Information Sciences 181(2011)1503-1516 Contents lists available at Science Direct Information sciences ELSEVIER journalhomepage:www.elsevier.com/locate/ins A google wave-based fuzzy recommender system to disseminate information in University Digital Libraries 2.0 Jesus Serrano-Guerrero Enrique Herrera-Viedma, Jose A Olivas Andres Cerezo francisco P. romero a echnologies and Systems, University of Castilla-La Mancha, 13071 Ciudad ReaL Spain b Department of Computer Science and Artificial Intelligence, University of Granada, 18071 Granada, Spain ARTICLE IN FO A BSTRACT Nowadays Digital Libraries 2.0 are mainly based on the interaction between users through collaborative applications such as wikis, blogs, etc or new possible paradigms like the d in revised form 17 December 2010 1 January 2011 vaves proposed by Google. This new concept, the wave, represents a common space where online 9 January 2011 resources and users can work together. The problem arises when the number of resources In this case a fuzzy linguistic recommender system based on the Google Wave capabilities ender system is proposed as tool for communicating researchers interested in common research line The system allows the creation of a common space by means a wave as a way of collabo- rating and exchanging ideas between several researchers interested in the same topic. In 2-Tuple fuzzy linguistic modeling addition, the system suggests, in an automatic way, several researchers and useful esources for each wave. These recommendations are computed following several previ- usly defined preferences and characteristics by means of fuzzy linguistic labels. Thus he system facilitates the possible collaborations between multi-disciplinar researchers Ind recommends complementary resources useful for the interaction. In order to test he effectiveness of the proposed system, a prototype of the system has been developed and tested with several research groups from the same university achieving successful e 2011 Elsevier Inc. All rights re Digital information allows the storage, access and transmission of millions of resources in an easy way but at the same time this fact involves problems for finding the suitable information. This problem is present in digital libraries Digital libraries are an extension of the classic libraries where information about different topics can be found easily, all available information is accessible through the Web[ 44. The apparition of digital libraries has changed the perception of traditional libraries [31]. Digital libraries can be focused on different contexts. In our case, we are especially interested in the University Digital Libraries (UDL). These kinds of libraries store information about books, electronic papers, electronic journals or official dailies [42, 47 and user profiles. The advent of University Digital Libraries meant a change in the life of the researchers, the amount of information avail- able grew amazingly and the necessary time to access to that information was considerably reduced. However the continued Corresponding author. Tel:+34 651504322 doi:10.1016ins201101.012
A google wave-based fuzzy recommender system to disseminate information in University Digital Libraries 2.0 Jesus Serrano-Guerrero a,⇑ , Enrique Herrera-Viedma b , Jose A. Olivas a , Andres Cerezo a , Francisco P. Romero a aDepartment of Information Technologies and Systems, University of Castilla-La Mancha, 13071 Ciudad Real, Spain bDepartment of Computer Science and Artificial Intelligence, University of Granada, 18071 Granada, Spain article info Article history: Received 19 February 2010 Received in revised form 17 December 2010 Accepted 1 January 2011 Available online 9 January 2011 Keywords: Recommender system University Digital Library Google wave 2-Tuple fuzzy linguistic modeling abstract Nowadays Digital Libraries 2.0 are mainly based on the interaction between users through collaborative applications such as wikis, blogs, etc. or new possible paradigms like the waves proposed by Google. This new concept, the wave, represents a common space where resources and users can work together. The problem arises when the number of resources and users is high, then tools for assisting the users in their information needs are necessary. In this case a fuzzy linguistic recommender system based on the Google Wave capabilities is proposed as tool for communicating researchers interested in common research lines. The system allows the creation of a common space by means a wave as a way of collaborating and exchanging ideas between several researchers interested in the same topic. In addition, the system suggests, in an automatic way, several researchers and useful resources for each wave. These recommendations are computed following several previously defined preferences and characteristics by means of fuzzy linguistic labels. Thus the system facilitates the possible collaborations between multi-disciplinar researchers and recommends complementary resources useful for the interaction. In order to test the effectiveness of the proposed system, a prototype of the system has been developed and tested with several research groups from the same university achieving successful results. 