DSpace at VNU: HU-FCF: A hybrid user-based fuzzy collaborative filtering method in Recommender Systems

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ESWA 9318 No of Pages 10, Model 5G 15 May 2014 Expert Systems with Applications xxx (2014) xxx–xxx Contents lists available at ScienceDirect Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa HU-FCF: A hybrid user-based fuzzy collaborative filtering method in Recommender Systems Q1 Le Hoang Son ⇑ Q2 VNU University of Science, Vietnam National University, Viet Nam 10 2 13 14 15 16 17 18 19 20 a r t i c l e i n f o Keywords: Football results prediction Fuzzy Recommender Systems Fuzzy similarity degrees Hard user-based degrees Hybrid fuzzy collaborative filtering a b s t r a c t Recommender Systems (RS) have been being captured a great attraction of researchers by their applications in various interdisciplinary fields Fuzzy Recommender Systems (FRS) is an extension of RS with the fuzzy similarity being calculated based on the users’ demographic data instead of the hard user-based degree Based upon the observations that the FRS researches did not offer a mathematical definition of FRS accompanied with its algebraic operations and properties, and the fuzzy similarity degree is not enough to express accurately the analogousness between users, in this paper we will present a systematic mathematical definition of FRS including theoretical analyses of algebraic operations and properties and propose a novel hybrid user-based fuzzy collaborative filtering method that integrates the fuzzy similarity degrees between users based on the demographic data with the hard user-based degrees calculated from the rating histories into the final similarity degrees in order to obtain high accuracy of prediction Experimental results on some benchmark datasets show that the proposed method obtains better accuracy than other relevant methods Lastly, an application for the football results prediction is given to illustrate the uses of the proposed method Ó 2014 Published by Elsevier Ltd 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 Introduction Recommender Systems (RS) have been being captured a great attraction of researchers by their applications in various interdisciplinary fields RS, which are a subclass of decision support systems, can give users information about predictive ‘‘rating’’ or ‘‘preference’’ that they would like to assess an item; thus helping them to choose the appropriate item among numerous possibilities This kind of expert systems is now commonly popularized in numerous application fields such as books, documents, images, movie, music, Q3 shopping and TV programs personalized systems as stated by Park, Kim, Choi, and Kim (2012) in a survey of 210 articles on Recommender Systems from 46 journals published between 2001 and 2010 A large number of researches involving the uses of RS to practical applications have been found in those journals especially those focusing on expert and knowledge-based systems, for example the work of Ghazanfar and Prügel-Bennett (2014) offering a hybrid recommendation algorithm to make reliable recommendations for gray-sheep users that reduce the recommendation error rate and maintain reasonable computational performance Christidis and Mentzas (2013) handled the difficulty of processing ⇑ Address: 334 Nguyen Trai, Thanh Xuan, Hanoi, Viet Nam Tel.: +84 904171284; fax: +84 0438623938 E-mail address: sonlh@vnu.edu.vn a large number of items bought and sold every day in auction marketplaces across the web by the mean of a RS system that exploits the hidden topics of unstructured information The analysis of student’s academic performance by a RS system determining the level of learning productivity integrally through physiological, psychological and behavioral was studied by Kaklauskas (2013) Fang et al (2012) developed a mobile RS to capture users’ preferences in indoor shopping context through users’ positions and contextual information Costa-Montenegro, Barragáns-Martínez, and ReyLópez (2012) addressed the issue of information overload when downloading applications in markets by an integrated RS solution Carrer-Neto, Hernández-Alcaraz, Valencia-García, and GarcíaSánchez (2012) employed knowledge and social networks to a hybrid RS for the cinematographic domain Shih, Yen, Lin, and Shih (2011) implemented the most common three kinds of RS techniques in order to recommend to customers which countries are the best traveling locations Borges and Lorena (2010) applied RS to the domain of news and listed some typical examples such as GroupLens, NewsWeeder, online newspaper P-Tango and Google news personalization Drachsler (2010) gave an application of RS for technology enhanced learning Duan, Street, and Xu (2011) studied nursing care plans in a healthcare RS Tag recommendation for Social RS was investigated by Derntl (2011), Song, Zhang, and Giles (2011) and Zheng and Li (2011) Industrial RS applications http://dx.doi.org/10.1016/j.eswa.2014.05.001 0957-4174/Ó 2014 Published by Elsevier Ltd Q1 Please cite this article in press as: Son, L H HU-FCF: A hybrid user-based fuzzy collaborative filtering method in Recommender Systems Expert Systems with Applications (2014), http://dx.doi.org/10.1016/j.eswa.2014.05.001 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 ESWA 9318 No of Pages 10, Model 5G 15 May 2014 Q1 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 L.H Son / Expert Systems with Applications xxx (2014) xxx–xxx could be named but a few such as the personalized online store of Amazon.com, music recommendation of YouTube, the hottest news of Yahoo, Netflix, etc (Ricci, Rokach, & Shapira, 2011) Other applications of RS could be referenced in Shapira (2011), Son, Cuong, Lanzi, and Thong (2012), Son, Cuong, and Long (2013a), Son, Minh, Cuong, and Canh (2013b), Son, Linh, and Long (2014), Son (in press) and Son and Thong (submitted for publication) These researches of RS applications clearly depict two remarks: (i) RS is getting more and more important to practical applications; (ii) the studies of RS and its computational intelligence techniques such as the association rule, clustering algorithms, decision tree, knearest neighbor, link analysis, neural network, regression and other heuristic methods to enhance the accuracy of prediction are significant to not only