A fuzzy content-based group recommender system with dynamic selection of the aggregation functions

A fuzzy content-based group recommender system with1 dynamic selection of the aggregation functions2 Raciel Yeraa, Ahmad A. Alzahranib, Luis Martíneza,∗ 3 aComputer Science Department, University of Jaén, Jaén, Spain4 bFaculty of Computing and Information Technology, King Abdulaziz University, Jeddah,5 Saudi Arabia6 Abstract7 Recommender systems are currently software tools that are focused on providing users with the best choices in an overloaded search space of possible options. Hence, group recommender systems have recently become an important trend in recommendation, because they aim at recommending a special type of items so-called social items, that tend to be consumed in groups such as TV programs, travel packages, etc. Among the different types of algorithms applied for group recommender systems, this paper is focused on content-based group recommender systems, as a novel group recommendation paradigm that exploits item features in the recommendation generation process. Specifically, our goal is to introduce a new content-based group recommendation approach, based on the recommendation aggregation paradigm whose main novelty is the development of a dynamic selection process of the aggregation scheme. Such an approach is centered on the identification of group’s characteristics that are matching with the most appropriate function to use in the individual recommendation aggregation step. To perform such a matching, it is proposed a fuzzy decision tree induction process. The experimental evaluation shows that this scheme improves the recommendation performance of previous content-based group recommendation approaches, as well as it serves a starting point for further research based on this dynamic selection paradigm. Keywords: content-based recommendation,group recommender systems,8 dynamic aggregation selection,machine learning9 1. Introduction10 Recommender systems (RSs) are currently important tools in online11 scenarios, focused on providing suggestions to users with items that best fit12 their preferences and needs, in an overloaded product search space of possible13 options (Adomavicius & Tuzhilin, 2005; Francesco Ricci, 2015; Yera &14 Martínez, 2017a). Considering their working principles, RSs have been widely15 used in several and diverse domains, such as e-commerce (Baltrunas et al.,16 ∗Corresponding author Email addresses: [email protected] (Raciel Yera), [email protected] (Ahmad A. Alzahrani), [email protected] (Luis Martínez) Preprint submitted to Elsevier June 17, 2022 Originally published at: Yera, R., Alzahrani, A. A., & Martínez, L. (2022). A fuzzy content-based group recommender system with dynamic selection of the aggregation functions. International Journal of Approximate Reasoning, 150, 273-296. 2011), e-learning (Yera & Martínez, 2017b), e-health (Yera et al., 2019), or17 e-tourism (Nilashi et al., 2015).18 Two main directions have driven the development of RSs. At first, the19 content-based recommendation paradigm (Lops et al., 2011) is focused on20 recommending to the active user items which have similar characteristics to21 other items previously preferred by the same user. This paradigm is then22 mainly focused on user and item profiling for reaching a more representative23 matching between them. On the other hand, the collaborative filtering24 paradigm (Ekstrand et al., 2011) is focused on recommending to the current25 user items which are preferred by other users similar to the active one.26 Specifically, collaborative filtering methods can be classified in27 neighborhood-based or model-based methods (Adomavicius & Tuzhilin, 2005).28 These recommendation paradigms have been usually used to build RSs for29 providing suggestions to individual users. However, in the last few years,30 several kind of items that tend to be consumed by groups, have appeared in31 recommendation contexts (Castro et al., 2018b; Dara et al., 2020). As example32 of such items, can be cited movies and touristic routes (De Pessemier et al.,33 2015a; Quijano-Sanchez et al., 2014). The recommendation of such items34 requires an additional effort in relation to individual recommendation, because35 it should manage the preferences both at the individual and the group level.36 Such a requirement has made the development of group recommender systems37 (GRSs) as an independent research branch in RS field (De Pessemier et al.,38 2014).39 Basically, GRSs are centered on aggregating the information associated to40 the group members (De Pessemier et al., 2014). Such an aggregation can be41 done by recommendation aggregation, in which first it is computed individual42 recommendations for every group member, and then such recommendations are43 combined through a recommendation aggregation approach. Alternatively, a44 preference aggregation can also be used, where it is created a pseudo-user that45 globally represents the preferences of the group and such a pseudo-user profile46 is used for computing the group recommendation.47 Using previous schemes, several research works have been focused on48 proposing new GRSs approaches, having as common characteristic the use of a49 collaborative filtering approach as a core of the recommendation method50 (Castro et al., 2015, 2017; Seo et al., 2018; Wang et al., 2018; Cui et al., 2020;51 Yalcin et al., 2021), motivated by the advantages related to collaborative52 filtering, in relation to the ability of generating recommendations using only53 rating values. However, a well-documented shortcoming of collaborative54 filtering is the poor performance in highly sparse recommendation scenarios55 including cold-start (Son, 2015), considering that it depends on the presence56 on items co-evaluated by several users for a proper performance. In contrast,57 content-based group recommender systems (CB-GRSs, including the proposal58 developed at the current work), usually obtain a greater success in such59 scenario, considering that it is different from collaborative filtering because60 they only depend on the current user preference data and the attributes’61 information associated to the available items.62 2 Nevertheless, the recent research literature reflects too few efforts for63 boosting the use of CB-GRS. De Pessemier et al. (2014), in one of the firstly64 documented surveys on GRS, slightly mentioned and evaluated an alternative65 for group recommendation supported by item features for predicting user66 preferences. However, this work is mainly focused on comparing social-choice67 based group recommendation algorithms, and therefore do not perform an68 in-depth analysis of the specific content-based scenario. Furthermore, the69 architecture of a content-based recommendation algorithm has been screening70 by Felfernig et al. (2018), but again such presentation lacks of a detailed71 analysis of each component and experimentation. Recently, Pérez-Almaguer72 et al. (2021) have discussed three basic design alternatives for building73 CB-GRSs, that consider the aggregation paradigm (preferences-driven or74 recommendations-driven), the way of aggregating recommendations75 (ranking-based or similarity-based), the social choice-based schemes to76 perform aggregation (e.g. average, least misery, most pleasure), and other77 relevant design decisions. That work also explores the possible hybridization78 between some of the presented schemes. In addition, other research works have79 also exploited the content-based dimension