different alternatives of the set Items, depending on the selected deci- sion problematics In the MCDM literature, a number of methodologies have been developed, which can be classified in different categories according to the form of global preference model that they use and the process of creating this model According to[30] and [641, the following categories of global preference modeling approaches can be identified Value-Focused models, where a value system for aggregating the user preferences on the different criteria is constructed. In such approaches, marginal preferences upon each criterion are synthesized into a total value function, which is usually alled the utility function [ 33]. These approaches are often referred to as multi- attribute utility theory(MAUt) approaches Multi-Objective Optimisation models, where criteria are expressed in the form of multiple constraints of a multi-objective optimization problem. In such ap- proaches, usually the goal is to find a Pareto optimal solution for the original op- timization problem[ 102]. They are also sometimes referred to as multi-objective mathematical programming methodologie Outranking Relations models, where preferences are expressed as a system of outranking relations between the items, thus allowing the expression of incom- parability. In such approaches, all items are pair-wise compared to each other, and preference relations are provided as relations "a is preferred to b","a and b equally preferable, or"a is incomparable to b[77 Preference Disaggregation models, where the preference model is derived by analyzing past decisions. Such approaches are sometimes considered as a sub- preference model of a given form(e.g, value function or outranking relatio s category of other modeling categories mentioned above, since they try to infer from some given preferential structures that have led to particular decisions the past. Inferred preference models aim at producing decisions that are at least identical to the examined past ones [301 Methodologies from all categories can be used in order to create global prefer- ence models for recommender systems, depending on the selected decision prob lematic and the environment in which the recommender system is expected to oper

6 Gediminas Adomavicius, Nikos Manouselis, YoungOk Kwon assume that all types of criteria could be potentially engaged in multi-criteria recommender systems, although (as shown later) it seems that some types are used in currently developed systems more often than others. 2.3 Global Preference Model The development of a global preference model provides a way to aggregate the values of each criterion gc (where c = 1,...,k) in order to express the preferences between the different alternatives of the set Items, depending on the selected decision problematics. In the MCDM literature, a number of methodologies have been developed, which can be classified in different categories according to the form of the global preference model that they use and the process of creating this model. According to [30] and [64], the following categories of global preference modeling approaches can be identified: • Value-Focused models, where a value system for aggregating the user preferences on the different criteria is constructed. In such approaches, marginal preferences upon each criterion are synthesized into a total value function, which is usually called the utility function [33]. These approaches are often referred to as multiattribute utility theory (MAUT) approaches. • Multi-Objective Optimization models, where criteria are expressed in the form of multiple constraints of a multi-objective optimization problem. In such approaches, usually the goal is to find a Pareto optimal solution for the original optimization problem [102]. They are also sometimes referred to as multi-objective mathematical programming methodologies. • Outranking Relations models, where preferences are expressed as a system of outranking relations between the items, thus allowing the expression of incomparability. In such approaches, all items are pair-wise compared to each other, and preference relations are provided as relations “a is preferred to b”, “a and b are equally preferable”, or “a is incomparable to b” [77]. • Preference Disaggregation models, where the preference model is derived by analyzing past decisions. Such approaches are sometimes considered as a subcategory of other modeling categories mentioned above, since they try to infer a preference model of a given form (e.g., value function or outranking relations) from some given preferential structures that have led to particular decisions in the past. Inferred preference models aim at producing decisions that are at least identical to the examined past ones [30]. Methodologies from all categories can be used in order to create global preference models for recommender systems, depending on the selected decision problematic and the environment in which the recommender system is expected to operate