the community of expert and knowledge-based systems researches but also the applied sciences Our objective in this paper is to investigate an advanced computational intelligence technique for RS to enhance the accuracy of prediction We have already known that Collaborative Filtering (CF) is one of the most popular, traditional hard user-based filtering methods to predict the ratings of items based on the similarities between users through the Pearson coefficient Rating of a user is indeed approximated to the most frequent of those of other similar users Nevertheless, the problem of CF can be recognized that the calculation of similarities between users based on the rating histories is not accurate in many practical applications, and other information such as users’ demographic data should be used instead since those data reflect the correlation between users expressed through various attributes of users more strictly than the rating history An important issue in this observation is that the attributes of users are not only continuous values but also discrete ones such as ‘‘Gender’’, ‘‘Occupation’’, etc Thus, in order to calculate the similarity between users based on the demographic data, it is necessary to integrate fuzzy logic with RS, and this research orientation belongs to the class of Fuzzy Recommender Systems (FRS) Yager (2003) stated that the usefulness of information is dependent upon its representation visualized by fuzzy sets so that the final rating, calculated through the ordered weighted averaging operator, bases solely on the preferences of the single individual and makes no use of the preferences of other collaborators Zenebe and Norcio (2009) presented a fuzzy set theoretic method for RS including a representation method, similarity measures and aggregation methods that handles the non-stochastic uncertainty induced from subjectivity, vagueness and imprecision in the data, and the domain knowledge and the task under consideration Cao and Li (2007) presented a fuzzy-based system for consumer electronics that ranks customer needs by their importance and sets up fuzzy rules between customer needs and product features Porcel, López-Herrera, and Herrera-Viedma (2009) used some filtering tools and a particular fuzzy linguistic modeling, called multi-granular fuzzy linguistic modeling, which is useful when different qualitative concepts have to be assessed for research resources Porcel and Herrera-Viedma (2010) investigated the problem of incomplete information in a fuzzy linguistic RS and presented a new system that facilitates the acquisition of the user preferences to characterize the user profiles Palanivel and Siavkumar (2010) adopted the fuzzy linguistic and fuzzy multi-criteria decision making approaches to represent the user ratings and accurately rank the relevant items Romero, Ferreira-Satler, Olivas, Prieto-Mendez, and Menéndez-Domínguez (2011) proposed a fuzzy linguistic model based on three dimensions such as structural, contextual and personal and applied it to learning object repository Serrano-Guerrero, Herrera-Viedma, Olivas, Cerezo, and Romero (2011) introduced a novel fuzzy linguistic RS based on the Google Wave capabilities for communicating researchers interested in common research lines Boulkrinat, Hadjali, and Mokhtari (2013) used linguistic terms for the rating of users’ preferences and calculated the similarity between users on the basis of the similarity of their preference relations which can better capture similar users’ ratings patterns Some authors used soft computing method for the calculation of similarities between users, for instance Park, Yoo, and Cho (2006) applied Fuzzy Bayesian Networks to fuzzify information obtained from sensors and Internet and to get suitable contexts with the probability; thus determining the similarities between users Al-Shamri and Bharadwaj (2008) presented a hybrid fuzzy-genetic approach to fuzzify the user model and to reflect more appropriately the fuzziness of each fuzzy feature Terán and Meier (2010) designed a fuzzy interface for voters and candidates to write their profiles, and used fuzzy clustering to calculate the top-N recommendation in eElections Nadi, Saraee, Bagheri, and Davarpanh Jazi (2011) focused on web users’ behaviours problem and proposed a fuzzy-ant based RS based on collaborative behaviour of ants Sevarac, Devedzic, and Jovanovic (2012) proposed neuro-fuzzy pedagogical recommender, which is an adaptive RS based on neuro-fuzzy inference, to create pedagogical rules in technology enhanced learning Lucas, Laurent, Moreno, and Teisseire (2012) and Zhang et al (2013) proposed hybrid methodologies for RS, which use collaborative filtering and content-based approaches in a joint method taking advantage from the strengths of both approaches From the summary of relevant researches to FRS, some important issues are drawn out as follows 149  Those relevant FRS researches solely used fuzzy sets to model uncertain information existed in the users’ demographic data but did not offer a mathematical definition of FRS accompanied with its algebraic operations and properties  According to these researches, FRS is merely a small extension of RS with the users’ demographic data being provided in addition to other datasets, and the calculation of the similarity degrees between users is conducted on the demographic data only Even though demographic data contain multiple-dimensions comprehensive information of users, relying solely on this type of data for the calculation of the similarity degrees without the knowledge of rating histories may lead to erroneous and inaccurate results Since previous ratings could somehow affect the constitution of the considered one, it is better if the similarities between users are evaluated both by the demographic data and the rating histories 173 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 Motivated by the problems of the relevant FRS researches and the work of Shih et al (2011) concluding that hybrid RS could conquer the shortcomings of the available filtering approaches, our contributions in this article are expressed as follows 190  A systematic mathematical definition of FRS accompanied with its algebraic operations and properties  A novel hybrid user-based fuzzy collaborative filtering method so-called HU-FCF that integrates