Availableonlineatwww.sciencedirect.com ScienceDirect FUZZY sets and systems ELSEVIER Fuzzy Sets and Systems 160(2009)76-94 Representation, similarity measures and aggregation methods using uzzy sets for content-based recommender systems Azene Zenebea,*. Anthony F norco Systems Department, Bowie State University, 14000 Jericho Park Rd, Bowie, MD 20715-9465, USA iNformation Systems Department, University of Maryland at Baltimore County(UMBC). 1000 Hilltop Circle, MD 21250,USA Received 17 July 2007; received in revised form 8 March 2008: accepted 10 March 2008 Available online 26 march 2008 Abstract Representation of features of items and user feedback, and reasoning about their relationships are major problems in recommender systems. This is because item features and user feedback are subjective, imprecise and vague. The paper presents a fuzzy set theoretic method(FTM) for recommender systems that handles the non-stochastic uncertainty induced from subjectivity, vagueness and precision in the data, and the domain knowledge and the task under consideration. The research further advances the application of fuzzy modeling for content-based recommender systems initially presented by Ronald Yager. The paper defines a representation method, similarity measures and aggregation methods as well as empirically evaluates the methods performance through simulation using a benchmark movie data FTM consist of a representation method for items'features and user feedback using fuzzy sets, and a content-based algorithm based on various fuzzy set theoretic similarity measures (the fuzzy set extensions of the Jaccard index, cosine, proximity or correlation similarity measures ), and aggregation methods for computing recommendation confidence scores(the maximum-minimum or Weighted-sum fuzzy set theoretic aggregation methods). Compared to the baseline crisp set based method(CSM) presented, the empirical evaluation of the FTM using the movie data and simulation shows an improvement in precision without loss of recall. Moreover, the paper provides a guideline for recommender systems designers that will help in choosing from a combination of one of the fuzzy set theoretic aggregation methods and similarity measures. Published by Elsevier B.V. Keywords: Fuzzy sets; Fuzzy connectives and aggregation operators; Recommender systems; Learning: Empirical evaluation 1. Introduction Recommender systems are systems that provide users with an ordered list of items and information that help the to decide which items to consider or look at based on the individual user preferences [25]. Recommendation systems use background data such as historical data consisting of ratings from users before the recommendation begins, input data such as features of items or users 'ratings in order to initiate a recommendation and models and algorithms to combine the former two and generate a recommendation [8] There have been many advances in recommender systems research. An extensive review of the different approa used in recommender systems is presented in Burke [8]. Recently, Adomavicius and Tuzhilin [1] have identified Corresponding author. Tel: +1301 3641: fax: +1301 8603593 E-mail address: azenebe@bowiestate edu(A. Zenebe) 0165-0114S-see front matter Published by Elsevier B V. doi:10.1016js2008.03017
Fuzzy Sets and Systems 160 (2009) 76 – 94 www.elsevier.com/locate/fss Representation, similarity measures and aggregation methods using fuzzy sets for content-based recommender systems Azene Zenebea,∗, Anthony F. Norciob aManagement Information Systems Department, Bowie State University, 14000 Jericho Park Rd., Bowie, MD 20715-9465, USA bInformation Systems Department, University of Maryland at Baltimore County (UMBC), 1000 Hilltop Circle, MD 21250, USA Received 17 July 2007; received in revised form 8 March 2008; accepted 10 March 2008 Available online 26 March 2008 Abstract Representation of features of items and user feedback, and reasoning about their relationships are major problems in recommender systems. This is because item features and user feedback are subjective, imprecise and vague. The paper presents a fuzzy set theoretic method (FTM) for recommender systems that handles the non-stochastic uncertainty induced from subjectivity, vagueness and imprecision in the data, and the domain knowledge and the task under consideration. The research further advances the application of fuzzy modeling for content-based recommender systems initially presented by Ronald Yager. The paper defines a representation method, similarity measures and aggregation methods as well as empirically evaluates the methods’ performance through simulation using a benchmark movie data. FTM consist of a representation method for items’ features and user feedback using fuzzy sets, and a content-based algorithm based on various fuzzy set theoretic similarity measures (the fuzzy set extensions of the Jaccard index, cosine, proximity or correlation similarity measures), and aggregation methods for computing recommendation confidence scores (the maximum–minimum or Weighted-sum fuzzy set theoretic aggregation methods). Compared to the baseline crisp set based method (CSM) presented, the empirical evaluation of the FTM using the movie data and simulation shows an improvement in precision without loss of recall. Moreover, the paper provides a guideline for recommender systems designers that will help in choosing from a combination of one of the fuzzy set theoretic aggregation methods and similarity measures. Published by Elsevier B.V. Keywords: Fuzzy sets; Fuzzy connectives and aggregation operators; Recommender