2011 Elsevier Inc. All rights reserved. 1. Introduction Digital information allows the storage, access and transmission of millions of resources in an easy way but at the same time this fact involves problems for finding the suitable information. This problem is present in digital libraries. Digital libraries are an extension of the classic libraries where information about different topics can be found easily, all available information is accessible through the Web [44]. The apparition of digital libraries has changed the perception of traditional libraries [31]. Digital libraries can be focused on different contexts. In our case, we are especially interested in the University Digital Libraries (UDL). These kinds of libraries store information about books, electronic papers, electronic journals or official dailies [42,47] and user profiles. The advent of University Digital Libraries meant a change in the life of the researchers, the amount of information available grew amazingly and the necessary time to access to that information was considerably reduced. However the continued 0020-0255/$ - see front matter 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.ins.2011.01.012 ⇑ Corresponding author. Tel.: +34 651504322. E-mail address: jesus.serrano@uclm.es (J. Serrano-Guerrero). Information Sciences 181 (2011) 1503–1516 Contents lists available at ScienceDirect Information Sciences journal homepage: www.elsevier.com/locate/ins
1504 J. Serrano-Guerrero et al Information Sciences 181 (2011)1503-1516 nformation 2.0 N-way information ow Nonlinear Participatory Interactive Librarian 2.0 Collaborative Fig. 1. Library 2.0. development of new technologies has allowed the appearance of new paradigms: this is the case of Web 2.0 and conse- quently the appearance of Library 2.0. o The first person who used the term Web 2.0 was Dale Dougherty from the company O Reilly Media in 2004 and from that oment, Tim O'Reilly [37] started to use that term in his conferences to refer to the new developments that the Web The precise definition of Web 2.0 is not clear. Many definitions can be found but the researchers are still discussing the definitive definition. It is not clear if the Web 2.0 is a new paradigm or simply a natural evolution of the current Web. Web 2.0 is based on the user as the main figure who is capable of creating, modifying and publishing the content of the Web pages in collaboration with other users. The user is able to interact in simplified way with the applications because they are very lightweight, and it is not required to be an expert in computer science to write your own content in applications such as blogs, wikis, social networks, etc. Many new services 2.0 are appearing everyday: Facebook, Flickr, Wikipedia and Blogspot are some clear examples of this fact. The continued development of new and innovative applications involves the appearance of new paradigms, such as in the case of Google Wave, a new tool which is capable of encapsulating typical functions from other Web applications such as RSS, blogs, chats, wikis, social networks, etc. The application of the capabilities of this new technology to the UDLs is one he objectives of this work in order to extend the concept of Library 2.0. The first person who used the term Library 2.0 was Casey [12] and since that moment many related works have emerged [15,48, 50. Xu 51 depicted a model (see Fig. 1)of the Library 2.0 based on three components, (i)the information. (ii) the users and (iii)the librarians. He summarizes several applications based on Web 2.0 tools(blogs, RSS, tagging, wikis, social networks, and podcasts) applied to Academic libraries and this is the objective of this work as well, the application of the Google wave technology to develop a recommender system that will suggest users and digital resources for collaborative purposes between the users of a University Digital Library, specially the researchers. This system allows the reduction of the necessary time to find col- laborator and information about digital resources depending on the user needs. An example of an application of the system would be when several research groups want to request a European project. These research groups have decided to collaborate for research purposes and they request a common environment(a wave) from the university staff. They are the first members of the wave and for example the official announcement and other re- lated documents are the first resources of the wave but it is necessary to find new partners and old documents