the fuzzy similarity degrees between users based on the demographic data with the hard user-based degrees calculated from the rating histories into the final similarity degrees in order to obtain high accuracy of prediction  An application of HU-FCF for the football results prediction problem 194 191 192 193 195 196 197 198 199 200 201 202 203 204 The difference and the novel of the proposed approach in comparison with the relevant FRS ones are expressed in the contributions above Even though the idea of HU-FCF is quite simple, it could help accelerating the accuracy of prediction since the final similarity is evaluated more accurately through the integration of both the fuzzy and hard user-based similarity degrees The relevant approaches were based solely on either the hard similarities between users (the CF method and its variants) or fuzzy similarities from the Q1 Please cite this article in press as: Son, L H HU-FCF: A hybrid user-based fuzzy collaborative filtering method in Recommender Systems Expert Systems with Applications (2014), http://dx.doi.org/10.1016/j.eswa.2014.05.001 150 205 206 207 208 209 210 211 212 ESWA 9318 No of Pages 10, Model 5G 15 May 2014 Q1 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 demographic data (the group of FRS methods) so that the group of the most similar users to the considered one may admit irrelevant users as a result of incorrect selection and computation Intuitively, the proposed HU-FCF may result in better accuracy and flexibility than other relevant approaches through the using of the hybrid similarity degrees This may be verified and validated by experiments in some benchmark RS datasets such as the MovieLens (GroupLens research, 2014) and Book-Crossing (Ziegler, McNee, Konstan, & Lausen, 2005) The advantage of the proposed method HU-FCF may be not only the better accuracy than other relevant approaches but also the capability to handle more numbers of cases than other algorithms since when the coefficient or weight of the fuzzy (hard) user-based similarity degree is set to zero, the HU-FCF algorithm works similarly to the available relevant algorithms Additionally, HU-FCF is constructed on the basis of a systematic mathematical definition of FRS accompanied with its algebraic operations and properties so that the theoretical foundation of the algorithm can be guaranteed The disadvantage of HU-FCF is somehow the large computational time since it has to compute more numbers of similarity degrees than other algorithms However, this limitation could be compromised if the priority of RS is dedicated to the accuracy of prediction The rest of the paper is structured as follows Section presents the main contributions of the paper including a mathematical definition of FRS accompanied with its algebraic operations and properties and a novel hybrid user-based fuzzy collaborative filtering method named HU-FCF Section validated HU-FCF by experiments on some benchmark datasets Section introduces an application of HU-FCF for the football results prediction Section draws the conclusions and delineates the future research directions 243 The proposed methodology 244 245 2.1 Definitions 246 Definition (Recommender Systems – RS Adomavicius and Tuzhilin, 2005; Borges and Lorena, 2010; Ricci et al., 2011) Suppose U is a set of all users and I is the set of items in the system The utility function R is a mapping specified on U & U and I1 & I as follows 247 248 249 250 R : U  I1 ! P; 252 L.H Son / Expert Systems with Applications xxx (2014) xxx–xxx ð1Þ ðu1 ; i1 Þ # Rðu1 ; i1 Þ; Example Suppose that U = {John, David, Jenny, Marry} and I = {Titanic, Hulk, Scallet} The set of criteria of a movie is P = {Story, Visual effects} The ratings are assigned numerically from (bad) to (excellent) Table describes the utility function Q4 From this table, it is clear that MCRS can help us to predict the ratings of a user (Marry) to a movie that was not rated by her beforehand (Titanic) This kind of systems also recommends her favourite movie through available ratings In cases that there is only an criterion in P, MCRS returns to the traditional RS Now, we extend MCRS by the definition below 272 Definition (Fuzzy Recommender Systems – FRS) Suppose U is a set of all users, I is the set of items and C is the set of fuzzy contexts in the system The utility function R is a mapping specified on U & U; I1 & I and C & C as follows 282 R : U  I1  C ! P1  P  Á Á Á  Pk ; 273 274 275 276 277 278 279 280 281 283 284 285 286 ð3Þ ðu1 ; i1 ; fc1 ; lc gÞ # ðfR1 ; l1 g; fR2 ; l2 g; ; fRk ; lk gÞ; 288 where lc ½0; 1Š is the membership value of context c1 Ri i ẳ 1; kị is the rating of user u1 to item i1 in context c1 by criteria P i with fuzzy membership li ½0; 1Š FRS are the systems that provide two basic functions below 289 à (a) Prediction: the capability to determine Rðuà ; i ; fcÃ1 ; lÃc gÞ for à any ðuà ; i ; fcÃ1 ; lÃc gÞ ðU; I; CÞ n ðU ; I1 ; C Þ Ã (b) Recommendation: the capability to choose i I satisfying i ẳ arg maxi2I Ru; i; fc; lc gị for all u U; fc; lc g C and a certain criterion 290 291 292 293 294 295 296 297 298 As we can recognize in Definition 3, FRS is the generalized definition of MCRS (Definition 2) and RS (Definition 1) since in cases that C ¼ f/g and li ẳ 8i ẳ 1; kị, FRS returns to MCRS If the condition: k ¼ is appended, FRS returns to the traditional RS Now, let us consider the example below to illustrate the difference between FRS and other types of RS 299 Example Suppose that U = {John, David, Jenny, Marry}, I = {Titanic, Hulk, Scallet} and C = {Weather, Mood} The fuzzy linguistic labels of ‘‘Weather’’ are {‘‘Fine’’, ‘‘Normal’’, ‘‘Bad’’}, and those of ‘‘Mood’’ are {‘‘Happy’’, ‘‘Normal’’, ‘‘Angry’’} The set of criteria of a movie is P = {Story, Visual effects} whose fuzzy linguistic labels are {‘‘Very good’’, ‘‘Fair’’, ‘‘Boring’’} and {‘‘Amazing’’, ‘‘Thrill’’, ‘‘Melody’’}, respectively Table describes the utility function of FRS 305 300 301 302 303 304 306 307 308 309 310 311 312 253 254 255 where Rðu1 ; i1 Þ is a non-negative integer or a real number within a certain range P is a set of available ratings in the system Thus, RS is the system that provides two basic functions below 259 256 260 257 261 258 262 263 264 265 à à à à (a) Prediction: determine Rðu ; i Þ for any ðu ; i Þ ðU; IÞ n ðU ; I1 Þ Ã (b) Recommendation: choose