2. 4 Decision Support Process In this step, a final decision for a given MCDM problem is made by choosing an appropriate method among the ones defined in each of the previous steps. Like in traditional MCDM, multi-criteria recommendation problems may also need to use different methods for different domains or applications. Note, however, that this ICDM perspective is broad and not very restrictive when modeling multi-criteria recommendation problems, because many existing recommender systems can be thought to fit directly in the MCDM category, since they usually take into account information from multiple sources(e. g, user profiles and item attributes), thus mak ing them de facto multi-criteria decision makers. Therefore, later in the chapter, we will focus on a particular category of MCDM recommender systems that can be differentiated from most existing recommender systems In Tables 1-3, we provide an overview of some sample recommender systems based on the work of [48]. This survey covers systems the ecommender)systems that could be broadly classified as MCDM(or multi-criteria methods discussed in the previous section and, thus, provides insights into the way that existing MCDM approaches can be employed to support the decision-making in recommender systems The multi-criteria recommender systems are categorized according to the deci- ion problematic they support(Table 1), the types of criteria they use(Table 2), and the global preference modelling approach they follow(Table 3). Based on Table 1,it is interesting to note that most of the existing research focuses on the decision prob- lematic of ranking the items (i.e, ranking candidates for recommendation). There also several systems that support the sorting of items into different categories according to their suitability for the user(e.g, recommended vS non-recommended items). Very few systems support the choice and description problematic, although clearly there exist some applications in which they would prove relevant. Further more, as Table 2 illustrates, the families of criteria used are mainly measurable: that is, users rate items upon a measurable scale for each criterion. Nevertheless, there are also several systems that engage fiery, ordinal, and probabilistic criteria for the expression of user preferences regarding the candidate items. Finally, Table 3 in- dicates that only a few of the multi-criteria recommenders engage in the creation of the global preference model using a multi-objective optimization or outranking relations. On the contrary, the vast majority uses some value-focused model that typically calculates prediction in the form of an additive utility function. There are also some systems that do not synthesize the predictions from the multiple criteria, but rather use the raw vector models as their outcome(e.g, by providing a vector of ratings from all the criteria It is important to note that existing systems are sometimes violating the con- sistency rules that Roys methodology proposes(e.g, not using an exhaustive set of dimensions). Nevertheless, experimental results often indicate that performance of multi-criteria systems is satisfactory(e.g, see the survey of algorithms that fol- lows) even in cases where no formal modelling methodology has been followed

