C Porcel et al / Expert Systems with Applications 36(2009)5173-5183 Definition 5. Linguistic weighted average operator: Let x=((r1, a1) (. (n, Mn)) be a set of linguistic 2-tuples and W=l(wi, am (Wn, a)) be their linguistic 2-tuple asso linguistic weighted average x is x[(r1,x1),(W1,x7)…(rn,n),Wwn,xn)=4 ∑1B1·Bw with B=A"(, a) and Bw=4"(w, a]). 2.2.2. The multi-granular fuzzy linguistic modeling In any fuzzy linguistic approach, an important parameter to determinate is the "granularity of uncertainty",i.e, the cardinali of the linguistic term set S. According to the uncertainty degi 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 Fig. 2. Linguistic Hierarchy of 3, 5 and 9 labels. on the phenomenon, then several linguistic term sets with a differ ent granularity of uncertainty are necessary(herrera Martinez 2001: Herrera-Viedma et al, 2005). The use of different labels sets we select a level to make uniform the information( for instance, the to assess information is also necessary when an expert has to as- great granularity level)and then we can use the operators defined ess different concepts, as for example it happens in information in the 2-tuple FLM. retrieval problems, to evaluate the importance of the query terms and the relevance of the retrieved documents(Herrera-Viedma et 3. SIRE2IN, a Recommender system for research resources L 2003). In such situations, we need tools for the management of multi-granular linguistic information. In Herrera Martinez (2001)is proposed a multi-granular 2-tuple FLM based on the con- based on multi-granular FLM F SIRE2IN, a recommender system In this section, we pre cept of linguistic hierarchy( Cordon, Herrera, Zwir, 2001). A Linguistic Hierarchy, LH, is a set of levels I(t, n(t), i.e., As we said in the introduction, the Tto technicians manage and LH=U,I(t, n(t)). where each level t is a linguistic term set with dif- SPread a lot of information about research information such as calls or projects. Nowadays, this amount of information is growing up ferent granularity n(t)from the remaining of levels of the hierarchy and the experts are in need of automatic tools to filter and spread ( Cordon et al, 2001 ). The levels are ordered according to their the information in a simple and timely manner. Because of this,our granularity. i.e,a level t+ 1 provides a linguistic refinement of system incorporates in its activity a filtering process that follows the previous level t. We can define a level from its predecessor le- the content-based approach. Moreover, to improve the representa- el as: I(t, n(t))-(t+1,2,.,n(t)-1). Table 1 shows the granu- tion of the information in the system we use multi-granular lin- larity 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 guistic information, that is, different label sets to represent the graphical example of a linguistic hierarchy is shown in Fig. 2 ifferent concepts to be assessed for different users in the filtering In Herrera Martinez(2001) was demonstrated that the lin activity guistic hierarchies are useful to represent the multi-granular lin Then, SIRE2IN filters the incoming information stream and gen guistic information and allow to combine multi-granular erates useful recommendations to the suitable researchers in accordance with their research areas. For each user the system linguistic information without loss of information. To do this, a generates an email with a summary about the resources, its rele- family of transformation functions between labels from different vance degrees and recomm ns about collaboration Definition 6. Let LH=U(t, n(t)) be a linguistic hierarchy whose linguistic term sets are denoted as S()=(so",., s n(t-1). The 3. 1. Architecture transformation function between a 2-tuple that belongs to level t and another 2-tuple in level tzt is defined The architecture of SIRE2IN(Fig 3)has three main components: F:lt,n(t)→l(t,n(t) Resources management. This module is the responsible one of (=9-4(remo0=1) management the information sources from which the Tto xperts receive all the information about research resources. It obtains an internal representation of these items. Examples of As it was pointed out in Herrera Martinez(2001) this family of information sources are Internet, news bulletins, distribution transformation functions is bijective. This result guarantees the lists, forums, etc. To manage the items, we represent them in transformations between levels of a linguistic hierarchy are carried accordance with its scope using the UNESco terminology for ut without loss of information. To define the computational model, the science and technology(The UNESCO terminology, XXXX). This terminology is composed by three levels and each one is a refinement of the previous level. The first level includes gen eral topics and they are codified by two digits. Each topic includes some disciplines codified by four digits in a second Level 3 level. The third level is composed by subdisciplines that sent the activities developed in each discipline; these sub I(1.3 l(2.5) plines are codified by six digits. We are going to operat the first and second levels, because we think the third level sup-Definition 5. Linguistic weighted average operator: Let x ¼ fðr1; a1Þ; ð... ;ðrn; anÞg 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 l ½ððr1; a1Þ;ðw1; aw 1 ÞÞ...