i 2I satisfying à i ¼ arg maxi2I Rðu; iÞ for all u U Definition (Multi-criteria Recommender Systems – MCRS Shapira, 2011) MCRS are the systems providing similar basic functions with RS but following by multiple criteria In the other words, the utility function is defined below 266 R : U  I1 ! P  P  Á Á Á  P k ; ð2Þ 268 ðu1 ; i1 Þ # ðR1 ; R2 ; ; Rk Þ; 269 where Ri i ẳ 1; kị is the rating of user u1 U for item i1 I1 following by criteria i In this case, the recommendation is performed according to a given criteria 270 271 It is obvious that the ratings for a movie of a user are expressed by fuzzy linguistic labels in terms of criteria For example, when the weather is ‘‘Normal’’ and the mood of user John is ‘‘Happy’’, he would like to assess the story and visual effect of movie ‘‘Hulk’’ being ‘‘Fair’’ and ‘‘Amazing’’, respectively Contrary to the utility function of MCRS in Table where the rating is assigned by numeric values, the rating for a criterion is expressed by the set of fuzzy linguistic labels In the example above, the set of fuzzy Table Movies’s rating User Movie Story Visual effects John John David David David Jenny Jenny Marry Marry Hulk Scallet Titanic Hulk Scallet Hulk Titanic Hulk Titanic 4 3 ? 2 ? Q1 Please cite this article in press as: Son, L H HU-FCF: A hybrid user-based fuzzy collaborative filtering method in Recommender Systems Expert Systems with Applications (2014), http://dx.doi.org/10.1016/j.eswa.2014.05.001 313 314 315 316 317 318 319 320 ESWA 9318 No of Pages 10, Model 5G 15 May 2014 Q1 Q6 Table The utility function of FRS L.H Son / Expert Systems with Applications xxx (2014) xxx–xxx User Movie John John David David David Jenny Jenny Marry Marry n FRS12 ¼ U 12 ;I12 ;C 12 ; Context Hulk Scallet Titanic Hulk Scallet Hulk Titanic Hulk Titanic Criteria Weather Mood Story Visual effects Nornal Bad Fine Bad Normal Bad Fine Normal Normal Happy Normal Happy Angry Normal Angry Normal Happy Normal Fair Very good Very good Fair Boring Boring Very good Fair ? Amazing Melody Amazing Thrill Amazing Thrill Melody Amazing ? 2.2 Some algebraic operations of FRS 336 Suppose that we have FRS ¼ fU; I; C; fP i g j i ¼ 1; ng below 324 325 326 327 328 329 330 331 332 333 337 338 340 o o  FRS1 ¼ U ; I1 ; C ; P1ii i ¼ 1; n ; n n o o  FRS2 ¼ U ; I2 ; C ; P2i i ¼ 1; n ; n n o o  FRS3 ¼ U ; I3 ; C ; P3i i ¼ 1; n ; 341 where, 342 n three subsets of n 344 n  o  c1;j ; lc1;j j ¼ 1; l ; n  o lc1;j ¼ cg1;j ; lgc1;j g ¼ 1; h ; n o n  o  P1i ¼ R1i ; l1i ¼ R1i;q ; l1i;q q ¼ 1; r ; n  o  c2;j ; lc2;j j ¼ 1; l ; C2 ¼ n  o lc2;l ¼ cg2;j ; lgc2;j g ¼ 1; h ; n o n  o  P2i ¼ R2i ; l2i ¼ R2i;q ; l2i;q q ¼ 1; r ; n  o  C3 ¼ c3;j ; lc3;j j ¼ 1; l ; n  o lc3;j ¼ cg3;j ; lgc3;j g ¼ 1; h ; n o n  o  R3i;q ; l3i;q q ¼ 1; r ; P3i ¼ R3i ; l3i ¼ n  o  C¼ cj ; lcj j ¼ 1; l ; n  o lcj ¼ cgj ; lgcj g ¼ 1; h ;  o È É n  Pi ¼ Ri ; li ¼ Ri;q ; li;q q ¼ 1; r : 345 Some algebraic operations of FRS are defined below C1 ¼ 346 347 349 350 g c1;j ; g c2;j g; ð9Þ ð10Þ ð11Þ ð12Þ ð13Þ ð14Þ ð15Þ ð16Þ ð17Þ ð18Þ ð24Þ ð25Þ ð26Þ ð27Þ ð28Þ where FRS12 ¼ U 12 ;I12 ;C 12 ; n P12 l o o  l ¼ 1;k ; U 12 ¼ U \ U ; I12 ¼ I1 \ I2 ; n  o  C 12 ¼ c12;j ; lc12;j  j ¼ 1;l ; n  o lc12;j ¼ cg12;j ; lgc12;j g ¼ 1;h ; n o lgc12;j ¼ lgc1;j ; lgc2;j ; n o n o n  o 12 12  ¼ R12 ¼ R12 P12 i i ; li i;q ; li;q q ¼ 1;r;l N;k N ; n o l12 i;q ¼ li;q ; li;q : 359 ð29Þ ð30Þ ð31Þ ð32Þ ð33Þ ð34Þ ð35Þ ð36Þ (c) Complement: 363 ð37Þ 367 ð39Þ ð40Þ ð38Þ n  o  ¼ c1C ;j ; lc C j ¼ 1;l ; ;j n  o lc12;j ¼ cg1C ;j ; lgc C g ¼ 1;h ; ;j g c1C ;j g c1;j ; ¼1Àl o n C o n C  o C C  P1i ¼ R1i ; l1i ¼ R1i;q ; l1i;q q ¼ 1;r;l N;k N ; C l ¼1Àl 1C i;q : ð41Þ ð42Þ ð43Þ ð44Þ 2.3 Properties (a) Commutative: 374 45ị FRS1 \ FRS2 ẳ FRS2 \ FRS1 : 46ị (b) Associative: where FRS1 [ FRS2 ¼ FRS12 ; n n o o  FRS12 ¼ U 12 ; I12 ; C 12 ; P 12 l ¼ 1; k ; l 376 377 378 ð47Þ ð48Þ 380 381 382 383 384 ð49Þ ð50Þ Q1 Please cite this article in press as: Son, L H HU-FCF: A hybrid user-based fuzzy collaborative filtering method in Recommender Systems Expert Systems with Applications (2014), http://dx.doi.org/10.1016/j.eswa.2014.05.001 370 373 372 FRS1 [ FRS2 ¼ FRS2 [ FRS1 ; FRS1 [ FRS2 ị [ FRS3 ẳ FRS1 [ ðFRS2 [ FRS3 Þ; ðFRS1 \ FRS2 Þ \ FRS3 ẳ FRS1 \ FRS2 \ FRS3 ị: 369 371 We prove the first commutative property in Eq (45) Other properties are proven analogously ð19Þ 365 366 C C1 1C i;q 361 362 n n C o o  ¼ U C1 ; IC1 ; C C1 ; P1i i ¼ 1; n ; U C1 ¼ U n U ; IC1 ¼ I n I1 ; n 355 357 358 n l 353 354 FRS1 \ FRS2 ¼ FRS12 ; where ð8Þ ð23Þ (b) Intersection: ð5Þ (a) Union: FRS1 [ FRS2 ẳ FRS12 ; g c12;j 4ị 7ị 20ị 22ị FRSC1 6ị 351 21ị ẳ maxfl l o n o n  o 12 12  P12 ¼ R12 ¼ R12 i i ; li i;q ; li;q q ¼ 1;r;l N;k N ; n o l12 i;q ¼ max li;q ; li;q : 335 323 o o  l ¼ 1;k ; U 12 ¼ U [ U ; n 334 322 P12 l I12 ¼ I1 [ I2 ; n  o  C 12 ¼ c12;j ; lc12;j j ¼ 1;l ; n  o lc12;j ¼ cg12;j ; lgc12;j g ¼ 1;h ; l linguistic labels for criterion ‘‘Story’’ accompanied with fuzzy memberships as stated in Eq (3) is {(‘‘Very good’’, 0.2); (‘‘Fair’’, 0.7); (‘‘Boring’’, 0.1)} Since the fuzzy membership of label ‘‘Fair’’ is the maximum among all, the rating value for criterion ‘‘Story’’ is ‘‘Fair’’ as shown in Table By using the fuzzy linguistic labels, FRS has tackled the problem of vague, incomplete and uncertainty that exist in RS and MCRS The aims of FRS consist of the prediction and the recommendation of a user for a movie in a specific context For example, we would like to know the ratings of user Marry in terms of {‘‘Story’’, ‘‘Visual effects’’} for the movie ‘‘Titanic’’ in the contexts of weather and mood being ‘‘Normal’’ and ‘‘Normal’’, respectively Furthermore, the best movie in term of a specific criterion that Marry has ever seen should be recommended 321 n 386 ESWA 9318 No of Pages 10, Model 5G 15 May 2014 Q1 387 388 where U 12 ¼ U [ U ; I12 ¼ I1 [ I2 ; n  o  C 12 ¼ c12;j ; lc12;j j ¼ 1; l ; n  o lc12;j ¼ cg12;j ; lgc12;j g ¼ 1; h ; l g c12;j g c1;j ; g c2;j g; 390 ¼ maxfl l n o n o n  o 12 12 12  ¼ R12 ¼ R12 Pi i ; li i;q ; li;q q ¼ 1; r; l N; k N ; n o l12 i;q ¼ max li;q ; li;q : 391 Similarly, we have 392 394 n n o o  FRS21 ¼ U 21 ; I21 ; C 21 ; P21 l ¼ 1; k ; l 395 where 396 398 U 21 ¼ U [ U ; I21 ¼ I2 [ I1 ; n  o  C 21 ¼ c21;j ; lc21;j j ¼ 1; l ; n  o lc21;j ¼ cg21;j ; lgc21;j g ¼ 1; h ; n o lgc21;j ¼ max lgc2;j ; lgc1;j ; n o n o n  o 21 21  P 21 ¼ R21 ¼ R21 i i ; li i;q ; li;q q ¼ 1; r; l N; k N ; n o l21 i;q ¼ max li;q ; li;q : 399 Thus, 400 402 FRS1 [ FRS2 ¼ FRS2 [ FRS1 : ð51Þ ð52Þ ð55Þ ð56Þ ð57Þ ð58Þ ð59Þ ð60Þ ð61Þ ð62Þ ð63Þ ð64Þ ð66Þ In this section, we present a novel hybrid user-based fuzzy collaborative filtering method so-called the Hybrid User-based Fuzzy Collaborative Filtering (HU-FCF) Since most of the available RS datasets are designed in the forms of {User, Item, Criterion} and a fuzzy filtering method could be developed either on the set of {User, Item, Context} or the set of {Criteria} or both of them, we consider the reduction of the definition of FRS (Definition 3) to that of RS (Definition 1) and perform the fuzzy filtering method on the user dataset Most of the relevant FRS approaches were also designed by this way, and the proposed HU-FCF would be an extension of them in order to achieve the objective of better accuracy of prediction To be frank, the HU-FCF method is designed for the original RS but not truly for the FRS as stated in Definition Nonetheless, by providing an appendage of fuzzy similarity degrees, this method could be considered as one of the fuzzy filtering methods for FRS The basic idea of HU-FCF method is to integrate the fuzzy similarity degrees between users based on the demographic data with the hard user-based degrees calculated from the rating histories into the final similarity degrees As such, those degrees would reflect more exactly the correlation between users in terms of the internal (attributes of users) and external information (interactions between users) Each similarity degree (fuzzy/hard) is accompanied by weights automatically calculated according to the numbers of analogous users Once the final similarity degrees are calculated, the final rating will be constructed based on the rating values of neighbors of the considered user Depending on the domain of a specific problem, the final rating will be approximated to its nearest value in that domain accompanied by an error threshold, which is normally smaller than 5% A list of nearest values with equivalent error thresholds is also given as the prediction ratings of a user for an item The following pseudo-code will describe the ideas more details 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 i ẳ 1; lị; Output: Rða; iÃ Þ or ra;ià for any ða; iÃ Þ ðU; IÞ HU-FCF: 1: Set the number of similarity degrees in the users’ demographic data: c ¼ 0; 2: Determine the membership functions for demographic attributes and calculate the membership values of all users according to the demographic attributes The most frequent used function for various type of data is the standard normal Gaussian as recommended by Subasi (2006); 3: For each demographic attribute i: 4: Based upon the membership function, calculate the fuzzy distances between the considered user and other ones by the formula below: FDðai ; bi Þ ¼j À bi j; ð65Þ 404 407 number of users and l is the number of demographic attributes; – The items set: I ¼ fI1 ; ; IM g where M is the number of items; – The rating histories: R ¼ fRðU i ; Ij Þ j U i U; Ij Ig; – The similarity threshold: h ½0; 1Š; – The weights of the demographic attributes: wi ð54Þ 2.4 The HU-FCF algorithm 406 Input: – The users’ demographic data: U ¼ fU ; ; U N g n o where each U i ¼ U 1i ; ; U li i ẳ 1; Nị; N is the ð53Þ 403 405 L.H Son / Expert Systems with Applications xxx (2014) xxx–xxx ð67Þ where ; bi are the membership values according to the demographic attribute i of the considered user a and another user b ð68Þ 5: If FDðai ; bi Þ h then c ẳ c ỵ 6: End for 7: Calculate the global fuzzy distances between the considered user and other ones by the formula: GFDa; bị ẳ l X wi FDai ; bi ị; 69ị iẳ1 where wi ½0; 1Š is the weight of the demographic attribute i showing the influence to the global results and satisfying the condition, l X wi ẳ 1: 70ị iẳ1 8: Calculate the fuzzy similarity degrees between the considered user and other ones by the formula: FSDa; bị ẳ GFDa; bÞ: ð71Þ 9: Determine the hard (user-based) similarity degrees between the considered user and other ones from the rating histories by the Pearson coefficient below: PM i¼1 ðr a;i À r a Þ Ã ðr b;i À r b Þ q ; HSDa; bị ẳ q PM PM 2 iẳ1 r a;i r a ị iẳ1 r b;i À r b Þ ð72Þ where ra;i is the rating value of the considered user a for item i I; rb;i is the rating value of user b for item i I; is the average rating value of the considered user a by all items; rb is the average rating value of user b by all items; 10: Calculate the final similarity degrees between the considered user and other ones from Eqs (71), (72) as follows (continued on next page) Q1 Please cite this article in press as: Son, L H HU-FCF: A hybrid user-based fuzzy collaborative filtering method in Recommender Systems Expert Systems with Applications (2014), http://dx.doi.org/10.1016/j.eswa.2014.05.001 ESWA 9318 No of Pages 10, Model 5G 15 May 2014 Q1 L.H Son / Expert Systems with Applications xxx (2014) xxxxxx SIMa; bị ẳ a FSDa; bị ỵ b HSDa; bị; 73ị where a ðbÞ is the weight of the fuzzy (hard) similarity degree, and is calculated through the equations below c ; Nỵc1 a ỵ b ẳ 1: aẳ 74ị 75ị 11: Calculate the final rating by the equation below P à Rða; i ị ẳ r a ỵ b2Unfag SIMa; bị P b2Unfag à ðr b;ià À r b Þ j SIMða; bÞ j ð76Þ : à 12: Determine the nearest value of Rða; i Þ in the domain D of the problem as the final result, and calculate the error threshold as follows à D ¼ 100  j Rða; i Þ À d j ; à maxfRða; i Þ; dg ð77Þ 529 531 532 533 534 In Step of the HU-FCF algorithm, the weights of the demographic attributes are normally taken from the experience of experts according to a given context Nevertheless, the formula below could be used to estimate those weights in a general case.