Multi-Criteria Recommender Systems 7 2.4 Decision Support Process In this step, a final decision for a given MCDM problem is made by choosing an appropriate method among the ones defined in each of the previous steps. Like in traditional MCDM, multi-criteria recommendation problems may also need to use different methods for different domains or applications. Note, however, that this MCDM perspective is broad and not very restrictive when modeling multi-criteria recommendation problems, because many existing recommender systems can be thought to fit directly in the MCDM category, since they usually take into account information from multiple sources (e.g., user profiles and item attributes), thus making them de facto multi-criteria decision makers. Therefore, later in the chapter, we will focus on a particular category of MCDM recommender systems that can be differentiated from most existing recommender systems. In Tables 1-3, we provide an overview of some sample recommender systems that could be broadly classified as MCDM (or multi-criteria recommender) systems based on the work of [48]. This survey covers systems that use one of the MCDM methods discussed in the previous section and, thus, provides insights into the way that existing MCDM approaches can be employed to support the decision-making in recommender systems. The multi-criteria recommender systems are categorized according to the decision problematic they support (Table 1), the types of criteria they use (Table 2), and the global preference modelling approach they follow (Table 3). Based on Table 1, it is interesting to note that most of the existing research focuses on the decision problematic of ranking the items (i.e., ranking candidates for recommendation). There are also several systems that support the sorting of items into different categories according to their suitability for the user (e.g., recommended vs. non-recommended items). Very few systems support the choice and description problematic, although clearly there exist some applications in which they would prove relevant. Furthermore, as Table 2 illustrates, the families of criteria used are mainly measurable: that is, users rate items upon a measurable scale for each criterion. Nevertheless, there are also several systems that engage fuzzy, ordinal, and probabilistic criteria for the expression of user preferences regarding the candidate items. Finally, Table 3 indicates that only a few of the multi-criteria recommenders engage in the creation of the global preference model using a multi-objective optimization or outranking relations. On the contrary, the vast majority uses some value-focused model that typically calculates prediction in the form of an additive utility function. There are also some systems that do not synthesize the predictions from the multiple criteria, but rather use the raw vector models as their outcome (e.g., by providing a vector of ratings from all the criteria). It is important to note that existing systems are sometimes violating the consistency rules that Roy’s methodology proposes (e.g., not using an exhaustive set of dimensions). Nevertheless, experimental results often indicate that performance of multi-criteria systems is satisfactory (e.g., see the survey of algorithms that follows) even in cases where no formal modelling methodology has been followed

Gediminas Adomavicius, Nikos Manouselis, YoungOk Kwon This could mean that a modelling inconsistency does not al ways imply problematic performance, although this is an issue that calls for further investigation Table 1 Decision problematics supported by existing multi-criteria recommender systems Choice Ariely et al. 2004 161, Falle et al. 2004 23), Kleinberg and Sandler 2003 38 Lee et al. 2002 145, Lee 2004 [44], Price and Messinger 2005 [69), Tewari et 94] orting et al. 2006[12], Choi and Cho 2004 [15), Emi et al. 2003 22]. al. 2002 [28), Kim and Yang 2004 [361, Liu and Shih 2005 [47 2003 153, Montaner et al. 2002 [57], Nguyen and Haddawy 1999 60], Nguyen and Haddawy 1998 [59], Stolze and Rjaibi 2001 191, Wang 2004[99Yu2002[100J,Yu2004[01l, Zimmerman et al.2004[103 Ranking Adomavicius and Kwon 2007 [2 Ardissono et al. 2003 5, Balabanovic and 2051 1997 [71 Ghosh et al. 1999 [27] Karacapilidis and Hatzieleftheriou erschberg et al. 2001 [35], Kim et al. 2002 [37, Lakiotaki et al 2008(42), Lee and Tang 2007 143 Lee et al. 2002 [45 Li et al. 2008[46 Manouselis and Costopoulou 2007b 149), Manouselis and Costopoulou 2007c 50, Manouselis and Sampson 2004 [], Mukherjee et al. 2001 58, Noh 2004 [61], Perny and Zucker 1999[66], Permy and Zucker 2001 167), Plantie et al. 2005 68), Ricci and Werthner 2002 [74 Ricci and Nguyen 2007 Sahoo et al. 2006 80) Schafer 2005 [83], Schickel-Zuber and Faltings 2005 [84], Srikumar and Bhasker 2004 190, Tang and McCalla 2009193), Tsai et al.200697 Description