in group recommendation, with a80 greater or lesser extent (Pera & Ng, 2013; Kaššák et al., 2016).81 This lack of works in CB-GRS in spite of its promising but not achieved82 great performance, evidences the necessity of developing more sophisticate83 approaches for CB-GRS, in order to obtain a better recommendation84 performance. This paper aims at proposing a new CB-GRS scheme centered85 on taking benefits of the nature of the data, for improving the86 recommendation performance. Particularly, we are interested in proposing a87 dynamic aggregation process, in the recommendation aggregation step in88 CB-GRS, that will choose an appropriate aggregation function according to89 the group’s characteristics.90 According to the Cambridge Dictionary, the word dynamic 1is related to a91 continuous changing or developing. In this case, we have used the dynamic tag92 in our proposal, to make reference to the nature of the function used to aggregate93 the preference of the member of the groups. In this way the selected function,94 used with this goal, will be continuously changing based on the characteristics95 of the current group.96 Considering that the aggregation process can produce loss of information97 (De Pessemier et al., 2014), the choice of the appropriate aggregation function98 can lead to decrease the information loss and consequently improving the99 recommendation performance.100 In this direction, this research is driven by the following problem definition:101 Given a set Gof groups of users and a specific group c, find the most102 appropriate function fto aggregate individual preferences in the103 recommendation aggregation step inside the group, which leads to the better104 recommendation performance in a CB-GRS framework.105 1https://dictionary.cambridge.org/dictionary/english/dynamic 3 Focused on this research problem, the main contributions of our proposal106 are:107 •A new CB-GRS approach that introduces a component for the dynamic108 selection of the recommendation aggregation function for composing109 group recommendations. This component will receive the current group110 features, and returns the most suitable aggregation function for such a111 group characterization.112 •The inner modeling of the dynamic selection component, done as a113 supervised classification scenario using classification rules. Such114 classification rules are obtained by a fuzzy classification tree using the115 ID3 algorithm (Umanol et al., 1994; Kantarci & Nasibov, 2018). From a116 machine learning perspective, our proposal can be seen as a117 meta-learning approach.118 •An exploratory study of group’s features in CB-GRS, such as amount of119 ratings, minimum user’s correlation, or amount of co-rated items, that120 could contribute to a better characterization of groups and therefore121 improving their recommendations.122 •An experimental study in order to evaluate the proposal, in contrast to123 previous baselines.124 The paper is structured as follows. Section 2 presents the necessary125 background for the proposal presentation, including content-based126 recommendation, group recommendation, and previous works in content-based127 group recommendation. Section 3 introduces the new CB-GRS proposal,128 supported by the dynamic selection of the aggregation function. Subsequently,129 a case study is also presented to show how the proposal works (Section 4).130 Furthermore, Section 5 is focused on evaluating the proposal, discussing the131 main findings and pointing out future works. Section 6 concludes the paper.132 2. Background133 This section is focused on presenting some concepts that are necessary for134 the later proposal presentation. This content involves fundamentals on content-135 based recommendation and group recommender systems. At last, a related136 works section on CB-GRS will be briefly introduced.137 2.1. Content-based recommendation138 Since 90s, content-based recommender systems has been widely used as one139 of the most popular recommendation approaches (Adomavicius & Tuzhilin,140 2005). Here the recommendation process is composed of the following steps141 (see Figure 1) :142 4 Figure 1: General scheme of content-based recommendation •The first step in content-based recommendation comprises the143 construction of an item profile Content(i), that is represented by a set of144 features that can be explicitly or implicitly associated to the item i. A145 key example of explicit features, can be genre, director, country or year,146 in a movie recommendation scenario. On the other hand, implicit147 features are usually identified with techniques such as the latent148 semantic analysis (LSA), in domains such as news or question-answering149 item recommendation (Castro et al., 2019). In such an scenario, the150 TF-IDF approach is usually used for managing the free-text items.151 Specifically, such a text is converted into structured data stemming152 words, and after that, a vector of weights of each term is generated,153 according to the TF-IDF scheme. Finally, techniques such as LSA are154 applied for a most precise item representation (Lops et al., 2011).155 •The second step of any content-based recommender systems is the user156 profiling. Usually, this profile ContentBasedP rofile(u)is built by fusing157 the profiles of all the items preferred by the active user u. Several158 strategies have been proposed for performing such a fusion, including the159 use of computational intelligence techniques Adomavicius & Tuzhilin160 (2005); Lops et al. (2011).161 •Both previous profiles are used to calculate the utility of item ifor user162 u. Such utility v(u,i) = score(ContentBasedP rofile(u),Content(i)) is163 usually represented with a similarity measure such as cosine (Adomavicius164 & Tuzhilin, 2005). In this way, cosine metric has been used for comparing165 profiles linked to the vector space model (e.g. keywords-based profiles,166 term-based profiles), usually related to content-based recommendations167 (Adomavicius & Tuzhilin, 2005; Pazzani & Billsus, 2007; de Gemmis et al.,168 2015). More complex approaches focused on semantic similarity have been169 also incorporated (Pera & Ng, 2014), however their application depends170 on further knowledge sources (e.g. ontologies, linked open data cloud,171 etc), which incorporation goes beyond the current proposal of this work172 that is the screening of a new CB-GRS approach.173 •Finally, the top-n items with the higher utility, will be suggested for the174 active user u.175 Most of research works on recommender systems have been focused on176 individual users. However, since the last decade there is an increasing in the177 5 Figure 2: Group recommendation based on rating aggregation Figure 3: Group recommendation based on recommendation aggregation interest over group recommender systems (GRSs) as a novel recommendation178 scenario. The next section is focused on briefly presenting the fundamentals of179 GRSs.180 2.2. Group recommender systems181 The appearing of GRSs has been coupled with the need of recommending182 some items that are usually consumed in groups, such as movies, touristic routes,183 or TV programs (Castro et al., 2018c; De Pessemier et al., 2014). In such cases,184 it is necessary to recommend items that maximize the overall satisfaction of185 the group. With this goal in mind, GRSs extend individual RS, by taking into186 account the aggregation of information related to each individual group member.187 The literature identifies two main paradigms in group recommendation,188 