\ Ui wi ¼ P l i¼1 U 537 536 538 539 540 541 542 543 544 545 546 547 548 i ; User Age Education No children Living standard 10 11 12 13 14 15 0.04411765 0.08272059 0.07904412 0.07720588 0.06617647 0.03492647 0.06985294 0.03860294 0.04963235 0.08272059 0.06985294 0.07720588 0.08088235 0.07720588 0.06985294 0.058823529 0.029411765 0.058823529 0.088235294 0.088235294 0.117647059 0.058823529 0.088235294 0.058823529 0.029411765 0.029411765 0.029411765 0.117647059 0.058823529 0.088235294 0.046153846 0.153846154 0.107692308 0.138461538 0.123076923 0.092307692 0.015384615 0.046153846 0.123076923 0.030769231 0.061538462 0.015384615 0.015384615 0.030769231 0.066666667 0.088888889 0.088888889 0.066666667 0.044444444 0.066666667 0.044444444 0.044444444 0.088888889 0.044444444 0.066666667 0.066666667 0.088888889 0.066666667 0.066666667 Table The median values of demographic dataset Age Education No children Living standard 0.069852941 0.058823529 0.046153846 0.066666667 Table The weights à where d D is the nearest value of Rða; i Þ 530 Table The normalized demographic dataset i ẳ 1; l; 78ị w1 w2 w3 w4 0.28925 0.24358 0.19112 0.27606 Evaluation 549 3.1 Experimental design 550 In this part, we describe the experimental environments such &$  '  U i ¼ median U ij j ẳ 1; N ; 79ị as, 551 552 $ where U ij is the normalized value of U ij i ẳ 1; l; j ẳ 1; Nị Eqs ((78) and (79)) determine the values of weights according to their contributions in all demographic attributes Let us consider the example below to illustrate the calculation of weights Example Suppose that we have a demographic dataset of 15 users in Table Normalize the demographic dataset we obtain the results in Table Take the median values by demographic attributes in Eq (79) we have Table Use Eq (78) we get the values of weights in Table Table The demographic dataset User Age Education No children Living standard 10 11 12 13 14 15 24 45 43 42 36 19 38 21 27 45 38 42 44 42 38 2 3 1 3 10 8 1 4 3 2 3 3  Experimental tools: We have implemented the proposed algorithm – HU-FCF in addition to the fuzzy collaborative filtering algorithms of Lucas et al (2012) and Zenebe and Norcio (2009) in C programming language and executed them on a PC Intel Pentium Dual Core 1.80 GHz, GB RAM  Experimental dataset: the benchmark RS datasets such as the MovieLens (GroupLens research, 2014) and Book-Crossing (Ziegler et al., 2005) MovieLens datasets consist of types: 100k and 1M and show the rating values from (Bad) to (Excellent) of users for a collection of movies in the system The data were collected through the MovieLens web site (movielens.umn.edu) during the seven-month period from September 19th, 1997 through April 22nd, 1998 The Book-Crossing dataset was collected by Cai-Nicolas Ziegler in a 4-week crawl (August/September 2004) from the Book-Crossing community and showed the rating values from to 10 of users for a set of books Besides these data, there are other benchmark RS datasets such as Jester (http://goldberg.berkeley.edu/jesterdata), Sushi (http://www.kamishima.net/sushi), HetRec2011 (http://grouplens.org/datasets/hetrec-2011), WikiLens (http:// grouplens.org/datasets/wikilens), etc However, they not contain the demographic information so that for the best of comparison we adopt the MovieLens and Book-Crossing for Table The descriptions of datasets Dataset No users No attributes No items No Ratings MovieLens 100k MovieLens 1M Book-Crossing 943 6040 278,858 3 1682 3900 271,379 100,000 1,000,209 1,149,780 Q1 Please cite this article in press as: Son, L H HU-FCF: A hybrid user-based fuzzy collaborative filtering method in Recommender Systems Expert Systems with Applications (2014), http://dx.doi.org/10.1016/j.eswa.2014.05.001 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 ESWA 9318 No of Pages 10, Model 5G 15 May 2014 Q1 576 577 578 579 580 581 582 583 584 585 586 experiments The cross-validation method used to get the training and testing datasets is 3-fold Table gives an overview of those datasets  The validity indices: we use the Mean Accuracy (MA) and the computational time  Parameters setting: the similarity threshold is set as h ¼ 0:2  Objective: Å To compare the accuracy of HU-FCF with those of relevant algorithms; Å To evaluate the computational time of algorithms 587 588 3.2 Experimental results 589 In this section, we present the experimental results expressed in Table In this table, we compare the proposed algorithm HUFCF with the algorithms of Lucas et al (a.k.a Lucas) and Zenebe and Norcio (a.k.a ZN) in terms of accuracy and computational time The experimental datasets are denoted as 100k (MovieLens 100k), 1M (MovieLens 1M) and BC (Book-Crossing) In order to validate the efficiency of the method to determine the weights of demographic attributes in Eqs (78) and (79), we made the experiments by various cases of weights such as, 590 591 592 593 594 595 596 597 598 599 600 601 602 603  Weight 1: the values of weights wi ð8i ¼ 1; lÞ are calculated by Eqs (78) and (79);  Weight 2: the values of weights wi ð8i ¼ 1; lị are set up equally: wi ẳ 1=l;  Weight 3: the values of weights wi ð8i ¼ 1; lÞ are randomly set up in (0,1) satisfying constraint (70) 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 L.H Son / Expert Systems with Applications xxx (2014) xxx–xxx According to the results in Table 8, we clearly recognize that the accuracy of HU-FCF is better than those of Lucas and ZN For example, in cases of Weight and the 1M dataset, the MA value of HUFCF is 82.2% which is larger than those of Lucas and ZN with the numbers being 78.4% and 62.1% In cases of Weight and the BC dataset, we also recognize that the MA value of HU-FCF is still better than those of Lucas and ZN with the numbers being 79.4%, 79.4% and 63.4%, respectively Lastly, the MA values of all algorithms in cases of Weight and the 100k dataset also show that HU-FCF is better than the algorithms of Lucas and ZN with the numbers being 82.1%, 81.4% and 55%, respectively Those examples clearly affirm that the accuracy of the HU-FCF algorithm is better than those of Lucas and ZN Nevertheless, there are some cases that the accuracy of HUFCF is worse than those of Lucas and ZN For example, in cases of Weight and the 100k dataset, the MA value of HU-FCF is 76.7% which is smaller than that of Lucas with the number being 81.4% Similarly, in cases of Weight and the BC dataset, the MA values of HU-FCF, Lucas and ZN algorithms are 77.4%, 79.4% and 63.4%, respectively However, the numbers of such bad cases are small in comparison with the rests, and most of time the accuracy of HU-FCF is still better than those of other algorithms Taking the comparison of algorithms by various cases of weights, we clearly recognize that the case of Weight often results in better accuracy of the HU-FCF algorithm than the cases of Weight and Weight Even though there exists a bad case of the accuracy of HU-FCF in comparison with other algorithms in each case of weight, the average