Aciar et al. 2007 [1], Cheetham 2003 [14, Denguir-Rekik et al. 2006[19 Herrera- Viedma et al. 2004 291, Schmitt et al. 2002 185), Schmitt et al. 2003 186, Stolze and Stroebel 2003 [92] 3 MCDM Framework for Recommender Systems: Lessons earne While, as mentioned earlier, the recommender systems surveyed in Tables 1-3 can be considered to be multi-criteria recommender systems according to the mCDm framework, it is important to understand where the existing types of recommender systems fall within this framework and also whether this MCDM framework gives rise to any novel types of recommender systems Recommendation techniques are often classified based on the recommendation approach into several categories: content-based, collaborative filtering, knowledge based, and hybrid approaches [7. Content-based recommendation techniques find the best recommendations for a user based on what the user liked in the past [65, and collaborative filtering recommendation techniques make recommenda- tions based on the information about other users with similar preferences [8] nowledge-based approaches use knowledge about users and items to find the items that meet users'requirements [9]. The bottleneck of this knowledge-based approach

8 Gediminas Adomavicius, Nikos Manouselis, YoungOk Kwon This could mean that a modelling inconsistency does not always imply problematic performance, although this is an issue that calls for further investigation. Table 1 Decision problematics supported by existing multi-criteria recommender systems Choice Ariely et al. 2004 [6], Falle et al. 2004 [23], Kleinberg and Sandler 2003 [38], Lee et al. 2002 [45], Lee 2004 [44], Price and Messinger 2005 [69], Tewari et al. 2003 [94] Sorting Cantador et al. 2006 [12], Choi and Cho 2004 [15], Emi et al. 2003 [22], Guan et al. 2002 [28], Kim and Yang 2004 [36], Liu and Shih 2005 [47], Masthoff 2003 [53], Montaner et al. 2002 [57], Nguyen and Haddawy 1999 [60], Nguyen and Haddawy 1998 [59], Stolze and Rjaibi 2001 [91], Wang 2004 [99], Yu 2002 [100], Yu 2004 [101], Zimmerman et al. 2004 [103] Ranking Adomavicius and Kwon 2007 [2], Ardissono et al. 2003 [5], Balabanovic and Shoham 1997 [7], Ghosh et al. 1999 [27], Karacapilidis and Hatzieleftheriou 2005 [32], Kerschberg et al. 2001 [35], Kim et al. 2002 [37], Lakiotaki et al. 2008 [42], Lee and Tang 2007 [43], Lee et al. 2002 [45], Li et al. 2008 [46], Manouselis and Costopoulou 2007b [49], Manouselis and Costopoulou 2007c [50], Manouselis and Sampson 2004 [52], Mukherjee et al. 2001 [58], Noh 2004 [61], Perny and Zucker 1999 [66], Perny and Zucker 2001 [67], Plantie et al. 2005 [68], Ricci and Werthner 2002 [74], Ricci and Nguyen 2007 [75], Sahoo et al. 2006 [80], Schafer 2005 [83], Schickel-Zuber and Faltings 2005 [84], Srikumar and Bhasker 2004 [90], Tang and McCalla 2009 [93], Tsai et al. 2006 [97] Description Aciar et al. 2007 [1], Cheetham 2003 [14], Denguir-Rekik et al. 2006 [19], Herrera-Viedma et al. 2004 [29], Schmitt et al. 2002 [85], Schmitt et al. 2003 [86], Stolze and Stroebel 2003 [92] 3 MCDM Framework for Recommender Systems: Lessons Learned While, as mentioned earlier, the recommender systems surveyed in Tables 1-3 can be considered to be multi-criteria recommender systems according to the MCDM framework, it is important to understand where the existing types of recommender systems fall within this framework and also whether this MCDM framework gives rise to any novel types of recommender systems. Recommendation techniques are often classified based on the recommendation approach into several categories: content-based, collaborative filtering, knowledgebased, and hybrid approaches [7]. Content-based recommendation techniques find the best recommendations for a user based on what the user liked in the past [65], and collaborative filtering recommendation techniques make recommendations based on the information about other users with similar preferences [8]. Knowledge-based approaches use knowledge about users and items to find the items that meet users’ requirements [9]. The bottleneck of this knowledge-based approach