systems; Learning; Empirical evaluation 1. Introduction Recommender systems are systems that provide users with an ordered list of items and information that help them to decide which items to consider or look at based on the individual user preferences [25]. Recommendation systems use background data such as historical data consisting of ratings from users before the recommendation begins, input data such as features of items or users’ ratings in order to initiate a recommendation, and models and algorithms to combine the former two and generate a recommendation [8]. There have been many advances in recommender systems research. An extensive review of the different approaches used in recommender systems is presented in Burke [8]. Recently, Adomavicius and Tuzhilin [1] have identified ∗ Corresponding author. Tel.: +1 301 860 3641; fax: +1 301 860 3593. E-mail address: azenebe@bowiestate.edu (A. Zenebe). 0165-0114/$ - see front matter Published by Elsevier B.V. doi:10.1016/j.fss.2008.03.017
A. Zenebe, A F. Norcio/ Fuzzy Sets and Systems 160(2009)76-94 various areas of improvements for current recommender systems. They are: (i) better methods for representing user behavior and information about items; (ii) more advanced recommendation modeling methods; (iii) incorporation of contextual information into recommendation process; (iv)utilization of multi-criteria ratings; (v) development of less intrusive and more flexible recommendation methods; and(vi) development of recommender systems effective ness measures. This paper attempts to address the improvement need stated in(i)and (ii) using the fuzzy modelin L.I. The problem A content-based recommendation requires data on the behavior of users and features of items. Its performance depends on the data and how this data is used, i.e. represented and inferred. Representation of and reasoning about the behavior of users and features of items raised a number of challenging issues Features of items and users'be- havior are subjective, vague and imprecise. These, in turn, induce uncertainty on representation of and reasonin about the items'features, users'behavior, and their relationship. Such uncertainty is non-stochastic or non-random and is induced from subjectivity, vagueness and imprecision in the data, the domain knowledge and the task under consideration [20] In relation to items, the uncertainty is associated to the extent(e. g. low to high) in which the items have some features For instance, to what extent does a movie have drama content or is it highly drama related? In relation to the behavior such as interest, the uncertainty is associated to methods employed to measure and represent users'interest as precisely as possible. In relation to the recommendation task, uncertainty is associated to types of relationship that exist between first. user behavior and item features. second. among users in terms of their behavior. and third among items in terms of their features Such non-stochastic uncertainty is not studied well and modeled in previous recommender systems research such as [25, 12] 1. 2. The proposed method In fuzzy modeling membership functions in fuzzy set theory are deliberately designed to treat the vagueness and imprecision in the context of the application [22]. This capability is used to provide the framework to address the representation and inference challenges associated to non-stochastic uncertainty [20] in recommender systems. The study is motivated by the"reclusive methods" proposed by Yager [30]. Yager [30] discusses the potential of fuzzy modeling and also presents a methodology consisting of collection of justifications and heuristic rules for the recommendations based on fuzzy set and fuzzy logic. He assumes the availability of a representation scheme for each object that allows the development of an appropriate tool to calculate the similarity relationship over the set of objects He also assumes the availability of similarity index between two objects. However, he did not conduct an empirical tudy to support or refute the effectiveness of using fuzzy modeling. This research is an attempt to further develop and empirically evaluate fuzzy set theoretic method (FTM) for content-based recommender systems using the problem of movie recommendation as its domain. Particularly, the proposed approach uses features of items as background data and user's feedback such as ratings of items as input. The study defines a representational method, aggregation methods, and similarity measures for content-based ommender systems. It also develops algorithms and carries out an empirical assessment of the effect of the fuzzy set theoretic method(FTM) on the performance of a movie recommender system by comparing its results to the re- sults of the baseline crisp set based method(CSM). An empirical assessment of the effect of the various inference mechanisms--combinations of the aggregation methods and similarity measures is also performed. The study also considers analyzing the effect of the model size(also called training size-number of rated items initially needed from a user), and recommendation size(number of items recommended at one time to a user)on the performance of a movie recommender system. 13. Results. conclusion and contributions Using actual data on movies, the results of the simulation study provide empirical evidence that supports the ef fectiveness of FTM. The results show a modest increase in precision without loss of recall. It also requires a modest training size and recommendation size. Moreover, the results of analysis of variance show that there are significant