MA value of HU-FCF by various datasets in the case of Weight is 80.7% whilst those in cases of Weight and Weight are 80.1% and 79.3%, respectively This clearly affirms the fact that using the generation method in Eqs (78) and (79) to create the values of weights wi 8i ẳ 1; lị is more efficient than other methods of weights As we have early predict the drawback of the computational time of HU-FCF over other relevant methods, the results in Table re-confirm that the computational time of HU-FCF is longer than those of other Table The comparison of algorithms Data MA (%) Time (s) HU-FCF Lucas ZN HU-FCF Lucas ZN Weight 100k 1M BC 76.7 82.2 83.1 81.4 78.4 79.4 55.0 62.1 63.4 22.7 113 132 15.3 78 96 18.4 93 115 Weight 100k 1M BC 81.3 79.7 79.4 81.4 78.4 79.4 55.0 62.1 63.4 27.4 122 148 15.3 78 96 18.4 93 115 Weight 100k 1M BC 82.1 78.4 77.4 81.4 78.4 79.4 55.0 62.1 63.4 28.3 136 155 15.3 78 96 18.4 93 115 algorithms For example, in case of the 100k dataset, it takes the HU-FCF algorithm approximately 26.1 s on average by various cases of weights This number is larger than those of Lucas and ZN with the numbers being 15.3 and 18.4 s, respectively In case of the 1M dataset, the values of computational time of HU-FCF, Lucas and ZN are 123, 78 and 93 s, respectively Lastly, the values of computational time of HU-FCF, Lucas and ZN in case of the BC dataset are 145, 96 and 115 s, respectively Even though the computational time of HU-FCF is larger than those of other algorithms, it is obvious that the difference is unremarkable and can be acceptable 641 3.3 Concluding remarks 652 Throughout the experimental results, we have extracted the following concluding remarks 653  The accuracy of HU-FCF is better than those of other relevant algorithms;  The generation method of weights of demographic attributes in Eqs (78) and (79) of Section 2.4 is the most effective ones among other methods of weights;  The drawback of the computational time of HU-FCF can be acceptable 655 643 644 645 646 647 648 649 650 651 654 656 657 658 659 660 661 662 An application of HU-FCF for football results prediction 663 In this section, we illustrate an application of HU-FCF for the football results prediction problem The experimental datasets were taken from the Barclays English Premier League (BEPL) including 20 teams and 38 rounds (Statto organisation, 2014) From the datasets, we have summarized some characteristics of a team by Table 664 Table Statistical information of a football team in BEPL Psychological/non-psychological information The number of games that failed to score The number of goals scored (in home team) The number of goals against (home team) The number of clean sheets (home team) The average age of players Injury per game The number of red (yellow) cards The number of penalties (against) The average number of shots per game Q1 Please cite this article in press as: Son, L H HU-FCF: A hybrid user-based fuzzy collaborative filtering method in Recommender Systems Expert Systems with Applications (2014), http://dx.doi.org/10.1016/j.eswa.2014.05.001 642 665 666 667 668 669 ESWA 9318 No of Pages 10, Model 5G 15 May 2014 Q1 L.H Son / Expert Systems with Applications xxx (2014) xxx–xxx Fig Results of BEPL season 2012–2013 670 671 672 673 674 675 676 677 678 Now, we describe how the HU-FCF algorithm can be applied to predict the football results Let us take a look at the statistics of BEPL season 2012–2013 visualized by Fig From this figure, we split the scoring results into subsets: the training and testing by the hold-out method, and use the training as the rating histories The users and items sets in this case are identical and consist of 20 football teams whose demographic data are shown in Table Next, we use the HU-FCF algorithm to predict the result of the match between Manchester United (Home team) and Arsenal 0:29 0:21 0:15 0:39 0:09 0:32 0:45 0:34 B 0:46 B B B 0:17 B B B 0:34 B T FD ¼ B B 0:48 B B 0:11 B B 0:09 B B @ 0:18 0:2 0:4 (Away team) The similarity threshold is set as h ¼ 0:2, and the weights of the demographic attributes are wi ẳ 1=9 i ẳ 1; 9ị From the rating histories, we encode a result ‘‘x—y’’ to the form of x 10 ỵ y for easy calculation so that the domain of the problem is now transformed to D ẳ ẵ0; ; 99 According to Eq (67), the fuzzy distances matrix is calculated as, 0:15 0:25 0:23 0:14 0:34 0:15 0:46 0:41 0:49 0:33 0:28 0:38 0:38 0:28 0:25 0:42 0:42 0:45 0:16 0:25 0:04 0:41 0:18 0:09 0:35 0:31 0:41 0:13 0:42 0:42 0:36 0:23 0:12 0:13 0:21 0:05 0:2 0:37 0:38 0:11 0:44 0:06 0:43 0:22 0:5 0:08 0:18 0:29 0:21 0:1 0:06 0:22 0:44 0:09 0:27 0:05 0:47 0:31 0:31 0:02 0:38 0:43 0:04 0:13 0:06 0:29 0:35 0:3 0:37 0:48 0:33 0:12 0:28 0:12 0:47 0:03 0:35 0:37 0:42 0:2 0:33 0:27 0:04 0:14 0:08 0:22 0:13 0:25 0:2 0:03 0:38 0:3 0:38 0:38 0:19 0:45 0:16 0:25 0:33 0:24 0:1 0:03 0:07 0:08 0:44 0:2 0:12 0:06 0:37 0:27 0:31 0:37 0:01 0:01 0:12 0:01 0:1 0:05 0:37 0:12 0:22 0:25 0:09 0:25 0:12 0:31 0:37 0:49 0:15 0:16 0:28 0:4 0:03 0:09 0:29 0:37 0:17 0:06 0:47 0:3 0:2 0:04 0:13 0:28 0:06 0:3 C C C 0:35 C C C 0:14 C C 0:42 C C; C 0:35 C C 0:26 C C C 0:21 A 0:34 ð80Þ Q1 Please cite this article in press as: Son, L H HU-FCF: A hybrid user-based fuzzy collaborative filtering method in Recommender Systems Expert Systems with Applications (2014), http://dx.doi.org/10.1016/j.eswa.2014.05.001 679 680 681 682 683 684 685 ESWA 9318 No of Pages 10, Model 5G 15 May 2014 Q1 L.H Son / Expert Systems with Applications xxx (2014) xxx–xxx Table 10 The comparison of accuracy (%) BEPL season HU-FCF Lucas ZN 2012–2013 2011–2012 2010–2011 33.3 38.3 31.1 30.6 35.4 29.8 32.7 37.3 30.2 Table 11 The comparison of accuracy (%) with the new domain 686 687 688 689 690 BEPL season HU-FCF Lucas et al Zenebe and Norcio 2012–2013 2011–2012 2010–2011 94.1 90.4 92.3 91.7 90.1 91.7 92.8 90.4 90.6 From Eq (80), we calculate the number of similarity degrees as c ¼ 65 Thus, a ¼ 0:77 and b ¼ 0:23 The fuzzy similarity degrees matrix is then expressed in Eq (81) From the rating histories we calculate the hard similarity degrees and the final similarity degrees matrices in Eqs (82) and (83), respectively between users Thus, we have made the following contributions: (i) a systematic mathematical definition of Fuzzy Recommender Systems that is a generalization of the existing definitions of Recommender Systems and