based on the nature of the information aggregation approach (De Pessemier189 et al., 2014):190 •Rating aggregation: This approach combines the preferences of the191 individual users, to build a pseudo-user profile that is later used as a192 typical user profile to receive recommendations that in this case are193 delivered to the group (Figure 2).194 •Recommendation aggregation: This approach at first generates individual195 recommendations for each member of the group. Such individual196 recommendations are then aggregated to composed the final197 recommendation list for the group (Figure 3).198 The following subsection will present in further detail a recent GRS model199 built over the content-based recommendation paradigm (Pérez-Almaguer et al.,200 2021), which will be used as starting point for the proposal developed at the201 current paper.202 6 Term Meaning uUser iItem GGroup fi kValue of the feature kfor item i fu kValue of the feature kfor user u fG kValue of the feature kfor group G Vk={vk 1,vk 2,vk 3,...,vk p}Possible values of the feature kin the item profile, for multivalued features vki Value of the feature kin the item i, for multivalued features vku ppth value of the feature kfor the user u, for multivalued features topuList of top n recommendations for user u Sui Matching value between user uand item i SG iMatching value between group Gand item i IGTop k items recommended to the group G Table 1: Relevant notation Figure 4: CB-GRS based on recommendation aggregation and user-item matching values 2.2.1. CB-GRS based on recommendation aggregation and user-item matching203 values204 This section describes in further detail, the CB-GRS approach based on205 recommendation aggregation and user-item matching values, initially206 presented at Pérez-Almaguer et al. (2021), where it was evidenced that it is207 able to outperform other GRS models including collaborative filtering-based.208 Table 1 presents the notation used across this section. This basic209 content-based group recommendation model (Figure 4) is composed of four210 phases: 1) Item modeling, 2) User modeling, 3) User-item matching value211 calculation, and 4) Matching value aggregation for obtaining the top k items212 for the group.213 Item modeling: In a similar way to the typical content-based214 recommendation, this step is focused on representing the items to be215 recommended, through the modelling of a feature vector (Fig. 4). Considering216 that the information associated to items can be represented through different217 formats, here it will be considered two ways for modeling items:218 1. A basic approach that considers a binary profile that contains 1 whether219 the item has the corresponding feature, and 0 whether the item does not220 contain it. Formally, items are represented as the vector i= (fi 1,fi 2,...,fi m),221 where fi k= 1 whether the feature kis associated to the item i, and fi k= 0222 7 otherwise.223 2. A more sophisticated approach that considers multivalued features (Castro224 et al., 2014). In this case, items are also represented as the vector i=225 (fi 1,fi 2,...,fi m), but here fi kis associated to nominal or numeric values, in226 a domain associated to the feature k(Castro et al., 2014).227 User modeling: In a similar way to items, here it will be considered two228 approaches for user modeling.229 1. An approach based on TF-IDF (Aizawa, 2003), considering the preferred items. This approach assumes a binary item profile, and here users are represented through a vector u= (fu 1,fu 2,...,fu m).fu kis defined as: fu k=FF(u,k)∗IUF(k)(1) where FF(u,k)is calculated as the number of items ipreferred by the230 user u, having fi k= 1 where iis any item profile built in the previous item231 modeling phase. On the other hand, IUF (k) = log |U| UF (k), being UF (k)232 the number of users that have preferred any item that has the feature k,233 and |U|the total number of users.234 2. An approach that assumes the presence of multivalued features (Castro235 et al., 2014), having the presence of nominal or numeric values in the item236 features. In this scenario, it is necessary a new formulation of the user237 profile (Eq. 2).238 fu k={(vk 1,frvku 1 ),(vk 2,frvku 2 ),(vk 3,frvku 3 ),...,(vk p,frvku p)}, if k is qualitative average(fi k)for each item i preferred by u, if k is quantitative (2) For items associated to qualitative features, fu kis formalized as a set of239 pairs (value, frequency) composed of each one of the possible values vk pof240 the feature k, and the frequency frvku pof such value at the feature kin241 all the items preferred by the user u.242 In the case of quantitative features in the items, fu kwill be the average of243 all the values associated to the feature, for all items preferred by the user244 u.245 User-item matching value calculation: Subsequently, the current246 content-based GRS requires the calculation of the matching degree between247 the corresponding user and item profile (Castro et al., 2014). Depending on248 the presence of a binary user profile or multivalued features, a different249 approach will be used:250 1. For the binary item profiles, it will be directly used the cosine similarity function between the user and item profiles uand i(Eq. 3) 8 (Adomavicius & Tuzhilin, 2005), as the reference metric for content-based recommendation (see Section 2.1). Sui =Pu,i fu k∗fi k q(fui k)2q(fi k)2 (3) 2. In the case of the items with multivalued features, at first it is necessary to251 define the matching value between users and items, but in the context of a252 specific feature k(Eq. 4). For qualitative features, this value is calculated253 as frvk, being vthe associated key in the list of pairs at fu k, as well as254 the value at fi k. For quantitative features, this value is calculated as the255 inverse of the difference between fu kand fi k.256 Sk ui =(frvk, for k qualitative 1 |fu k−fi k|, for k quantitative (4) Such matching values are normalized independently for the qualitative257 and quantitative scenarios. The matching values are then denoted as Sk∗ ui .258 At last, the overall matching value between the user uand item iis259 calculated as the average matching value of all the features (Eq. 5),260 being Kthe set of item features:261 Sui =Pk∈KSk∗ ui |K|(5) Matching value aggregation for obtaining the top k items for the262 group: In the next step, the method depends on an aggregation function to263 obtain the matching values associated to all the group’s members, and each item264 in the dataset.265 The popular Average and Minimum aggregation functions will be266 considered in this scenario (De Pessemier et al., 2014), which have been267 reported in previous research in GRS as the aggregation measures that lead to268 a better performance regarding typical alternatives (Castro et al., 2017,269 2018b), and specifically focused on CB-GRS (Pérez-Almaguer et al., 2021).270 Furthermore, more sophisticated aggregation measures such as those recently271 discussed by Yalcin et al. (2021) will be explored in the next future. However,272 they are out of the scope of this work.273 The Average and Minimum aggregation functions are formalized as follows:274 1. Average: It calculates the average matching value for all the users in the group, being nthe number of users. SG i=Pu∈GSui n(6) 9 •Execute twice the core content-based GRS already presented at470 Section 2.2.1 for the current group and sampled dataset, initially471 using the average aggregation and at second using minimum472 aggregation.473 •Compare both recommendation