A. Zenebe, A.F. Norcio / Fuzzy Sets and Systems 160 (2009) 76–94 77 various areas of improvements for current recommender systems. They are: (i) better methods for representing user behavior and information about items; (ii) more advanced recommendation modeling methods; (iii) incorporation of contextual information into recommendation process; (iv) utilization of multi-criteria ratings; (v) development of less intrusive and more flexible recommendation methods; and (vi) development of recommender systems effectiveness measures. This paper attempts to address the improvement need stated in (i) and (ii) using the fuzzy modeling technique. 1.1. The problem A content-based recommendation requires data on the behavior of users and features of items. Its performance depends on the data and how this data is used, i.e. represented and inferred. Representation of and reasoning about the behavior of users and features of items raised a number of challenging issues. Features of items and users’ behavior are subjective, vague and imprecise. These, in turn, induce uncertainty on representation of and reasoning about the items’ features, users’ behavior, and their relationship. Such uncertainty is non-stochastic or non-random and is induced from subjectivity, vagueness and imprecision in the data, the domain knowledge and the task under consideration [20]. In relation to items, the uncertainty is associated to the extent (e.g. low to high) in which the items have some features. For instance, to what extent does a movie have drama content or is it highly drama related? In relation to the users’ behavior such as interest, the uncertainty is associated to methods employed to measure and represent users’ interest as precisely as possible. In relation to the recommendation task, uncertainty is associated to types of relationship that exist between first, user behavior and item features, second, among users in terms of their behavior, and third, among items in terms of their features. Such non-stochastic uncertainty is not studied well and modeled in previous recommender systems research such as [25,12]. 1.2. The proposed method In fuzzy modeling membership functions in fuzzy set theory are deliberately designed to treat the vagueness and imprecision in the context of the application [22]. This capability is used to provide the framework to address the representation and inference challenges associated to non-stochastic uncertainty [20] in recommender systems. The study is motivated by the “reclusive methods” proposed by Yager [30]. Yager [30] discusses the potential of fuzzy modeling and also presents a methodology consisting of collection of justifications and heuristic rules for the recommendations based on fuzzy set and fuzzy logic. He assumes the availability of a representation scheme for each object that allows the development of an appropriate tool to calculate the similarity relationship over the set of objects. He also assumes the availability of similarity index between two objects. However, he did not conduct an empirical study to support or refute the effectiveness of using fuzzy modeling. This research is an attempt to further develop and empirically evaluate fuzzy set theoretic method (FTM) for content-based recommender systems using the problem of movie recommendation as its domain. Particularly, the proposed approach uses features of items as background data and user’s feedback such as ratings of items as input. The study defines a representational method, aggregation methods, and similarity measures for content-based recommender systems. It also develops algorithms and carries out an empirical assessment of the effect of the fuzzy set theoretic method (FTM) on the performance of a movie recommender system by comparing its results to the results of the baseline crisp set based method (CSM). An empirical assessment of the effect of the various inference mechanisms—combinations of the aggregation methods and similarity measures is also performed. The study also considers analyzing the effect of the model size (also called training size—number of rated items initially needed from a user), and recommendation size (number of items recommended at one time to a user) on the performance of a movie recommender system. 1.3. Results, conclusion and contributions Using actual data on movies, the results of the simulation study provide empirical evidence that supports the effectiveness of FTM. The results show a modest increase in precision without loss of recall. It also requires a modest training size and recommendation size. Moreover, the results of analysis of variance show that there are significant
differences among the different alternative combination of fuzzy set theoretic similarity measures and aggregation methods in their recommendation accuracy. The paper has the following main contributions Compared to using crisp set theory, the paper shows using fuzzy set theory slightly improves precision without loss of recall for content-based movies recommendation application 2. The paper provides a representation framework for features of items and users feedback using fuzzy sets as well as new algorithms for content-based item recommender systems 3. The paper presents a practical and detailed description of how to apply fuzzy set theory in a new domain as well how to conduct extensive experimental study to validate the theory of the fuzzy set theoretic aggregation methods and the fuzzy set theoretic similarity measures ombination of 4. The paper provides a guideline for recommender systems designers that will help them to choose a The remainder of the paper is organized as follows. Section 2 presents a review of related literature. Section 3 presents the representation method, inference methods, similarity measures and algorithms. Section 4 describes the dataset, evaluation settings, and evaluation metrics. Section 5 presents the results of the evaluation followed by the discussion in Section 6. Finally, our conclusions and future research directions are presented in Section 7. 