about the announcements from past years, etc. That is the moment in which the recommender system suggests and relevant resources from the library to achieve the collaborative objectives of the wave. The proposed recommender system is mainly based on Fuzzy Logic [18, 21] which has been used successfully in other pre- vious approaches [14, 23, 40, 41 The rest of the paper is organized as follows. Section 2 presents the preliminaries of this work: Google Wave, Recom- lender Systems and Fuzzy Linguistic Modeling. Section 3 presents the architecture and the main characteristics of the pro- posed fuzzy linguistic recommender system. Section 4 presents the results of an experiment using this system and finally ome conclusions and future works are pointed out. 2. Foundations 2.1. Google wave Web 2.0 proposes the use of many new applications with collaborative purposes, now the interaction between users is one of the main points of the information and communication technologies. Following this idea google wave has introduced a new communication and collaboration platform built around hosted conversations called waves. The wave model enables https://wavegoogle.com
development of new technologies has allowed the appearance of new paradigms; this is the case of Web 2.0 and consequently the appearance of Library 2.0. The first person who used the term Web 2.0 was Dale Dougherty from the company O’Reilly Media in 2004 and from that moment, Tim O’Reilly [37] started to use that term in his conferences to refer to the new developments that the Web is undergoing. The precise definition of Web 2.0 is not clear. Many definitions can be found but the researchers are still discussing the definitive definition. It is not clear if the Web 2.0 is a new paradigm or simply a natural evolution of the current Web. Web 2.0 is based on the user as the main figure who is capable of creating, modifying and publishing the content of the Web pages in collaboration with other users. The user is able to interact in simplified way with the applications because they are very lightweight, and it is not required to be an expert in computer science to write your own content in applications such as blogs, wikis, social networks, etc. Many new services 2.0 are appearing everyday; Facebook, Flickr, Wikipedia and Blogspot are some clear examples of this fact. The continued development of new and innovative applications involves the appearance of new paradigms, such as in the case of Google Wave,1 a new tool which is capable of encapsulating typical functions from other Web applications such as RSS, blogs, chats, wikis, social networks, etc. The application of the capabilities of this new technology to the UDLs is one the objectives of this work in order to extend the concept of Library 2.0. The first person who used the term Library 2.0 was Casey [12] and since that moment many related works have emerged [15,48,50]. Xu [51] depicted a model (see Fig. 1) of the Library 2.0 based on three components, (i) the information, (ii) the users and (iii) the librarians. He summarizes several applications based on Web 2.0 tools (blogs, RSS, tagging, wikis, social networks, and podcasts) applied to Academic Libraries and this is the objective of this work as well, the application of the Google Wave technology to develop a recommender system that will suggest users and digital resources for collaborative purposes between the users of a University Digital Library, specially the researchers. This system allows the reduction of the necessary time to find collaborators and information about digital resources depending on the user needs. An example of an application of the system would be when several research groups want to request a European project. These research groups have decided to collaborate for research purposes and they request a common environment (a wave) from the university staff. They are the first members of the wave and for example the official announcement and other related documents are the first resources of the wave, but it is necessary to find new partners and old documents about the announcements from past years, etc. That is the moment in which the recommender system suggests new participants and relevant resources from the library to achieve the collaborative objectives of the wave. The proposed recommender system is mainly based on Fuzzy Logic [18,21] which has been used successfully in other previous approaches [14,23,40,41]. The rest of the paper is organized as follows. Section 2 presents the preliminaries of this work: Google Wave, Recommender Systems and Fuzzy Linguistic Modeling. Section 3 presents the architecture and the main characteristics of the proposed fuzzy linguistic recommender system. Section 4 presents the results of an experiment using this system and finally some conclusions and future works are pointed out. 2. Foundations 2.1. Google wave Web 2.0 proposes the use of many new applications with collaborative purposes, now the interaction between users is one of the main points of the information and communication technologies. Following this idea Google Wave has introduced a new communication and collaboration platform built around hosted conversations called waves. The wave model enables Fig. 1. Library 2.0. 1 https://wave.google.com. 1504 J. Serrano-Guerrero et al. / Information Sciences 181 (2011) 1503–1516