Multi-Criteria Recommender Systems Table 2 Criteria types engaged in existing multi-criteria recommender systems Measurable Adomavicius and Kwon 2007 [2], Ariely et al. 2004 161, Balabanovic and Shoham 1997 [7 Cantador et al. 2006 [12]. Choi and Cho 2004 [15], Falle et al. 2004 [23], Ghosh et al. 1999 [27], Guan et al. 2002 [28], Kerschberg et al. 2001 [35, Kim and Yang 2004 36, Kim et al. 2002 [37, Lakiotaki et al 2008[42], Lee and Tang 2007 143], Lee 2004 [44], Lee et al. 2002 [45), Li et al 2008 146], Liu and Shih 2005 [47], Manouselis and Costopoulou 2007b[49] Manouselis and Costopoulou 2007e[50), Manouselis and Sampson 2004 52 Masthoff 2003 [53], Montaner et al. 2002 57) Mukherjee et al. 2001 [58], Noh 2004 [61], Plantie et al. 2005[68], Ricci and Werthner 2002 [741, Ricci and Nguyen 2007 [75], Sahoo et al. 2006[80], Schafer 2005[83], Schickel- Zuber and Faltings 2005[84 Schmitt et al. 2003 1861, Schmitt et al. 2002 185), Srikumar and Bhasker 2004 [90] Stolze and Rjaibi 2001 191], Tang and McCalla 2009 193) Tewari et al. 2003 194, Tsai et al. 2006 197), Yu 2002 [100], Yu 2004 [101], Zimmerman et al. 2004 [103] Ordinal Aciar et al. 2007 [1 Cheetham 2003 [14], Emi et al. 2003 22), Nguyen and Haddawy 1998[ 59], Nguyen and Haddawy 1999[60] F Herrera-Viedma et al. 2004 29), Karacapilidis and Hatzieleftheriou 2005 [32]. Perny and Zucker 1999 166], Perny and Zucker 2001 [67], Stolze and Stroebel 2003[92]Wang2004p99 Probabilistic Ardissono et al. 2003 5 Kleinberg and Sandler 2003 [38], Price and 200569 Table 3 Global preference models used in existing multi-criteria recommender systems Value-focused Aciar et al. 2007 [1] Adomavicius and Kwon 2007 [2], Ariely et al. 2004 161, Balabanovic and Shoham 1997 [7] Cantador et al. 2006[12 Choi and Che 2004 [15], Denguir-Rekik et al. 2006[ 19), Falle et al. 2004 [23], Ghosh et al 1999 [27], Guan et al. 200 (28), Herrera-Viedma et al. 2004(29], Karacapilidis and Hatzieleftheriou 2005 [ 32], Kerschberg et al. 2001 1351, Kim and Yang 2004 [36], Kim et al. 2002[37, Kleinberg and Sandler 2003 [38), Lakiotaki et al. 2008[42], Lee 2004[44, Lee et al. 2002 [45], Li et al. 2008 [46,Liu and Shih 2005 [47, Manouselis and Costopoulou 2007b[49), Manouselis and Costopoulou 2007c [50], Manouselis and Sampson 2004 152), Masthoff 2003 [53], Montaner et al. 2002 [57], Mukherjee et al. 2001 [58], Noh 2004 61 Perny and Zucker 1999[66), Perny and Zucker 2001 [67], Plantie et al. 200 68 Ricci and Werthner 2002 [74], Sahoo et al. 2006[80), Schafer 2005[83], Schickel-Zuber and Faltings 2005[84, Schmitt et al. 2003 [], Schmitt et al. 2002[85], Srikumar and Bhasker 2004 1901, Stolze and Stroebel 2003 192] Yu 2004[101], Yu 2002 (100), Zimmerman et al. 2004/et al. 2006(971 Stolze and Rjaibi 2001 191],Tang and Mc Calla 2009[93], Tsai Optimization Lee and Tang 2007143), Price and Messinger 2005 169), Tewari et al. 2003 94 Outranking re- Emi et al. 2003 [22], Nguyen and Haddawy 1999 1601, Nguyen and Haddawy 1999159 prefer- Ardissono et al, 2003 [5 Cheetham 2003 [14], Lee et al. 2002 [45 ] Ricci and ence models Nguyen 2007[75), Wang 2004 1991

Multi-Criteria Recommender Systems 9 Table 2 Criteria types engaged in existing multi-criteria recommender systems Measurable Adomavicius and Kwon 2007 [2], Ariely et al. 2004 [6], Balabanovic and Shoham 1997 [7], Cantador et al. 2006 [12], Choi and Cho 2004 [15], Falle et al. 2004 [23], Ghosh et al. 1999 [27], Guan et al. 2002 [28], Kerschberg et al. 2001 [35], Kim and Yang 2004 [36], Kim et al. 2002 [37], Lakiotaki et al. 2008 [42], Lee and Tang 2007 [43], Lee 2004 [44], Lee et al. 2002 [45], Li et al. 2008 [46], Liu and Shih 2005 [47], Manouselis and Costopoulou 2007b [49], Manouselis and Costopoulou 2007c [50], Manouselis and Sampson 2004 [52], Masthoff 2003 [53], Montaner et al. 2002 [57], Mukherjee et al. 2001 [58], Noh 2004 [61], Plantie et al. 2005 [68], Ricci and Werthner 2002 [74], Ricci and Nguyen 2007 [75], Sahoo et al. 2006 [80], Schafer 2005 [83], SchickelZuber and Faltings 2005 [84], Schmitt et al. 2003 [86], Schmitt et al. 2002 [85], Srikumar and Bhasker 2004 [90], Stolze and Rjaibi 2001 [91], Tang and McCalla 2009 [93], Tewari et al. 2003 [94], Tsai et al. 2006 [97], Yu 2002 [100], Yu 2004 [101], Zimmerman et al. 2004 [103] Ordinal Aciar et al. 2007 [1], Cheetham 2003 [14], Emi et al. 2003 [22], Nguyen and Haddawy 1998 [59], Nguyen and Haddawy 1999 [60] Fuzzy Herrera-Viedma et al. 2004 [29], Karacapilidis and Hatzieleftheriou 2005 [32], Perny and Zucker 1999 [66], Perny and Zucker 2001 [67], Stolze and Stroebel 2003 [92], Wang 2004 [99] Probabilistic Ardissono et al. 2003 [5], Kleinberg and Sandler 2003 [38], Price and Messinger 2005 [69] Table 3 Global