2. Related literature 2./. Recommender systems There are various classifications of recommendation methods based on the sources of data and how these data are used for recommendation, Burke [8 has classified recommendation methods into: collaborative, content-based, demographic, utility-based, and knowledge-based. There are also various variants of hybrid methods that combine these methods. These hybrid methods are discussed in detail in [8]. Moreover, a recent survey of state-of-the-art recommender systems along with suggestions for improvements is found in [1] The two most widely used methods of recommendation are content-based and collaborative filtering(CF). In collab- orative filtering, an item is recommended to a user based on other similar users actions like interests, preferences and ratings[24]. Because of the availability of ratings data, CF is the most fully explored and several numbers of studies are eported Deshpande and Karypis [12] developed item-based Top-N recommendation algorithms that are collaborative ype and faster than traditional user-user collaborative algorithms with comparable recommendation hit-rate. More- over, results of evaluation of these CF algorithms for recommender systems using the MovieLens dataset are reported in terms of precision and Fl-measure in [21] In content-based recommendation, an item is recommended to a user mainly based on the characteristics of the em and the user's past actions like purchases, queries, and ratings. Moreover, in content-based recommendation, standard machine learning techniques such as clustering, Bayesian networks and induction learning are applied in forming attribute-based models [8]. Alspector et al. [2] used a set of seven movie features--category, MAAP rating, academy award, origin, length, director and Maltin rating, in addition to the rating. They showed that the pure CF method produces significantly better results(in terms of correlation measure between predicted and actual rating)than the ones obtained with the content -based method Basu et al. [6] applied inductive learning approaches that use Ripper for recommendation of movies. They showed that content-based approaches result in loss of precision with modest increase in recall; collaborative approaches improve precision with modest loss of recall; and hybrid approaches increase both precision and recall. Weng and George [27] have also reported similar result for precision. These studies indicated that the mere introduction of movie features alone does not improve precision. The present study attempts to show that a proper introduction of movie features does improve precision without loss of recall. 2.2. Fuzzy modeling Fuzzy set theory offers a rich spectrum of methods for the management of non-stochastic uncertainty. It is well suited to handle imprecise information, the un-sharpness of classes of objects or situations, and the gradualness of preference profiles [31]
78 A. Zenebe, A.F. Norcio / Fuzzy Sets and Systems 160 (2009) 76–94 differences among the different alternative combination of fuzzy set theoretic similarity measures and aggregation methods in their recommendation accuracy. The paper has the following main contributions: 1. Compared to using crisp set theory, the paper shows using fuzzy set theory slightly improves precision without loss of recall for content-based movies recommendation application. 2. The paper provides a representation framework for features of items and users feedback using fuzzy sets as well as new algorithms for content-based item recommender systems. 3. The paper presents a practical and detailed description of how to apply fuzzy set theory in a new domain as well as how to conduct extensive experimental study to validate the theory. 4. The paper provides a guideline for recommender systems designers that will help them to choose a combination of one of the fuzzy set theoretic aggregation methods and the fuzzy set theoretic similarity measures. The remainder of the paper is organized as follows. Section 2 presents a review of related literature. Section 3 presents the representation method, inference methods, similarity measures and algorithms. Section 4 describes the dataset, evaluation settings, and evaluation metrics. Section 5 presents the results of the evaluation followed by the discussion in Section 6. Finally, our conclusions and future research directions are presented in Section 7. 