approaches according to some474 specific evaluation method. In this case, it will be used the475 precision metric which has been an appropriate metric for476 characterizing content-based GRS, according to the most recent477 literature (Pérez-Almaguer et al., 2021). In the future, other478 metrics such as NDCG, or even a multicriteria approach479 simultaneously considering several metrics, will be developed.480 •Finally, the class of the current group is tagged as the aggregation481 scheme (average or minimum) that performs best according to the482 evaluation metric. Future works will also consider other aggregation483 operators like the maximum aggregation in this context484 (De Pessemier et al., 2014). However, we discard it at this moment485 because it leads to poor recommendation performance in recent486 evaluations done by the literature (Pérez-Almaguer et al., 2021).487 Overall, this phase retrieves as output a dataset containing several group488 profiles, each one characterized by their associated attribute values.489 Furthermore, each group is also linked to a class value that represents the490 aggregation function that leads to the best recommendation performance (i.e.491 average or minimum). This dataset is used as input for the next phase of the492 proposal, which is the fuzzy decision tree induction.493 3.2. Fuzzy decision tree induction494 Here, it is presenting the fuzzy decision tree induction process, made in this495 case over the group characterization, built in the previous step.496 This phase assumes Das fuzzy set, that is characterized by a membership497 value for each group Gin the dataset. (Initially with membership 1 for all498 groups, at the root of the tree). Furthermore, each group is represented by499 four numerical values respectively for attributes Ai∈ {M,A,C,AV }, and one500 class Ck∈ {Average,Minimum}(see Section 2.2.1 for justifying the classes501 selection). In addition, assumes DCkas a fuzzy subset of D, where µDCk(G) =502 µD(G)if the class of Gis Ck, and µDCk(G) = 0 otherwise. Finally, |DCk|is the503 cardinality of the fuzzy set DCk, defined as the sum of the membership value504 of each associated object (Umanol et al., 1994).505 In the current scenario, it is considered that each attribute Ai, always506 represented by numerical values, will be characterized by three triangular507 fuzzy sets low,medium, and high (Figure 8). More complex fuzzy508 representations could be also used, for modeling this membership. Therefore,509 each group is then characterized by the membership values for each mentioned510 fuzzy sets, considering each of the four attributes (Table 3).511 The algorithm for constructing the fuzzy decision tree is then as follows:512 16 g1(µM,low(g1),µM,medium(g1),µM,high(g1),µA,low (g1),µA,medium(g1),µA,high(g1), µC,low(g1),µC,medium(g1),µC,high(g1),µAV,low (g1),µAV,medium(g1),µAV,high(g1)) g2(µM,low(g2),µM,medium(g2),µM,high(g2),µA,low (g2),µA,medium(g2),µA,high(g2), µC,low(g2),µC,medium(g2),µC,high(g2),µAV,low (g2),µAV,medium(g2),µAV,high(g2)) ... ... Table 3: Representation of each group, using the four attributes and the corresponding fuzzy sets low,medium, and high. Figure 8: Membership functions 1. Initially build the root node which is composed of all the data, and then513 is represented as a fuzzy set with all the objects having 1 as membership514 value.515 2. If a candidate node t with a fuzzy set of data Dverifies:516 (a) If the relative frequency of some class Ck∈Average,Minimum in the dataset is over some threshold θr: |DCk| |D|≥θr(13) (b) Or the cardinality of the dataset is under a given threshold: |D| ≤ θn(14) (c) Or there are no attributes for more classification517 17 Then it is a leaf node and the weight of each class in this leaf is assigned518 as the cardinality |DCk|of the corresponding class Ckin such node.519 3. Otherwise, the new decision node is constructed as follows, by selecting the attribute that maximizes the information gain G(Ai,D). Therefore, for each attribute Ai∈ {M,A,C,AV }not considered before, calculate the information gain G(Ai,D)(Eqs 15-19) and select the attribute Amax that maximizes it: G(Ai,D) = I(D)−E(Ai,D)(15) where, I(D) = − n X k=1 (pk∗log2pk)(16) E(Ai,D) = m X j=1 (pij ∗I(DAi,j)) (17) pk=|DCk| |D|(18) pij =|DAi,j| Pm l=1 |DAi,l|(19) Here I(D)at Eq. (16) is the total entropy of certain dataset D, while520 E(Ai,D)at Eq. (17) is the fuzzy classification entropy of the attribute521 Ai.pkis the relative frequency of the class Ckin the dataset, and pij is522 the relative frequency of all objects within the branch associated to the523 corresponding linguistic label jand attribute Ai, into each class. DAi,j is524 the fuzzy subset which membership is represented by the linguistic term525 j∈ {low,medium,high}linked to the group attribute Ai∈ {M,A,C,AV }.526 4. Once the attribute Amax that maximizes the information gain is chosen,527 the decision node Dis divided into three fuzzy subsets528 DAmax,low ,DAmax,medium ,DAmax,high according to such attribute,529 each subset for each linguistic label that characterizes such attribute.530 The membership value of each group gto DAmax,j 531 (j∈ {low,medium,high}), is then the product of the membership value532 of gto D, and the value µAmax,j (g)associated to Amax in D.533 5. Generate new nodes t1,t2,t3for fuzzy subsets534 DAmax,low ,DAmax,medium ,DAmax,high , labelling with each corresponding535 linguistic term j∈ {low,medium,high}, to each edge that connect them536 with D.537 6. For each fuzzy subset DAmax,low ,DAmax,medium ,DAmax,high , repeat538 recursively this algorithm from step 2.539 18 Once the fuzzy decision tree is generated, it will be used in the next phase of540 the proposal as the base of the fuzzy rules building and classification processes.541 3.3. Fuzzy rules building and classification542 Once the fuzzy decision tree is built, their branches lead to the creation of543 decision rules which are directly used for classification. The rules are544 formulated as follows, considering for every branch all the associated attributes545 and linguistic terms at the nodes from the root, to the leaf of the branch.546 Rule R =If Ai1is j1and ... and If Ain is jn then Class =Ckwith weight Wk (20) Here Ai1∈ {M,A,C,AV }is an attribute used for identifying groups, and547 j1∈ {low,medium,high}is a linguistic term for representing the corresponding548 fuzzy set for characterizing such attribute, linked to the corresponding path in549 the inferred decision tree. Ck∈ {Average,Minimum}is the class label in the550 leaf node. Wkis the weight of the leaf node, calculate through the addition of551 the membership of all objects of class kat this node.552 In this context, and assuming a new group g, the fuzzy classification is553 performed as follows:554 1. Matching degree: Here, the activation degree of the if part for a rule R, with the group g, is calculated as: µR(g) = T(µAi1,j1(g),µAi2,j2(g),...,µAin,jn (g)) (21) where µAi,j (g)is the membership degree of the value of the555 Ai∈ {M,A,C,AV }attribute of the example gwith the fuzzy set556 associated to the same attribute Aiand the linguistic term557 j∈ {low,medium,high}, at the corresponding antecedent of the rule R.558 Tis a T-norm (Pedrycz, 1993).559 2. Association degree: The degree of the association of the group gwith each rule Rat the rule base and for the class kis computed as: bRk(g) = T(µR(g),Wk)(22) where Wkis the weight of the rule Rfor the class k(i.e. the rule weight,560 see Eq. 20). Tis a T-norm (Pedrycz, 1993).561 3. Confidence degree: Finally, the confidence