preference models used in existing multi-criteria recommender systems Value-focused models Aciar et al. 2007 [1], Adomavicius and Kwon 2007 [2], Ariely et al. 2004 [6], Balabanovic and Shoham 1997 [7], Cantador et al. 2006 [12], Choi and Cho 2004 [15], Denguir-Rekik et al. 2006 [19], Falle et al. 2004 [23], Ghosh et al. 1999 [27], Guan et al. 200 [28], Herrera-Viedma et al. 2004[29], Karacapilidis and Hatzieleftheriou 2005 [32], Kerschberg et al. 2001 [35], Kim and Yang 2004 [36], Kim et al. 2002 [37], Kleinberg and Sandler 2003 [38],Lakiotaki et al. 2008 [42], Lee 2004 [44], Lee et al. 2002 [45], Li et al. 2008 [46], Liu and Shih 2005 [47], Manouselis and Costopoulou 2007b [49], Manouselis and Costopoulou 2007c [50], Manouselis and Sampson 2004 [52], Masthoff 2003 [53], Montaner et al. 2002 [57], Mukherjee et al. 2001 [58], Noh 2004 [61], Perny and Zucker 1999 [66], Perny and Zucker 2001 [67], Plantie et al. 2005 [68], Ricci and Werthner 2002 [74], Sahoo et al. 2006 [80], Schafer 2005 [83], Schickel-Zuber and Faltings 2005 [84], Schmitt et al. 2003 [86], Schmitt et al. 2002 [85], Srikumar and Bhasker 2004 [90], Stolze and Stroebel 2003 [92], Stolze and Rjaibi 2001 [91],Tang and McCalla 2009 [93], Tsai et al. 2006 [97], Yu 2004 [101], Yu 2002 [100], Zimmerman et al. 2004 [103] Optimization Lee and Tang 2007 [43], Price and Messinger 2005 [69], Tewari et al. 2003 [94] Outranking relations Emi et al. 2003 [22], Nguyen and Haddawy 1999 [60], Nguyen and Haddawy 1999 [59] Other preference models Ardissono et al. 2003 [5], Cheetham 2003 [14], Lee et al. 2002 [45], Ricci and Nguyen 2007 [75], Wang 2004 [99]

10 Gediminas Adomavicius, Nikos Manouselis, YoungOk Kwon Is that it needs to acquire a knowledge base beforehand, but the obtained knowledge base helps to avoid cold start or data sparsity problems that pure content-based or collaborative filtering systems encounter by relying on solely the ratings obtained by users. Hybrid approaches combine content-based, collaborative filtering, and knowledge-based techniques in many different ways[10]. Upon more in-depth anal ysis of the representative MCDM recommender systems surveyed in the previous section, we discover that the multi-criteria nature of the majority of these systems can be classified in the following three general categories Multi-attribute content preference modeling. Even though these systems typi- cally use single-criterion ratings(e.g, numeric or binary ratings), for any given user these systems attempt to understand and model the commonalities of multi- attribute content among the items the user preferred in the past, and recommend to the user the items that best match this preferred content. For example, in a movie recommender system, these commonalities may be represented by specific genres, actors, directors, etc that the users preferred movies have in common Multi-attribute content search and filtering. These systems allow a user to spec fy her general preferences on content-based attributes across all items, through searching or filtering processes(e.g, searching for only"comedy"movies or specify ing that"comedy "movies are preferable to"action"movies), and recom mend to the user the items that are the most similar to her preferences and satisfy a specified search and/or filtering conditions Multi-criteria rating-based preference elicitation. These systems allow a user to specify her individual preferences by rating each item on multiple criteria(e.g rating the story of movie Wanted as 2 and the visual effects of the same movie as 5), and recommend to the user the items that can best reflect the users individual preferences based on the multi-criteria ratings provided by this and other users Multi-attribute content preference modeling. One way to model user prefer- ences is by analyzing multi-attribute content of items that users purchased or liked. lany multi-criteria recommender systems incorporate these content-based features either directly into the recommendation process(i.e, use a content-based approach) or in combination with collaborative recommendation techniques(i.e, use a hybrid approach). In these systems, users are typically allowed to implicitly or explicitly express their preferences with single-criterion ratings(e.g, item purchase history or ingle numeric ratings). Using these ratings, recommender systems then can learn users'content-based preferences