2. Related literature 2.1. Recommender systems There are various classifications of recommendation methods. Based on the sources of data and how these data are used for recommendation, Burke [8] has classified recommendation methods into: collaborative, content-based, demographic, utility-based, and knowledge-based. There are also various variants of hybrid methods that combine these methods. These hybrid methods are discussed in detail in [8]. Moreover, a recent survey of state-of-the-art recommender systems along with suggestions for improvements is found in [1]. The two most widely used methods of recommendation are content-based and collaborative filtering (CF). In collaborative filtering, an item is recommended to a user based on other similar users’ actions like interests, preferences and ratings [24]. Because of the availability of ratings data, CF is the most fully explored and several numbers of studies are reported. Deshpande and Karypis [12] developed item-based Top-N recommendation algorithms that are collaborative type and faster than traditional user–user collaborative algorithms with comparable recommendation hit-rate. Moreover, results of evaluation of these CF algorithms for recommender systems using the MovieLens dataset are reported in terms of precision and F1-measure in [21]. In content-based recommendation, an item is recommended to a user mainly based on the characteristics of the item and the user’s past actions like purchases, queries, and ratings. Moreover, in content-based recommendation, standard machine learning techniques such as clustering, Bayesian networks and induction learning are applied in forming attribute-based models [8]. Alspector et al. [2] used a set of seven movie features—category, MAAP rating, academy award, origin, length, director and Maltin rating, in addition to the rating. They showed that the pure CF method produces significantly better results (in terms of correlation measure between predicted and actual rating) than the ones obtained with the content-based method. Basu et al. [6] applied inductive learning approaches that use Ripper for recommendation of movies. They showed that content-based approaches result in loss of precision with modest increase in recall; collaborative approaches improve precision with modest loss of recall; and hybrid approaches increase both precision and recall. Weng and George [27] have also reported similar result for precision. These studies indicated that the mere introduction of movie features alone does not improve precision. The present study attempts to show that a proper introduction of movie features does improve precision without loss of recall. 2.2. Fuzzy modeling Fuzzy set theory offers a rich spectrum of methods for the management of non-stochastic uncertainty. It is well suited to handle imprecise information, the un-sharpness of classes of objects or situations, and the gradualness of preference profiles [31]
A. Zenebe, A F. Norcio/ Fuzzy Sets and Systems 160(2009)76-94 4. A fuzzy set A in X is characterized by its membership function, which is defined as [31]:PA(): xEX-[0, 1]. ere X is a domain space. Altematively, set A can be characterized by a set of pairs A =I(r, HA()),xE X). B.Ccording to the context in which X is used and the concept presented, the fuzzy membership function, HA(x),can A Ive different interpretations [7]. As a degree of similarity, it represents the proximity between different pieces of information. For example, the membership of movie x in the fuzzy set of"drama movies"can be estimated by the degree of similarity. As a degree of preference, it represents the intensity of preference in favor of x, or the feasibility satisfaction or liking with x based on certain criteria, like movie attributes such as content-intensity of actionL, dv of selecting x as a value of X. For instance a movie with rating of four out of five indicates the degree of a user and humor. These two interpretations are used in this research. The relationship between fuzzy set theory and probability has been the most controversial in uncertainty modeling mainly due to the possible confusion and differences between membership function and probability measure. It is lear now that they are two complementary theories. Dubois and Prade [16] presented some of the mathematical difference between possibility and the quantitative, explicit Kolmogoroff's probability Zimmerman [34] also indicated that comparing fuzzy set theory with probability theory is not easy because of the various aspects in which the comparison can be made, because of the many different ways of mathematically defining and operating fuzzy sets, and because of the various kinds of fuzziness that can be modeled. One difference between fuzziness and probability is probability theory measures the chance that a proposition is correct where as fuzzy set theory measures degree of correctness to which a proposition is correct [15] Possibility theory, introduced in 1978 by Zadeh [32], made it possible to deal with uncertainties of imprecise knowledge. It allows the quantification of uncertainty as a pair of numbers, possibility and necessity. In a proposition such as'X is A', where X is a variable and A is a fuzzy set, if all we know about the value of X is that X is a then this corresponds to a situation where information is incomplete. Then one can associate a possibility distribution to X(denoted by Tx) where the values of X are ordered according to their degree of plausibility or possibility. The possibility distribution function T(u) is defined to be numerically equal to the membership function HA(u)[32]. That is, a membership function has a possiblistic interpretation, which assumes the presence Forecasting, bidding and auctions, negotiation, targeting, recommender systems and profiling are pointed out as application areas that can benefit from soft computing paradigm and data mining [5, 29, 30]. Research efforts that address non-stochastic uncertainty using fuzzy modeling for recommendation systems have emerged recently, e.g [ 19,30]. These works use fuzzy sets to define linguistic categorizations of products in an e-commerce, and form overlapping clusters using fuzzy clustering FTM is case-based as""similar"cases are recalled, and based on them each possible decision is evaluated. "[17, p 609]. Dubois et al. [ 