degree of each class is calculated by aggregating the association degrees of the rules of that class through the use of an operator T∗, being a T-conorm (Pedrycz, 1993):. confk(g) = T∗(b1k(g),b2k(g),b3k(g),...,bRk(g)) (23) Here bRk(g), is the association degree of the group gto the class k562 according to the rule R.563 19 The group gis then classified as the class kwith the highest confidence564 degree confk(g), considering all the rules identified at the decision tree565 induction process.566 Section 4 will demonstrate the use of the procedure presented here, in a GRS567 scenario.568 3.4. Algorithmic overview of the approach569 As summary, Algorithm 1 presents an overview of the current approach,570 receiving as input the set of groups Gat the GRS, and the current group cfor571 finding the most appropriate aggregation function, which is the output of the572 approach.573 At first, Lines 4-12 are focused on the dataset building phase, calculating for574 each group the values of the four attributes for characterizing them, as well as575 the aggregation function that performs better in a recommendation generation576 process. Finally, a tuple with this information is added to a dataset D(Line577 12) that is used in the subsequent stages of the method.578 Furthermore, Line 13 obtains the fuzzy decision tree Tusing such dataset579 D. Subsequently, such tree is used for building the classification rules that will580 allow to obtain, for any group of users characterized by the four mentioned581 attributes, the most appropriate aggregation function to be used (Lines 14-16).582 Finally, such set of rules is used for finding the referred aggregation function583 for the current group c(Line 17), retrieving it as the output of the method (Line584 18).585 Algorithm 1 has presented all the phases of the proposal in order to expose586 a compact overview of its working principle. However, it is also worthy to note587 that in practice, the dataset building, tree induction, and rules building phases588 (Lines 4-16) can be executed previously in an offline stage, and stored the rules589 set R. In this way, in the real-time recommendation generation for a specific590 group c, it would be directly executed the fuzzy classification step (Line 17),591 using the stored rules set.592 In the next sections it will be presented a case study and the evaluation of593 an experimental protocol associated to the current proposal.594 4. Case study595 This subsection develops and describes a case study showing how the596 algorithm presented in the previous subsection can be used for the dynamic597 selection of the most appropriate function for individual recommendation598 aggregation.599 4.1. Fuzzy decision tree induction600 At first, Table 4 presents a dataset that can be obtained through the601 methodology at Section 3.1, that contains five groups. In this case, for602 simplicity it is composed of 3 attributes which are minimum correlation603 20 Algorithm 1 Algorithmic overview of the approach 1: procedure Fuzzy CB-GRS(a,b) 2: Input: c-currentGroup, G-set of groups 3: Output: selectedAggFunctionAggregation function to be used in the current group 4: for all group g in G do 5: Mg= MinimumCorrelation(g) 6: Ag= AmountGroupR(g) 7: Cg= CoRated(g) 8: AVg= RatingAverage(g) 9: Calculate recommendation performance with average preference aggregation for group g 10: Calculate recommendation performance with minimum preference aggregation for group g 11: Assign Classgas the aggregation scheme that performs better 12: Add tuple (Mg,Ag,Cg,AVg,Classg) to the dataset D 13: T=ObtainFuzzyDecisionTree(D) 14: for all path p from root to the leaves nodes in T do 15: Build the associated classification rules r 16: Add r to the rules set R 17: selectedAggFunction= Rule-basedClassifier(R, c) 18: return selectedAggFunction (MinCorr, i.e. M), amount of ratings in the group (AmountGroupR, i.e. A)604 and average amount of co-rated items across users (Co-RatedAvg, i.e. C). Two605 classes are considered, the average aggregation and the minimum aggregation606 (Avg, and Min). In the next future it will be additionally considered more607 sophisticated aggregation schemes such as the Additive Utilitarian hybridized608 with the Approval Voting (Yalcin et al., 2021), as well as the Agreement609 without Uncertainty approach (Yalcin et al., 2021). However, they are out of610 the scope of this work.611 Table 4 shows the value of each attribute at the five objects. Furthermore,612 it contains the membership value of each object, to the three previously613 mentioned fuzzy sets Alow,Amedium,Ahigh, for each attribute A(referred at614 the previous Section 3.2). Subsequently, in this section is developed the615 decision tree induction associated to such dataset, which is presented in Figure616 9. Furthermore, as parameters it is considered θr= 0.9, (i.e. a node is not617 expanded when the cardinality of some class over the total cardinality exceeds618 0.9); and θn= 0.01, (i.e. a node is not expanded when its fuzzy cardinality in619 under 0.01). We use this value for θnfor guaranteeing the generation of a620 decision tree as large as possible, with demonstrative proposals. Larger values621 of θnwould lead to a less-expanded decision tree. However, they are not622 included here due to space reasons.623 Root node: Following the steps of the decision tree induction procedure624 21 MinCorr(M) AmountGroupR(A) Co-RatedAvg(C) Class g1 0.3 300 20 Avg µM,low(g1)=0.24 µA,low(g1)=0 µC,low(g1)=0 µM,medium(g1)=0.76 µA,medium(g1)=0.9µC,medium(g1)=0.9 µM,high(g1)=0 µA,high(g1)=0.1µC,high(g1)=0.1 g2 0.7 150 10 Avg µM,low(g2)=0 µA,low(g2)=0.82 µC,low(g2)=0.82 µM,medium(g2)=0 µA,medium(g2)=0.18 µC,medium(g2)=0.18 µM,high(g2)=1 µA,high(g2)=0 µC,high(g2)=0 o3 0.05 450 30 Min µM,low(g3)=1 µA,low(g3)=0 µC,low (g3)=0 µM,medium(g3)=0 µA,medium(g3)=0 µC,medium(g3)=0 µM,high(g3)=0 µA,high(g3)=1 µC,high(g3)=1 g4 0.1 120 8 Min µM,low(g4)=0.84 µA,low(g4)=1 µC,low(g4)=1 µM,medium(g4)=0.16 µA,medium(g4)=0 µC,medium(g4)=0 µM,high(g4)=0 µA,high(g4)=0 µC,high(g4)=0 g5 0.5 400 15 Min µM,low(g5)=0 µA,low(g5)=0 µC,low (g5)=0.36 µM,medium(g5)=0.62 µA,medium(g5)=0.3µC,medium(g5)=0.64 µM,high(g5)=0.38 µA,high(g5)=0.7µC,high(g5)=0 Table 4: Case study for the dynamic selection of the aggregation function presented above, at first it is considered the current root node with the five625 objects with membership µn(g)=1. Therefore, the calculation of information626 amount I(D)of such node (Eq. 16) and the information gain G(A,D)at each627 attribute A(Eq. 15), lead to the following results:628 I(D)=0.971, G(M,D)=0.2143, G(A,D)=0.2897, G(C,D)=0.1301 (24) Here the attribute that maximizes the information gain is the amount of629 ratings in the group (AmountGroupR, A). Then, according to the steps 4 and 5630 at Section 3.2, the set of objects in the current root node is divided in three fuzzy631 subsets, characterized by the membership functions associated to such attribute632 A. Three new nodes are respectively created for such subsets. At Figure 9, these633 nodes are labeled as (alow), (amed), and (ahigh).634 Node alow:Analyzing the node alow, characterized by the objects g2 635 (µn(g2) = 0.82) and g4(µn(g4) = 1). Here it is analyzed the information636 amount I(DAlow )of this node, as well as the information gain for the637 remaining attributes Mand C:638 I(DAlow )=0.993, G(M,DAlow )=0.993, G(C,DAlow )=0.0998 (25) which lead to the selection of the attribute Mat this stage.639 This leads to the expansion of the nodes (alow,mlow), (alow,mmed), and640 (alow,mhigh) (see