J. Serrano-Guerrero et aL Information Sciences 181(2011)1503-1516 1505 people to communicate and work together in new and more effective ways. The system is based on the google Wave Fed- ration Protocol for sharing waves between wave providers According to the google development team, "Google Wave is an online tool for real-time communication and collabora- tion. a wave can be both a conversation and a document where people can discuss and work together using richly formatted text, photos, videos, maps, and more Therefore this new concept ofwave can be understood as a new application which merges capabilities from blogs, chats. wikis. etc on the platform. The wave can be understood as a conversation or a document where several participants n publish messages or edit the existing ones and see what, when and who edited each part of the wave Google wave has many innovative features such as (])real-time: you can see what someone else is typing. iiembedda- bility: waves can be embedded on any blog or website, (iii) applications and extensions: developers can build their own applications within waves, (iv)playback: the user can playback any part of the wave to see what was said, (v)open source, vi)wiki functionality: anything written within a Google wave can be edited by anyone else, because all of the conversations thin the platform are shared and therefore the users can correct information, append new information, comment the exist ng information within a developing conversation, (vii) drag-and-drop file sharing: the user can drag a file and drop it inside the wave and everyone will have access, etc. One of the most important Google Wave characteristics is the extensions. An extension is a mini-application that works within a wave. There are two main types of extensions: Gadgets and robots Gadgets are specific to individual waves, rather than to specific users, the gadget belongs to everyone within the wave Some of the gadgets already built include games for several participating players, maps for several navigating users on the same Google Map, etc. Robots are the other type of Google Wave extension. Robots are like having another person within a Google Wave con- ersation. Robots can carry out several actions such as the modification of information in waves, interaction with users, com- munication with the waves of others and the insertion of information from external sources the behavior of each robot is programmed and they can be working in the background while users are writing within the wave. 2. 2. Recommender systems Recommender systems are one of the most studied current research lines today however. despite all of the achieved ad- vances, the current generation of recommender systems still requires further improvement to make recommendations more effective and applicable to a broader range of applications [1. A recommendation system can be considered as a system which provides personalized information services in different to characterize recommender systems [38]. depending on how the system is.*381. It is necessary to study four dimensions ways reducing information overload taking into account the user preferences · modeled and designed targeted(to an individual, group, or topic). built an ed (online vs offline ). Manyclassifications can be found [43 ]. for example, based on how recommendations are made. Recommender systems can be classified into three main categories [3].(i)Content-based recommender he recommendations are based on an item chosen by the user in the past, (ii)Collaborative recommender systems: the recommendations are based on items hosen by other users with similar preferences to our user, and (iii) Hybrid recommender systems: this approach combines the two previous methods. The latter category can be sub-classified (i)implementing collaborative and content-based approaches in a separate way nd combining their results. (ii) incorporating some content-based characteristics into a collaborative method, (iii) incorpo- rating some collaborative characteristics into a content-based method, and (iv) developing a method capable of incorporat ing both content-based and collaborative characteristics [1]. Recommender systems have an underlying social element and consequently involve user modeling, i. e the representa tion of user preferences. This information can be directly provided by the user or inferred from user data stored in the system [3849 These kinds of systems have been applied successfully to different domains such as e-commerce [10, 13, 30], University D igital Libraries [35, 39, 41, movies recommendations and TV programms[2,4, 34], technology ti nsference[40, service loca- tion [46, education [11. news 29.etc. 2.3. 2-Tuple fuzzy linguistic approach The quantitative assessment of the different aspects of the real world is not always due to th precision of the underlying knowledge. For this reason a linguistic approach can be a mo resting alternative instead of the use of numerical values. The fuzzy linguistic approach is based on the representation