14] presented a fuzzy-set based counterpart to the case-based decision. As a case-based decision theory(CBDT)driven approach, FTM does have the following features[17]: each recommendation decision is evaluated over a different set of cases: to make recommendation decision there is no need to consider all possible states and the orresponding outcomes; the system is not assumed to know anything about the outside world, apart from past cases; and the system learns by including new cases and updated its similarity judgment and recommendation decisions continuously FTM differs from the previous recommendation systems in its representation and inference methods. Furthermore this study has done extensive empirical evaluation to identify the significance of the use of fuzzy representation and inference methods and other factors on the performance 3. The representation and inference methods The proposed fuzzy set theoretic content-based approach is based on a user's previous feedback, and features of the new items and features of the set of i for which the user has provided feedback. The rationale of this method is that users are more likely to have interest in items, like movies, that are similar to the items they have experienced and liked. The representation method, inference engine consisting of aggregation methods and similarity measures, and the algorithms are presented in this section 3.1. Item representation using fuzzy set A membership function in fuzzy set theory is deliberately designed to handle the vagueness and imprecision in the context of the application [22]. The type of function that is suitable depends on the application context, and in certain
A. Zenebe, A.F. Norcio / Fuzzy Sets and Systems 160 (2009) 76–94 79 A fuzzy set A in X is characterized by its membership function, which is defined as [31]: A(x) : x ∈ X → [0, 1], where X is a domain space. Alternatively, set A can be characterized by a set of pairs:A = {(x, A(x)), x ∈ X}. According to the context in which X is used and the concept presented, the fuzzy membership function, A(x), can have different interpretations [7]. As a degree of similarity, it represents the proximity between different pieces of information. For example, the membership of movie x in the fuzzy set of “drama movies” can be estimated by the degree of similarity. As a degree of preference, it represents the intensity of preference in favor of x, or the feasibility of selecting x as a value of X. For instance, a movie with rating of four out of five indicates the degree of a user’s satisfaction or liking with x based on certain criteria, like movie attributes such as content-intensity of action, drama, and humor. These two interpretations are used in this research. The relationship between fuzzy set theory and probability has been the most controversial in uncertainty modeling mainly due to the possible confusion and differences between membership function and probability measure. It is clear now that they are two complementary theories. Dubois and Prade [16] presented some of the mathematical difference between possibility and the quantitative, explicit Kolmogoroff’s probability. Zimmerman [34] also indicated that comparing fuzzy set theory with probability theory is not easy because of the various aspects in which the comparison can be made, because of the many different ways of mathematically defining and operating fuzzy sets, and because of the various kinds of fuzziness that can be modeled. One difference between fuzziness and probability is probability theory measures the chance that a proposition is correct where as fuzzy set theory measures degree of correctness to which a proposition is correct [15]. Possibility theory, introduced in 1978 by Zadeh [32], made it possible to deal with uncertainties of imprecise knowledge. It allows the quantification of uncertainty as a pair of numbers, possibility and necessity. In a proposition such as ‘X is A’, where X is a variable and A is a fuzzy set, if all we know about the value of X is that X is A, then this corresponds to a situation where information is incomplete. Then one can associate a possibility distribution to X (denoted by x ) where the values of X are ordered according to their degree of plausibility or possibility. The possibility distribution function x (u) is defined to be numerically equal to the membership function A(u) [32]. That is, a membership function has a possiblistic interpretation, which assumes the presence. Forecasting, bidding and auctions, negotiation, targeting, recommender systems and profiling are pointed out as application areas that can benefit from soft computing paradigm and data mining [5,29,30]. Research efforts that address non-stochastic uncertainty using fuzzy modeling for recommendation systems have emerged recently, e.g. [19,30]. These works use fuzzy sets to define linguistic categorizations of products in an e-commerce, and form overlapping clusters using fuzzy clustering. FTM is case-based as “ “similar” cases are recalled, and based on them each possible decision is evaluated.” [17, p. 609]. Dubois et al. [14] presented a fuzzy-set based counterpart to the case-based decision. As a case-based decision theory (CBDT) driven approach, FTM does have the following features [17]: each recommendation decision is evaluated over a different set of cases; to make recommendation decision there is no need to consider all possible states and the corresponding outcomes; the system is not assumed to know anything about the outside world, apart from past cases; and the system learns by including new cases and updated its similarity judgment and recommendation decisions continuously. FTM differs from the previous recommendation systems in its representation and inference methods. Furthermore, this study has done extensive empirical evaluation to identify the significance of the use of fuzzy representation and inference methods and other factors on the performance. 