Figure 9).641 These three nodes have only one associated object, therefore the process642 22 Figure 9: Fuzzy decision tree of the dataset at Table 4, for the dynamic selection of the aggregation function stops at this stage considering that here the cardinality of its associated class is643 1. Such nodes are then considered as leaves nodes, having as their corresponding644 classes, the class associated to their objects.645 Node amed:This node is characterized by the objects (µn(g1) = 0.9),g2 646 (µn(g2)=0.18), and g5(µn(g5)=0.3). In this node, the attributes Mand C647 are also analyzed:648 I(DAmed )=0.755, G(M,DAmed )=0.0779, G(C,DAmed )=0.0542 (26) which lead, in a similar way to node alow, to the selection of the attribute649 Mat this stage.650 This leads to the expansion of the nodes (amed,mlow), (amed,mmed), and651 (amed,mhigh) (see Figure 9).652 Here the node (amed,mlow) has only one associated object, therefore the653 process stops at this stage. On the other hand, the remaining two nodes are654 analyzed as follows.655 Node (amed,mmed): This node is characterized by two objects (g1 656 (µn(g1)=0.684),g5(µn(g5)=0.186)). It is then expanded through the657 remaining attribute C(see Figure 9), composing the three nodes658 (amed,mmed,clow), (amed,mmed,cmed), and (amed,mmed,chigh). These new659 nodes are not expanded because there are not any more attributes.660 Node (amed,mhigh): This node is characterized by two objects (g2 661 (µn(g2) = 0.18),g5(µn(g5) = 0.114)). It is then expanded through the662 23 R1if A is low and M is low, then Class=Min with W=0.84 R2if A is low and M is medium, then Class=Min with W=0.16 R3if A is low and M is high, then Class=Avg with W=0.82 R4if A is medium and M is low, then Class=Avg with W=0.216 R5if A is medium and M is medium and C is low, then Class=Min with W=0.066 R6if A is medium and M is medium and C is medium, then Class=Avg with W=0.616, and Class=Min with W=0.119 R7if A is medium and M is medium and C is high, then Class=Avg with W=0.0684 R8if A is medium and M is high and C is low, then Class=Avg with W=0.1476, and Class=Min with W=0.041 R9if A is medium and M is high and C is medium, then Class=Avg with W=0.0324, and Class=Min with W=0.073 R10 if A is high, then Class=Avg with W=0.1, and Class=Min with W=1.7 Table 5: Rules associated to the decision tree at Figure 9 remaining attribute C(see Figure 9), composing the two nodes663 (amed,mhigh,clow) and (amed,mhigh,cmed). These new nodes are not expanded664 because there are not any more attributes. The node (amed,mhigh,chigh) is665 not included because it does not contains any object with membership values666 different from zero (see Figure 9).667 Node ahigh:This node is characterized by the objects g1(µn(g1) = 0.1),668 g3(µn(g3) = 1), and g5(µn(g5)=0.7). At such node, it is verified the stop669 condition (a) at the second step of the procedure, regarding that for the class670 avg, |Davg|/|D|= 0.944 >0.9, assuming that θr= 0.9. Therefore this node is671 not expanded.672 This stage finishes the induction of the fuzzy decision tree presented at Figure673 9. According to Section 3.3, such tree leads to the rules based on the class of674 the objects at the leaves nodes, presented at Table 5675 4.2. Fuzzy classification676 Based on the rules presented at Table 5, as example it will be classified the677 group opresented at Table 6. The first row of the table presents the values of678 the attributes of the object, while the remaining rows present the membership679 values associated to the three fuzzy sets (Fig. 8) that characterize each attribute680 according to the current dataset presented at Table 6.681 Subsequently, Table 7 illustrates the three stages of the classification682 procedure at Section 3.3. At the first stage, it is calculated the matching683 degree of the object with the antecedents of the rules. At Table 7, it is only684 presented the rules with a matching degree different from 0, which are R6,R7,685 R9, and R10. Furthermore, in the next stage it is calculated the association of686 the object with the corresponding class linked to the rule. Here it is worthy to687 24 MinCorr(M) AmountGroupR(A) Co-RatedAvg(C) o 0.4 300 25 µM,low(o)=0 µA,low(o)=0 µC,low (o)=0 µM,medium(o)=0.92 µA,medium(o)=0.9µC,medium(o)=0.46 µM,high(o)=0.08 µA,high(o)=0.1µC,high(o)=0.54 Table 6: Classification example Stage 1 µR6(o)=0.46,µR7(o)=0.54,µR9(o)=0.08,µR10 (o)=0.1 Stage 2 Class Avg bR6,avg =T(µR6(o),RW avg 6) = T(0.46,0.616) = 0.46 bR7,avg =T(µR7(o),RW avg 7) = T(0.54,0.0684) = 0.0684 bR9,avg =T(µR9(o),RW avg 9) = T(0.08,0.0324) = 0.0324 bR10,avg =T(µR10 (o), RW avg 10 ) = T(0.1,0.1) = 0.1 Class Min bR6,min =T(µR6(o),RW min 6) = T(0.46,0.119) = 0.119 bR9,min =T(µR9(o),RW min 9) = T(0.08,0.073) = 0.073 bR10,min =T(µR10 (o), RW min 10 ) = T(0.1,1.7) = 0.1 Stage 3 confavg(o) = T∗(bR6,avg , bR7,avg,bR9,avg , bR10 ,avg )=0.46 confmin(o) = T∗(bR6,min,bR9,min,bR10 ,min)=0.119 classo=avg Table 7: Classification procedure note that in three of the four considered rules, there is a contribution value of688 the rule to both classes, therefore both values are individually computed at689 each individual class processing. Both stages depend on a T-norm, being used690 the min operator in this scenario.691 Finally, in the last stage at Table 7, it is calculated the confidence degree of692 each class, by using a T-conorm for joining the association degree of each rule,693 associated to each independent class. Here it is used the max operator as T-694 conorm. As final result it is reached that the avg class has a higher confidence;695 therefore the object ois classified with the avg class.696 Then, it means that the avg aggregation approach seems to be the best697 option for aggregating individual recommendations in the group characterized698 by the attributes associated to the object o.699 5. Experiments700 This section is focused on evaluating the content-based GRS presented across701 this paper. At first, they are presented the datasets (Section 5.1), the evaluation702 metric (Section 5.2), and the evaluation protocol used in the experimentation703 (Section 5.3). Subsequently, for each dataset it is presented an exploratory704 study on the values of such attributes across the datasets (Section 5.4); and it is705 then evaluated the performance of the proposal comparing it against baselines706 (Section 5.5). A discussion on the results is also included (Section 5.6), as well707 as future works to expand the current proposal (Section 5.7).708 25 Figure 16: Histogram presenting the frequency of the values for the attribute amount of corated items, across all the sampled groups in HetRec Figure 17: Histogram presenting the frequency of the values for the attribute rating average of the group, across all the sampled groups in HetRec Overall, this exploratory study suggested that the identified attributes are879 able to discriminate among groups, and that such discrimination can be useful880 for selecting the most appropriate CB-GRS approach.881 5.5. Results882 This section presents the results of the evaluation of the proposal, in both883 Movielens 100K and MovieTweeting datasets. This evaluation is focused on: 1)884 identifying the impact of the new proposal that incorporates the fuzzy decision885 tree approach, by comparing its performance with previous baselines that do886 not consider the fuzzy decision tree, and 2) measuring the performance of the887 proposal when one of the four identified group attributes (see Section 3.1) is not888 taken into account for the