Multi-Criteria Recommender Systems with an illustrated example from the MovieLens dataset was proposed; (ii) some basic algebraic operations in Fuzzy Recommender Systems such as the union, the intersection and the complement accompanied with their properties were presented; (iii) a novel hybrid user-based fuzzy collaborative filtering method for Fuzzy Recommender Systems so-called HU-FCF that utilizes both fuzzy and hard user-based similarity degrees and automatically calculates the weights of attributes and degrees was described Experimental results conducted on some benchmark RS datasets such as MovieLens and Book-Crossing showed that HU-FCF obtains better accuracy than other relevant fuzzy filtering methods The proposed methodology has good impacts and practical implications to the community researches of Recommender Systems and expert & knowledge-based systems Firstly, it enriches the knowledge of modeling and formulation of Fuzzy Recommender Systems Secondly, some basic algebraic operations of Fuzzy Recommender Systems could be used for further studies 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 FSDT ¼ ð 0:76 0:74 0:79 0:65 0:74 0:7 0:73 0:75 0:74 0:78 0:81 0:72 0:79 0:78 0:77 0:81 0:8 0:76 0:7 ị: 81ị HSDT ẳ À0:42 À0:42 À0:32 À0:43 0:14 0:33 0:28 0:06 À0:09 0:02 À0:12 À0:14 À0:64 0:21 À0:71 0:31 À0:28 À0:44 Þ; 82ị SIM T ẳ 0:49 0:48 0:61 0:43 0:48 0:57 0:64 0:64 0:59 0:58 0:63 0:53 0:58 0:46 0:64 0:47 0:69 0:52 0:44 Þ: 691 692 693 694 695 696 697 698 699 700 701 702 à Thus, the nal rating is Ra; i ị ẳ 21:248 From the domain, we à determine the nearest value of Rða; i Þ is ‘‘21’’ that means ‘‘2–1’’ with the error threshold being D ¼ 1:16% This result is identical to that in Fig If we use the existing fuzzy collaborative filtering methods such as the work of Lucas et al (2012) and Zenebe and Norcio (2009), the predictive results are ‘‘0–1’’ and ‘‘1–1’’, respectively Eventually, we have made the comparative experiments for the remaining matches in the testing data of the season 2012–2013 and the matches of other seasons and received the results in Table 10 If domain D returns to {‘‘Win’’, ’’Draw’’, ‘‘Lose’’} then we receive the results in Table 11 703 Conclusions 704 In this paper, we aimed to enhance the accuracy of prediction of the available filtering method in Fuzzy Recommender Systems From the scanning literature, we have pointed out the limitations of the relevant researches that are the lack of a well-defined mathematical definition of Fuzzy Recommender Systems accompanied with its algebraic operations and properties and the fuzzy similarity degree is not enough to express accurately the analogousness 705 706 707 708 709 710 ð83Þ involving the mathematical foundations of Recommender Systems Thirdly, an application of the fuzzy filtering method HU-FCF for the football results prediction in Section has shown the capability of the proposed method to be applied to various practical problems Last but not least, general readers could have a great benefit from taking the know-how of system modeling and algorithmic formulation; thus utilizing them for cross interdisciplinary researches As being mentioned in Section 2.4, the HU-FCF algorithm was designed on the basis of Recommender Systems so that one of further research directions is to extend this algorithm to work with truly Fuzzy Recommender Systems expressed in Definition by considering the fuzzification both in the left and right sides of Eq (3) Furthermore, some other algebraic operations of Fuzzy Recommender Systems should be developed for the completeness of the system Finally, a combination of the HU-FCF algorithm with a neuro-fuzzy network for some forecast problems to accelerate the accuracy is also our target 732 Acknowledgments 749 The authors are greatly indebted to the editor-in-chief Prof B Lin and anonymous reviewers for their comments and suggestions 750 Q1 Please cite this article in press as: Son, L H HU-FCF: A hybrid user-based fuzzy collaborative filtering method in Recommender Systems Expert Systems with Applications (2014), http://dx.doi.org/10.1016/j.eswa.2014.05.001 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 751 ESWA 9318 No of Pages 10, Model 5G 15 May 2014 Q1 10 L.H Son / Expert Systems with Applications xxx (2014) xxx–xxx 755 that improve the clarity and quality of the paper Other thanks are sent to Mr Khuat Manh Cuong, VNU for the calculation works This work is sponsored by the NAFOSTED under contract No 102.052014.01 756 References 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 Adomavicius, G., & Tuzhilin, A (2005) Toward the next generation of recommender systems: A survey of the state-of-the-art and possible extensions IEEE Transactions on Knowledge and Data Engineering, 17(6), 734–749 Al-Shamri, M Y H., & Bharadwaj, K K (2008) Fuzzy-genetic approach to recommender systems based on a novel hybrid user model Expert Systems with Applications, 35(3), 1386–1399 Borges, H L., & Lorena, A C (2010) A survey on recommender systems for news data In Smart information and knowledge management (pp 129–151) Berlin, Heidelberg, Germany: Springer Boulkrinat, S., Hadjali, A., & Mokhtari, A (2013) Towards recommender systems based on a fuzzy preference aggregation Proceeding of the eighth conference of the European society for fuzzy logic and technology (EUSFLAT-13), 146–153 Cao, Y., & Li, Y (2007) An intelligent fuzzy-based recommendation system for consumer electronic products Expert Systems with Applications, 33(1), 230–240 Carrer-Neto, W., Hernández-Alcaraz, M L., Valencia-García, R., & García-Sánchez, F (2012) Social knowledge-based recommender system Application to the movies domain Expert Systems with Applications, 39(12), 10990–11000 Christidis, K., & Mentzas, G (2013) A topic-based recommender system for electronic marketplace platforms Expert Systems with Applications, 40(11), 4370–4379 Costa-Montenegro, E., Barragáns-Martínez, A B., & Rey-López, M (2012) Which App? 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accompanied with its algebraic operations and properties and a novel hybrid user-based fuzzy collaborative filtering method. .. contributions in this article are expressed as follows 190  A systematic mathematical definition of FRS accompanied with its algebraic operations and properties  A novel hybrid user-based fuzzy collaborative