3. The representation and inference methods The proposed fuzzy set theoretic content-based approach is based on a user’s previous feedback, and features of the new items and features of the set of items for which the user has provided feedback. The rationale of this method is that users are more likely to have interest in items, like movies, that are similar to the items they have experienced and liked. The representation method, inference engine consisting of aggregation methods and similarity measures, and the algorithms are presented in this section. 3.1. Item representation using fuzzy set A membership function in fuzzy set theory is deliberately designed to handle the vagueness and imprecision in the context of the application [22]. The type of function that is suitable depends on the application context, and in certain
A. Zenebe, A F. Norcio/ Fuzzy Sets and Systems 160(2009)76-94 cases the meaning captured by fuzzy sets is not too sensitive to the variations in the shape [22]. In practice, triangular, trapezoid, Gaussian, S-function, and exponential-like functions are the most commonly used membership functions Moreover, in practice, a suitable membership function,s shape is assumed a priori and its parameters are determined by domain experts or using machine learning techniques [22]. The former approach, i.e. domain analysis and expertise, is used in this research For an item described with multiple attributes, more than one attribute can be used for recommendation. Some attributes can also be multi-valued involving overlapping or non-mutually exclusive possible values. One should note that, movies are multi-genres and multi-actors 3]. The values of multi-valued attributes in an item can be represented more accurately within a fuzzy set framework than within a crisp set framework. Items of this type are considered in his research. Moreover, the representation scheme presented for a movie can be generalized and applied to any item with similar characteristics to a movie. A few examples are music, TV shows, restaurants and books Let an item lj(=l,..., M) be defined in the space of an attribute X=(x1, x2, x3,...,L then Ij can take multiple values such as x1, x2,..., and xL. The membership function of item; to value xk(k=l,., L), denoted by Axg(j), needs to be determined. Hence, a vector Xj=I(xk, Hx(lD)),k=l,., L is formed for Ij, where ux(Ij) can be interpreted as the degree of similarity of lj to a hypothetical (or prototype) pure xk type of the item; or as the degree of presence of value xk in item I In a movie marketing application, most movies are selected for pleasure and expenditure of time. Users choose movies they like and enjoy. Furthermore, users use subjective features of movies such as"funny", "romantic", and ary"(all are kinds of movie genres )to select movies more than objective features such as the director, theatre location and price, which are useful but are less important [10]. We use the movie as an item and movie genre as the attribute to make the method operational and develop the heuristic. Analysis of descriptions of main film genres shows that genre gl of movies(e.g. action)and genre g2 of movies(e.g adventure)are overlapping in terms of their subject matter and other movie attributes [3]. Based on the result of the findings in [10), movies highly liked by users can be grouped into similar categories by subjective features of movies such as genre and MPAA rating. This assertion is also verified in Section 5 using the movie dataset. Indeterminingthegenrecontentofamovie,weuseaheuristicbasedonthegenres'rankordersavailableinImDb.com and provided by the movie producers, instead of the crisp representation-the genre is presence(1)or absence(0) data value. An ideal technique is automatic content analysis of a movie for automatic identification of its genres. The automatic content analysis of a movie for automatic identification of its genres will provide the extent or degree of presence or amount of a genre in a movie. For example, amount of dramatic feature in a movie A, amount of action features in a movie A, etc. However, automatic content analysis technologies are not yet well developed and available. For example, a preliminary research on the automatic identification of movie genres by exploiting audio-visual cues in a movie is reported in[26] In the absence of this technique, we conduct the domain analysis based on the literature in movies [ 3, 26] and the available data provided by movies producers in the movie database. Given the definition of a movie in the space of genre(G), a movie can have one major genre denoted by xI and one or more minor genres x2, x3, and so on, in the decreasing order of their degrees of presence in a movie. The degree of membership of movie lj(=l,., M)to genre xk(k= l,..., N)is denoted by px(j). Hence, for Ij, a vector Gj=((xk, H(D)),k=l,., N can be formed. The following steps are taken in the development of the heuristic for the determination of the membership function pn(j) +Step1:SortxkindescendingorderoftheirdegreeofpresenceinIj.InImDb(wWw.Imdb.com')thegenresof ovie lj are presented in the order of their significance. For example, movie'King Kong(2005)has Action as a major and Adventure as the first minor, Drama as the second minor, Fantasy as the third minor, and Thriller as the 2: Assign higher degrees of membership value to more important genres of a movie. For instance, If Ij has only one genre, then un (lj)=l and un(j)=0 for all k= 2 to N If lj has two genres, then ux(j)=0.9, ux(j)=0.4 and Ax(j)=0 for all k=3 to N If lj has three genres, then Px (j)=0.7 and Hx (j)=0.5,un(j)=0.2 and un(j)=0 for all k=4 to N: and so on I"imdbHistory"vol.2004:IntemetMovieDatabaseInc.,n.d.(http://www.imdb.com/)