people to communicate and work together in new and more effective ways. The system is based on the Google Wave Federation Protocol for sharing waves between wave providers. According to the Google development team,‘‘Google Wave is an online tool for real-time communication and collaboration. A wave can be both a conversation and a document where people can discuss and work together using richly formatted text, photos, videos, maps, and more’’. Therefore this new concept of ‘wave’ can be understood as a new application which merges capabilities from blogs, chats, wikis, etc. on the same platform. The wave can be understood as a conversation or a document where several participants can publish messages or edit the existing ones and see what, when and who edited each part of the wave. Google Wave has many innovative features such as (i) real-time: you can see what someone else is typing, (ii) embeddability: waves can be embedded on any blog or website, (iii) applications and extensions: developers can build their own applications within waves, (iv) playback: the user can playback any part of the wave to see what was said, (v) open source, (vi) wiki functionality: anything written within a Google Wave can be edited by anyone else, because all of the conversations within the platform are shared and therefore the users can correct information, append new information, comment the existing information within a developing conversation, (vii) drag-and-drop file sharing: the user can drag a file and drop it inside the wave and everyone will have access, etc. One of the most important Google Wave characteristics is the extensions. An extension is a mini-application that works within a wave. There are two main types of extensions: Gadgets and Robots. Gadgets are specific to individual waves, rather than to specific users, the gadget belongs to everyone within the wave. Some of the gadgets already built include games for several participating players, maps for several navigating users on the same Google Map, etc. Robots are the other type of Google Wave extension. Robots are like having another person within a Google Wave conversation. Robots can carry out several actions such as the modification of information in waves, interaction with users, communication with the waves of others, and the insertion of information from external sources. The behavior of each robot is programmed and they can be working in the background while users are writing within the wave. 2.2. Recommender systems Recommender systems are one of the most studied current research lines today, however, despite all of the achieved advances, the current generation of recommender systems still requires further improvement to make recommendations more effective and applicable to a broader range of applications [1]. A recommendation system can be considered as a system which provides personalized information services in different ways reducing information overload taking into account the user preferences [7,38]. It is necessary to study four dimensions to characterize recommender systems [38], depending on how the system is: modeled and designed, targeted (to an individual, group, or topic), built and maintained (online vs. offline). Manyclassifications can be found [43], for example, based on how recommendations are made. Recommender systems can be classified into three main categories [3], (i) Content-based recommender systems: the recommendations are based on an item chosen by the user in the past, (ii) Collaborative recommender systems: the recommendations are based on items chosen by other users with similar preferences to our user, and (iii) Hybrid recommender systems: this approach combines the two previous methods. The latter category can be sub-classified (i) implementing collaborative and content-based approaches in a separate way and combining their results, (ii) incorporating some content-based characteristics into a collaborative method, (iii) incorporating some collaborative characteristics into a content-based method, and (iv) developing a method capable of incorporating both content-based and collaborative characteristics [1]. Recommender systems have an underlying social element and consequently involve user modeling, i.e., the representation of user preferences. This information can be directly provided by the user or inferred from user data stored in the system [38,49]. These kinds of systems have been applied successfully to different domains such as e-commerce [10,13,30], University Digital Libraries [35,39,41], movies recommendations and TV programms [2,4,34], technology transference [40], service location [46], education [11], news [29], etc. 2.3. 