decision tree building. This second criteria contribute889 to quantify the effect of each individual group attribute, in the full proposal.890 Specifically, seven approaches will be evaluated:891 •The current proposal, detailed at Section 3 (dyn).892 •The current proposal, detailed at Section 3, but without considering the893 attribute minimum correlation between any pair of group members (dyn894 not M).895 32 top N 1 2 3 4 5 10 15 20 Approaches that does not consider the fuzzy decision tree induction process avg (baseline) 0.5787 0.5844 0.5788 0.5684 0.5740 0.5681 0.5628 0.563 min (baseline) 0.5813 0.5725 0.5829 0.5841 0.5845 0.5754 0.5708 0.5713 Approaches incorporating the fuzzy decision tree induction process dyn 0.6025 0.5806 0.5879 0.5844 0.5855 0.5760 0.5686 0.5685 dyn not AV 0.600 0.5788 0.5850 0.5838 0.5850 0.5763 0.5698 0.5693 dyn not C 0.5838 0.5844 0.5879 0.5841 0.5850 0.5744 0.5669 0.5651 dyn not M 0.5963 0.5763 0.5846 0.5853 0.5873 0.5785 0.5712 0.5712 dyn not A 0.5925 0.5725 0.5825 0.5813 0.5833 0.5769 0.5703 0.5699 Table 8: Evaluation of the proposal and comparison with baselines avg and min, presented at (Pérez-Almaguer et al., 2021). Movielens 100K dataset. Precision value. •The current proposal, detailed at Section 3, but without considering the896 attribute amount of ratings of the group (dyn not A).897 •The current proposal, detailed at Section 3, but without considering the898 attribute amount of co-rated items (dyn not C).899 •The current proposal, detailed at Section 3, but without considering the900 attribute rating average (dyn not AV ).901 •As baseline, the former CB-GRS based on recommendation aggregation902 and user-item matching values (Pérez-Almaguer et al., 2021), always using903 average aggregation (avg) and without the use of the fuzzy decision tree.904 •As baseline, the former CB-GRS based on recommendation aggregation905 and user-item matching values (Pérez-Almaguer et al., 2021), always using906 minimum aggregation (min), and without the use of the fuzzy decision907 tree.908 5.5.1. Movielens909 This subsection presents the results associated to the dataset Movielens910 100K.911 Here the proposal is evaluated considering as parameters θr= 0.9and θn=912 0.01, i.e. the stop conditions are executed once the relative frequency of some913 class in the current node is equal or higher that 0.9, or when the cardinality914 of the set as such node is under 0.01, see Section 3.2. Further executions were915 performed for other values of θrand θn, reporting here the values that lead to916 a better performance.917 The results are obtained for groups of size 4; and the size of the top n918 recommendation lists were in the range [1,5] with step 1, and [5,20] with step919 5.920 Table 8 shows these results, being differentiated those associated with our921 proposal that incorporates the fuzzy decision tree induction, and those922 associated to the baseline that does not consider it. Here it is presented that923 for 6 of the 8 experimental scenarios the proposal is able to outperform the924 33 baselines, and for n=2 and n=20, it reaches a similar behavior to the average925 and minimum approach respectively. Furthermore, it is relevant to mention926 that while for n=1 and n=3 the best performance is reached when the four927 group attributes are used, for the other scenarios it is reached with the928 exclusion of some attribute. Specifically, for n=2 the best result was obtained929 with the exclusion of the attribute amount of co-rated items. In addition, for930 n={4,5,10,15}, the best results were obtained with the exclusion of the931 attribute minimum correlation between any pair of members, even though the932 values of this attribute in the groups, have a tendency to a fair distribution933 across all the possible attribute values (Figure 10)934 Overall, the results evidence that for the Movielens dataset, the proposal935 is able to identify the best aggregation function to use in a CB-GRS based936 on recommendation aggregation, considering that it notably outperforms two937 baselines that always use the average and minimum aggregation.938 5.5.2. HetRec939 This subsection presents the results associated to the dataset HetRec.940 The proposal is evaluated considering as parameters θr= 0.9and θn= 0.01,941 and compared with the baselines also considered for the Movielens dataset. In942 a similar way to Movielens, further executions were performed for other values943 of θrand θn, reporting here the values that lead to a better performance.944 The results are obtained for groups of size 3 considering that larger groups945 were not able to obtain due to the sparsity of the dataset. Furthermore, the946 sizes of the top n recommendations lists were in the range [1,5] with step 1, and947 [5,20] with step 5.948 Table 9 presents the evaluation results, being differentiated those associated949 with our proposal, and those associated to the baseline that does not consider950 the fuzzy decision tree induction. In this case, for all the experimental scenarios,951 the new proposal outperforms the baselines. Specifically, for n={3,4,5}the use952 of the four group attributes for building the fuzzy decision tree leads to the best953 performance. Furthermore, for n={1,2,15}, such performance was achieved by954 discarding the attribute rating average, and for two cases (n={10,20}) it was955 achieved by discarding the amount of co-rated items.956 Overall, in this dataset is more clear the superiority of the proposal over the957 baselines, in relation to the previous dataset Movielens. Furthermore, it is also958 worthy to remark that there was not a specific group feature which exclusion959 globally leads to a performance improvement, across the different sizes of the960 recommendation lists.961 5.6. Final discussion962 This paper has introduced a content-based GRS framework, based on963 recommendation aggregation, and focused on performing a dynamic selection964 of the most appropriate aggregation functions according to the nature of the965 active group. The development of the proposal as well as the experimentation,966 lead to the following findings:967 34 top N 1 2 3 4 5 10 15 20 Approaches that does not consider the fuzzy decision tree induction process avg (baseline) 0.5050 0.5075 0.5039 0.5000 0.5013 0.4957 0.4952 0.4943 min (baseline) 0.5700 0.5483 0.5417 0.5358 0.5297 0.5080 0.5024 0.4994 Approaches incorporating the fuzzy decision tree induction process dyn 0.5817 0.5483 0.5422 0.5363 0.5299 0.5083 0.5029 0.4989 dyn not AV 0.5833 0.5492 0.5406 0.5350 0.5277 0.5080 0.5031 0.5000 dyn not C 0.5817 0.5467 0.5367 0.5333 0.5263 0.5090 0.5024 0.5003 dyn not M 0.5700 0.5500 0.5422 0.5354 0.5280 0.5083 0.5031 0.4993 dyn not A 0.5783 0.5483 0.5417 0.5358 0.5297 0.5080 0.5024 0.4994 Table 9: Evaluation of the proposal and comparison with baselines avg and min, presented at (Pérez-Almaguer et al., 2021). HetRec dataset. Precision value. •The analysis of the literature related to content-based GRS, suggested that968 as far as we know, there is not a direct antecedent focused on the use of969 machine learning techniques, to learn knowledge from the groups’ behavior970 and therefore using this knowledge for improving the recommendation971 generation for such groups.972 •The exploratory analysis of the four group attributes considered in this973 work, which are the minimum correlation between any pair of group974 members, the amount of ratings across the group, the amount of975 co-rated items by all the users, and the rating average of the group;976 