80 A. Zenebe, A.F. Norcio / Fuzzy Sets and Systems 160 (2009) 76–94 cases the meaning captured by fuzzy sets is not too sensitive to the variations in the shape [22]. In practice, triangular, trapezoid, Gaussian, S-function, and exponential-like functions are the most commonly used membership functions. Moreover, in practice, a suitable membership function’s shape is assumed a priori and its parameters are determined by domain experts or using machine learning techniques [22]. The former approach, i.e. domain analysis and expertise, is used in this research. For an item described with multiple attributes, more than one attribute can be used for recommendation. Some attributes can also be multi-valued involving overlapping or non-mutually exclusive possible values. One should note that, movies are multi-genres and multi-actors [3]. The values of multi-valued attributes in an item can be represented more accurately within a fuzzy set framework than within a crisp set framework. Items of this type are considered in this research. Moreover, the representation scheme presented for a movie can be generalized and applied to any item with similar characteristics to a movie. A few examples are music, TV shows, restaurants and books. Let an item Ij (j = 1,... ,M) be defined in the space of an attribute X = {x1, x2, x3,...,xL}, then Ij can take multiple values such as x1, x2,..., and xL. The membership function of item Ij to value xk(k = 1, . . . , L), denoted by xk (Ij ), needs to be determined. Hence, a vector Xj = {(xk, xk (Ij )), k = 1,..., L} is formed for Ij , where xk (Ij ) can be interpreted as the degree of similarity of Ij to a hypothetical (or prototype) pure xk type of the item; or as the degree of presence of value xk in item Ij . In a movie marketing application, most movies are selected for pleasure and expenditure of time. Users choose movies they like and enjoy. Furthermore, users use subjective features of movies such as “funny”, “romantic”, and “scary” (all are kinds of movie genres) to select movies more than objective features such as the director, theatre location and price, which are useful but are less important [10]. We use the movie as an item and movie genre as the attribute to make the method operational and develop the heuristic. Analysis of descriptions of main film genres shows that genre g1 of movies (e.g. action) and genre g2 of movies (e.g. adventure) are overlapping in terms of their subject matter and other movie attributes [3]. Based on the result of the findings in [10], movies highly liked by users can be grouped into similar categories by subjective features of movies such as genre and MPAA rating. This assertion is also verified in Section 5 using the movie dataset. In determining the genre content of a movie, we use a heuristic based on the genres’ rank orders, available in IMdb.com and provided by the movie producers, instead of the crisp representation—the genre is presence (1) or absence (0) data value. An ideal technique is automatic content analysis of a movie for automatic identification of its genres. The automatic content analysis of a movie for automatic identification of its genres will provide the extent or degree of presence or amount of a genre in a movie. For example, amount of dramatic feature in a movie A, amount of action features in a movie A, etc. However, automatic content analysis technologies are not yet well developed and available. For example, a preliminary research on the automatic identification of movie genres by exploiting audio-visual cues in a movie is reported in [26]. In the absence of this technique, we conduct the domain analysis based on the literature in movies [3,26] and the available data provided by movies producers in the movie database. Given the definition of a movie in the space of genre (G), a movie can have one major genre denoted by x1 and one or more minor genres x2, x3, and so on, in the decreasing order of their degrees of presence in a movie. The degree of membership of movie Ij (j = 1,... ,M) to genre xk (k = 1,...,N) is denoted by xk (Ij ). Hence, for Ij , a vector Gj = {(xk, xk (Ij )), k = 1,...,N} can be formed. The following steps are taken in the development of the heuristic for the determination of the membership function xk (Ij ). Step 1: Sort xk in descending order of their degree of presence in Ij . In IMDB (www.imdb.com 1 ) the genres of movie Ij are presented in the order of their significance. For example, movie ‘King Kong (2005)’ has Action as a major genre, and Adventure as the first minor, Drama as the second minor, Fantasy as the third minor, and Thriller as the fourth minor genres. Step 2: Assign higher degrees of membership value to more important genres of a movie. For instance, If Ij has only one genre, then xk (Ij ) = 1 and xk (Ij ) = 0 for all k = 2 to N. If Ij has two genres, then xk (Ij ) = 0.9, xk (Ij ) = 0.4 and xk (Ij ) = 0 for all k = 3 to N. If Ij has three genres, then xk (Ij ) = 0.7 and xk (Ij ) = 0.5, xk (Ij ) = 0.2 and xk (Ij ) = 0 for all k = 4 to N; and so on. 1 “IMDb History,” vol. 2004: Internet Movie Database Inc., n.d. http://www.imdb.com/.