2-Tuple fuzzy linguistic approach The quantitative assessment of the different aspects of the real world is not always possible due to the vagueness or imprecision of the underlying knowledge. For this reason a linguistic approach can be a more interesting alternative instead of the use of numerical values. The fuzzy linguistic approach is based on the representation of qualitative aspects as linguistic J. Serrano-Guerrero et al. / Information Sciences 181 (2011) 1503–1516 1505
J. Serrano-Guerrero et al Information Sciences 181 (2011)1503-1516 alues by means of linguistic variables 52. Its application has been successful to different problems such as information retrieval [5,6, 22-24, 28, recommender systems [40, 41]. quality evaluation [26, 27, 36 decision making 8,9, 17.3 The 2-tuple FLM [20 is a continuous model of representation of information which reduces the loss of typical of other fuzzy linguistic approaches (classical and ordinal [ 16, 52)). To define it we have to establish representation model and the 2-tuple computational model to represent and aggregate the linguistic respectively. Let S=(So, J be a linguistic term set with odd cardinality, where the middle term an indifference value and the rest of the terms are symmetrically related to it. We assume that the semantics of the labels are given by means of tri- ngular membership functions and we consider that all terms are distributed on a scale in which a total order is defined, S,<S)+isj. In this fuzzy linguistic context, a symbolic method [ 19, 16] aggregating linguistic information obtains a value BE[O, g] and B#(O,.... g) then an approximation function is used to express the result in S. Definition 1. Let B be the result of an aggregation of the indexes of a set of labels assessed ustic term set S, i.e the result of a symbolic aggregation operation, BE[O, g. Let i= round(e)and a=B-i be two such that,i∈[0.g]and ZIE[-5.5) then a is called a Symbolic Translation 20 The 2-tuple fuzzy linguistic approach is developed from the concept of symbolic translation by representing the linguistic S: represents the linguistic label of the information, and xi is a numerical value expressing the value of the translation from the original result B to the closest index label, i, in the nguistic term set (SiE S). This model defines a set of transformation functions between numeric values and 2-tuples. Definition 2. Let S=(so. l,.,Sg) be a linguistic term set and BE[O, g a value representing the result of a symbolic aggregation operation, then the 2-tuple that expresses the equivalent information to B is obtained with the following function[20 △:[0.g]→S×-0.50.5), △(=(sxwt(5 i= round (e) x=B-ix∈-5,5 where round() is the usual round operation, s, has the closest index label to"Banda"is the value of the symboli For all A there exists A-(Si, ax)=i+ a. On the other hand, it is obvious that the conversion of a linguistic term into a lin- guistic 2-tuple consists of adding a symbolic translation value of 0: SES=(S, O). The computational model is defined by presenting the following operator 1. Negation operator: Neg(s, x)=A(g-A"(si, a)) 2. Comparison of 2-tuples(Sk, a,)and(S, a2) if k< I then(Sk, &1) is smaller than(Si, a2) if k=I then (a) if a1=%2 then(Sk,a,)and(sp,a2)represent th e same l (b) if a1< 2 then(Sk, o) is smaller than(S, a2) (c) if 1> a2 then(Sk, M) is bigger than(s,2) 3. Aggregation operators. The aggregation of information consists of obtaining a value that summarizes a set of values, herefore, the result of the aggregation of a set of 2-tuples must be a 2-tuple. In the literature we can find many aggre- tion operators which allow us to combine the information according to different criteria Using functions A and A hat transform without loss of information numerical values into linguistic 2-tuples and vice versa, any of the existing gregation operator can be easily extended for dealing with linguistic 2-tuples. Some examples are Definition 3(Arithmetic mean). Let x=((r1, a1),... (n, Mn)) be a set of linguistic 2-tuples, the 2-tuple arithmetic mean x is omputed as xn2x)…-(2(0)-4(S) Definition 4(Weighted average operator). Let x=((r1, 1)..... (rn, an) be a set of linguistic 2-tuples and w=(wi,., wn) be their associated weights. The 2-tuple weighted average xis:
values by means of linguistic variables [52]. Its application has been successful to different problems such as information retrieval [5,6,22–24,28], recommender systems [40,41], quality evaluation [26,27,36], decision making [8,9,17,32,53], etc. The 2-tuple FLM [20] is a continuous model of representation of information which reduces the loss of information typical of other fuzzy linguistic approaches (classical and ordinal [16,52]). To define it we have to establish the 2-tuple representation model and the 2-tuple computational model to represent and aggregate the linguistic information respectively. Let S = {s0,..., sg} be a linguistic term set with odd cardinality, where the middle term represents an indifference value and the rest of the terms are symmetrically related to it. We assume that the semantics of the labels are given by means of triangular membership functions and we consider that all terms are distributed on a scale in which a total order is defined, si 6 sj () i 6 j. In this fuzzy linguistic context, a symbolic method [19,16] aggregating linguistic information obtains a value b 2 [0,g] and b R {0,...,g} then an approximation function is used to express the result in S. Definition 1. Let b be the result of an aggregation of the indexes of a set of labels assessed in a linguistic term set S, i.e., the result of a symbolic aggregation operation, b 2 [0,g]. Let i = round(b) and a = b i be two values, such that, i 2 [0,g] and ai 2 [.5, .5) then a is called a Symbolic Translation [20]. The 2-tuple fuzzy linguistic approach is developed from the concept of symbolic translation by representing the linguistic information by means of 2-tuples (si,ai), si 2 S and ai 2 [.5,.5): si represents the linguistic label of the information, and ai is a numerical value expressing the value of the translation from the original result b to the closest index label, i, in the linguistic term set (si 2 S). This model defines a set of transformation functions between numeric values and 2-tuples. Definition 2. Let S = {s0, s1,..., sg} be a linguistic term set and b 2 [0,g] a value representing the result of a symbolic aggregation operation, then the 2-tuple that expresses the equivalent information to b is obtained with the following function [20]: D : ½0; g ! S ½0:5; 0:5Þ; DðbÞ¼ðsi; aÞ; with si i ¼ roundðbÞ; a ¼ b i ai 2 ½:5; :5Þ; where round() is the usual round operation, si has the closest index label to ‘‘b’’ and ‘‘a’’ is the value of the symbolic translation. For all D there exists D1 (si,a) = i + a. On the other hand, it is obvious that the conversion of a linguistic term into a linguistic 2-tuple consists of adding a symbolic translation value of 0: si 2 S ) (si,0). The computational model is defined by presenting the following operators: 1. Negation operator: Neg(si,a) = D(g D1 (si,a)) 2. Comparison of 2-tuples (sk,a1) and (sl,a2): if k < l then (sk,a1) is smaller than (sl,a2) if k = l then (a) if a1 = a2 then (sk,a1) and (sl,a2) represent the same informations (b) if a1 6 a2 then (sk,a1) is smaller than (sl,a2) (c) if a1 P a2 then (sk,a1) is bigger than (sl,a2) 3. Aggregation operators. The aggregation of information consists of obtaining a value that summarizes a set of values, therefore, the result of the aggregation of a set of 2-tuples must be a 2-tuple. In the literature we can find many aggregation operators which allow us to combine the information according to different criteria. Using functions D and D1 that transform without loss of information numerical values into linguistic 2-tuples and vice versa, any of the existing aggregation operator can be easily extended for dealing with linguistic 2-tuples. Some examples are: Definition 3 (Arithmetic mean). Let x = {(r1,a1),..., (rn,an)} be a set of linguistic 2-tuples, the 2-tuple arithmetic mean xe is computed as: xe ½ðr1; a1Þ; ... ;ðrn; anÞ ¼ D Xn i¼1 1 n D1 ðri; aiÞ ! ¼ D 1 n Xn i¼1 bi !: Definition 4 (Weighted average operator). Let x = {(r1,a1),..., (rn,an)} be a set of linguistic 2-tuples and W = {w1,...,wn} be their associated weights. The 2-tuple weighted average xw is: 1506 J. Serrano-Guerrero et al. / Information Sciences 181 (2011) 1503–1516
J. Serrano-Guerrero et aL Information Sciences 181(2011)1503-1516 1507 (r1,x1)…(m,xn)=△ ∑1A()*w=△(∑w 1B1*W efinition 5(Linguistic weighted average operator). Let x=((ra,,. (n,an) be a set of linguistic 2-tuples and I(w1, a),.... (wn, aw)) be their linguistic 2-tuple associated we eights. The 2-tuple linguistic weighted average xy is: R"[(r1,a1,w1,x")…,(n,x1),w,z7) with B=△-(r,x)andw2=△-(w,x) In any fuzzy linguistic approach, an important parameter to determine is the"granularity of uncertainty, i.e., the cardi nality of the linguistic term set S. According to the uncertainty degree that an expert qualifying a phenomenon has on it, the linguistic term set chosen to provide his knowledge will have more or less terms. When different experts have different uncertainty degrees on the phenomenon then several linguistic term sets with a different granularity of