in an automated fashion by finding the common- alities among the individual content attributes of items that the users purchased or liked, e.g., by identifying favorite content attributes (e.g,"comedy"movies)for each user. As a result, recommendations are made taking into account these fa vorite content attributes [7] Numerous traditional recommender systems that em- ploy content-based, knowledge-based, or hybrid approaches in combination with some multi-attribute preference modeling of users can be found in this category Several scoring or utility functions have been developed and used to rank the candidate items based on users' content-based preferences, including information retrieval-based and model-based techniques, such as Bayesian classifiers and vari-

10 Gediminas Adomavicius, Nikos Manouselis, YoungOk Kwon is that it needs to acquire a knowledge base beforehand, but the obtained knowledge base helps to avoid cold start or data sparsity problems that pure content-based or collaborative filtering systems encounter by relying on solely the ratings obtained by users. Hybrid approaches combine content-based, collaborative filtering, and knowledge-based techniques in many different ways [10]. Upon more in-depth analysis of the representative MCDM recommender systems surveyed in the previous section, we discover that the multi-criteria nature of the majority of these systems can be classified in the following three general categories: • Multi-attribute content preference modeling. Even though these systems typically use single-criterion ratings (e.g., numeric or binary ratings), for any given user these systems attempt to understand and model the commonalities of multiattribute content among the items the user preferred in the past, and recommend to the user the items that best match this preferred content. For example, in a movie recommender system, these commonalities may be represented by specific genres, actors, directors, etc. that the user’s preferred movies have in common. • Multi-attribute content search and filtering. These systems allow a user to specify her general preferences on content-based attributes across all items, through searching or filtering processes (e.g., searching for only “comedy” movies or specifying that “comedy” movies are preferable to “action” movies), and recommend to the user the items that are the most similar to her preferences and satisfy specified search and/or filtering conditions. • Multi-criteria rating-based preference elicitation. These systems allow a user to specify her individual preferences by rating each item on multiple criteria (e.g., rating the story of movie Wanted as 2 and the visual effects of the same movie as 5), and recommend to the user the items that can best reflect the user’s individual preferences based on the multi-criteria ratings provided by this and other users. Multi-attribute content preference modeling. One way to model user preferences is by analyzing multi-attribute content of items that users purchased or liked. Many multi-criteria recommender systems incorporate these content-based features either directly into the recommendation process (i.e., use a content-based approach) or in combination with collaborative recommendation techniques (i.e., use a hybrid approach). In these systems, users are typically allowed to implicitly or explicitly express their preferences with single-criterion ratings (e.g., item purchase history or single numeric ratings). Using these ratings, recommender systems then can learn users’ content-based preferences in an automated fashion by finding the commonalities among the individual content attributes of items that the users purchased or liked, e.g., by identifying favorite content attributes (e.g., “comedy” movies) for each user. As a result, recommendations are made taking into account these favorite content attributes [7]. Numerous traditional recommender systems that employ content-based, knowledge-based, or hybrid approaches in combination with some multi-attribute preference modeling of users can be found in this category. Several scoring or utility functions have been developed and used to rank the candidate items based on users’ content-based preferences, including information retrieval-based and model-based techniques, such as Bayesian classifiers and vari-

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