shows that they are able to characterize groups’ behavior, even though it977 was with a larger or lesser success depending on the nature of the data.978 •As could be expected, an exploratory analysis using frequency979 histograms, shows that there are different imbalance levels across the980 groups attributes. In cases such as the minimum correlation between981 group members in both datasets, it can be observed some balance across982 the groups regarding the frequency values of this attribute. In contrast,983 in other cases such as the amount of co-rated items or the amount of984 groups’ ratings in HetRec, there are many groups that share the same or985 similar attribute values. This fact would need the introduction in this986 framework, of more sophisticated membership functions beyond the987 proposed in Figure 8, for a better characterization of the data in the988 fuzzy decision tree induction process.989 •The experimental results evidence a positive performance for Movielens990 100K and HetRec datasets. In both cases, the new proposal leads to an991 improvement of the recommendation performance, showing the suitability992 of our approach focused on using a fuzzy decision tree for dynamically993 selecting the most appropriate aggregation function in a CB-GRS scenario,994 based on the groups’ features. Specifically, it was evidenced that a CB-995 GRS with such dynamic selection, outperforms two CB-GRSs that always996 use average and minimum respectively, as aggregation operators.997 •From a general viewpoint, the results show that the incorporation of a998 35 fuzzy decision tree in a content-based group recommendation model, for999 supporting the recommendation generation process, is able to improve the1000 recommendation generation performance. In this way, for the Movielens1001 dataset it was able to reach a Precision value up to 0.6025, while the1002 baselines that does not use the fuzzy decision tree reach up to 0.5845. In1003 the HetRec dataset, the proposal reaches a Precision up to 0.5833, while1004 the baselines reach up to 0.5700.1005 •Overall, the experimental results show that the proposal can serve as a1006 starting point for developing a new research branch focused on the1007 dynamic selection of the most appropriate components of a GRS1008 framework, taking as input some attributes of the group.1009 5.7. Future works1010 The aim of this research paper is to be an starting point in the research1011 branch related to the dynamic selection of the components of a GRS, as it has1012 been previously commented. At this moment, the next future work to continue1013 this research would be:1014 •The exploration of more sophisticate t-norms, t-conorms, and1015 membership functions for the fuzzy sets low,medium, and high (Figure1016 8), that reflect better the nature of data. In the current work, we have1017 used the well-recognized triangular membership functions as the basic1018 approach. However, they could not be the most appropriate for some1019 scenarios. As future work it will be explored the role of trapezoidal and1020 sigmoidal membership functions for boosting or decreasing the effect of1021 some group’s attributes values, in the group’s membership to the nodes1022 in the induced decision tree. Furthermore, other t-norms (e.g. product)1023 and t-conorms (e.g. probabilistic sum), will be also explored (Zadeh,1024 1965; Dubois & Prade, 1978).1025 •The use of further schemes for calculating the relevance of the item1026 profiles for each corresponding user, in the inner content-based1027 recommendation approach. Being use in the current scenario the cosine1028 measure as the reference approach (see Section 2.1), in the next works it1029 will be considered more sophisticated schemes incorporating further1030 knowledge sources (e.g. ontologies, linked open data cloud, other1031 graph-based structures, etc) (de Gemmis et al., 2015).1032 •The use of feature engineering approaches for a better characterization of1033 the identified features, as well as the extracting of other features. Feature1034 management comprises a wide range of techniques that could be applied1035 here, such as feature weighting, or the discovery of latent features (Koren1036 et al., 2009).1037 •The use of other supervised classifiers beyond the fuzzy decision tree-1038 based. Fuzzy decision trees have been currently used as a white-box and1039 36 effective classifier. However, it is interesting to explore here other well-1040 recognized alternatives, such as multi-classifiers, support vector machines,1041 or deep learning-based classifiers (Arrieta et al., 2020).1042 •The use of the presented framework in other GRS scenarios, beyond1043 content-based group recommendation. Here, a primary direction is the1044 evaluation of the proposal in a collaborative filtering-based GRS.1045 6. Conclusions1046 This paper presents a novel framework for content-based group1047 recommendation, which main feature is the dynamic selection of the most1048 appropriate aggregation function, for the recommendation aggregation step.1049 Specifically, it is focused on proposing the use of four attributes for1050 characterizing groups in content-based GRS. Such attributes are the minimum1051 correlation between any pair of group members, the amount of ratings across1052 the group, the amount of co-rated items by all the users, and the rating1053 average of the group. Specifically the proposal is focused on building a fuzzy1054 decision tree that helps to match such attributes of a specific group, with the1055 best aggregation function (average or minimum), that can be use for such1056 group in the individual recommendation aggregation step for improving the1057 recommendation performance.1058 The proposal is evaluated by an experimental protocol over well-known1059 datasets. The results particularly show that it is able to outperform the1060 baseline for most of all scenarios in the Movielens and HetRec datasets.1061 Furthermore, it was also developed an exploratory analysis of the values of1062 such attributes in all the groups used in the experiments, showing different1063 imbalance degrees that could affect the application of the proposal in a higher1064 or lesser extent.1065 From a practical viewpoint, our work provides a methodology initially1066 presented for the content-based group recommendation context but that can1067 be also used in other GRSs, in order to guarantee a more dynamic1068 construction of the recommendation architecture, that could result in an1069 improvement of the recommendation accuracy. Furthermore, the nature of the1070 proposal would allow its use in a higher dimension and dense scenarios,1071 considering that its phases tend to have a linear dependency on the dimension1072 of the data, and that most of such phases can be executed in an offline mode1073 for saving computational cost.1074 The next future work to be developed, already pointed out in the previous1075 section, comprises some goals such as the use of feature engineering approaches1076 for a better characterization of groups, the use of more sophisticate membership1077 functions that represent better the nature of the data, and the use of other1078 supervised classifiers beyond the fuzzy decision tree.1079 37 Acknowledgements1080 This work was supported by the Deanship of Scientific Research (DSR), King1081 Abdulaziz University, Jeddah, under Grant Kep-15-611-42.1082 References1083 References1084 Adomavicius, G., & Tuzhilin, A. T. (2005). 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