uncertainty are n esry[21,25,33 The use of different label sets to assess information is also necessary when an expert has to assess different concepts, as for example it happens in information retrieval problems, to evaluate the importance of the query terms and the importance of the retrieved documents [27 In such situations, we need tools to manage multi-granular linguistic information. In[22, 28 a multi-granular 2-tuple FLm based on the concept of linguistic hierarchy is proposed A Linguistic Hierarchy, LH, is a set of levels I(t, n(t)), i.., LH= U(t, n(t)), where each level t is a linguistic term set with a different granularity n(t) from the remaining of levels of the hierarchy. the levels are ordered according to their granularity e, a level t+ 1 provides a linguistic refinement of the previous level t We can define a level from its predecessor level as I(t, n(t))-(t+ 1. 2*n(t)-1) table 1 shows the granularity needed in each linguistic term set of the level t depending on the value n(t) defined in the first level (3 and 7, respectively A graphical example of a linguistic hierarchy is shown in Fig. 2. Herrera [21] demonstrated that linguistic hierarchies are useful to represent multi-granular linguistic information and allow the combination of multi-granular linguistic information without loss of information. To do this, a family of transfor mation functions between labels from different levels was defined transformation function between a 2-tuple that belongs to level t and another 2-tuple in level t +t is defined.5i-i.The Definition 6. Let LH=Ur(t, n(t)be a linguistic hierarchy whose linguistic term sets are denoted as sn(=(som) TF=lt,n(t)→l(t,n(t) n(t)-1 Table 1 Linguistic hierarchies. Level 1 Level 2 Mr, n(r) I(2.5) KL, n(t) l(2,13) Fig. 2. Linguistic hierarchy of 3. 5 and 9 labels
xw½ðr1; a1Þ; ... ;ðrn; anÞ ¼ D Pn i¼1D1 ðri P ; aiÞ wi n i¼1wi ! ¼ D Pn i¼1 P bi wi n i¼1wi : Definition 5 (Linguistic weighted average operator). Let x = {(r1,a1),..., (rn,an)} be a set of linguistic 2-tuples and W ¼ fðw1; aw 1 Þ; ... ;ðwn; aw n Þg be their linguistic 2-tuple associated weights. The 2-tuple linguistic weighted average xw l is: xw ððr1; a1Þ;ðw1; aw 1 ÞÞ; ... ; ðr1; a1Þ; w1; aw 1 ¼ D Pn i¼1 P bi bwi n i¼1bwi !; with bi ¼ D1 ðri; aiÞ and bwi ¼ D1 wi; aw i : 2.4. The multi-granular fuzzy linguistic modeling In any fuzzy linguistic approach, an important parameter to determine is the ‘‘granularity of uncertainty’’, i.e., the cardinality of the linguistic term set S. According to the uncertainty degree that an expert qualifying a phenomenon has on it, the linguistic term set chosen to provide his knowledge will have more or less terms. When different experts have different uncertainty degrees on the phenomenon, then several linguistic term sets with a different granularity of uncertainty are necessary [21,25,33]. The use of different label sets to assess information is also necessary when an expert has to assess different concepts, as for example it happens in information retrieval problems, to evaluate the importance of the query terms and the importance of the retrieved documents [27]. In such situations, we need tools to manage multi-granular linguistic information. In [22,28] a multi-granular 2-tuple FLM based on the concept of linguistic hierarchy is proposed. A Linguistic Hierarchy, LH, is a set of levels l(t,n(t)), i.e., LH = S tl(t,n(t)), where each level t is a linguistic term set with a different granularity n(t) from the remaining of levels of the hierarchy. The levels are ordered according to their granularity, i.e., a level t + 1 provides a linguistic refinement of the previous level t. We can define a level from its predecessor level as: l(t,n(t)) ? l(t + 1,2⁄n(t) 1). Table 1 shows the granularity needed in each linguistic term set of the level t depending on the value n(t) defined in the first level (3 and 7, respectively). A graphical example of a linguistic hierarchy is shown in Fig. 2. Herrera [21] demonstrated that linguistic hierarchies are useful to represent multi-granular linguistic information and allow the combination of multi-granular linguistic information without loss of information. To do this, a family of transformation functions between labels from different levels was defined: Definition 6. Let LH = S tl(t,n(t)) be a linguistic hierarchy whose linguistic term sets are denoted as SnðtÞ ¼ fs nðtÞ 0 ; ... ; s nðtÞ t1g. The transformation function between a 2-tuple that belongs to level t and another 2-tuple in level t 0 – t is defined as: TFt t0 ¼ lðt; nðtÞÞ ! lðt 0 ; nðt 0 ÞÞ; TFt t0 s nðtÞ i ; anðtÞ ¼ D D1 ðs nðtÞ i ; anðtÞ Þðnðt 0 Þ 1Þ nðtÞ 1 !: Table 1 Linguistic hierarchies. Level 1 Level 2 Level 3 l(t,n(t)) l(1, 3) l(2,5) l(3, 9) l(t,n(t)) l(1, 7) l(2,13) Fig. 2. Linguistic hierarchy of 3, 5 and 9 labels. J. Serrano-Guerrero et al. / Information Sciences 181 (2011) 1503–1516 1507