ððrn; anÞ;ðwn; aw n ÞÞ ¼ D Pn i¼1bi P  bWi n i¼1bWi !; with bi ¼ D1 ðri; aiÞ and bWi ¼ D1ðwi; aw i Þ. 2.2.2. The multi-granular fuzzy linguistic modeling In any fuzzy linguistic approach, an important parameter to determinate 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 differ￾ent granularity of uncertainty are necessary (Herrera & Martı´ nez, 2001; Herrera-Viedma et al., 2005). The use of different labels sets to assess information is also necessary when an expert has to as￾sess different concepts, as for example it happens in information retrieval problems, to evaluate the importance of the query terms and the relevance of the retrieved documents (Herrera-Viedma et al., 2003). In such situations, we need tools for the management of multi-granular linguistic information. In Herrera & Martı´nez (2001) is proposed a multi-granular 2-tuple FLM based on the con￾cept of linguistic hierarchy (Cordón, Herrera, & Zwir, 2001). A Linguistic Hierarchy, LH, is a set of levels lðt; nðtÞÞ, i.e., LH ¼ S tlðt; nðtÞÞ, where each level t is a linguistic term set with dif￾ferent granularity nðtÞ from the remaining of levels of the hierarchy (Cordón et al., 2001). The levels are ordered according to their granularity, i.e., a level t þ 1 provides a linguistic refinement of the previous level t. We can define a level from its predecessor le￾vel as: lðt; nðtÞÞ ! lðt þ 1; 2; ... ; nðtÞ  1Þ. Table 1 shows the granu￾larity 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. In Herrera & Martı´nez (2001) was demonstrated that the lin￾guistic hierarchies are useful to represent the multi-granular lin￾guistic information and allow to combine 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 ¼ S tlðt; nðtÞÞ be a linguistic hierarchy whose linguistic term sets are denoted as SnðtÞ ¼ fs nðtÞ 0 ; ... ; s nðtÞ nðtÞ1g. 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 : lðt; nðtÞÞ ! lðt 0 ; nðt 0 ÞÞ; TFt t0ðs nðtÞ i ; anðtÞ Þ ¼ D D1 ðs nðtÞ i ; anðtÞ Þðnðt 0 Þ  1Þ nðtÞ  1 !: As it was pointed out in Herrera & Martı´nez (2001) this family of transformation functions is bijective. This result guarantees the transformations between levels of a linguistic hierarchy are carried out without loss of information. To define the computational model, we select a level to make uniform the information (for instance, the great granularity level) and then we can use the operators defined in the 2-tuple FLM. 3. SIRE2IN, a Recommender system for research resources In this section, we present SIRE2IN, a recommender system based on multi-granular FLM. As we said in the introduction, the TTO technicians manage and spread a lot of information about research information such as calls or projects. Nowadays, this amount of information is growing up and the experts are in need of automatic tools to filter and spread the information in a simple and timely manner. Because of this, our system incorporates in its activity a filtering process that follows the content-based approach. Moreover, to improve the representa￾tion of the information in the system we use multi-granular lin￾guistic information, that is, different label sets to represent the different concepts to be assessed for different users in the filtering activity. Then, SIRE2IN filters the incoming information stream and gen￾erates useful recommendations to the suitable researchers in accordance with their research areas. For each user the system generates an email with a summary about the resources, its rele￾vance degrees and recommendations about collaboration possibilities. 3.1. Architecture of SIRE2IN The architecture of SIRE2IN (Fig. 3) has three main components: Resources management. This module is the responsible one of management the information sources from which the TTO experts receive all the information about research resources. It obtains an internal representation of these items. Examples of information sources are Internet, news bulletins, distribution lists, forums, etc. To manage the items, we represent them in accordance with its scope using the UNESCO terminology for the science and technology (The UNESCO terminology, XXXX). This terminology is composed by three levels and each one is a refinement of the previous level. The first level includes gen￾eral topics and they are codified by two digits. Each topic includes some disciplines codified by four digits in a second level. The third level is composed by subdisciplines that repre￾sent the activities developed in each discipline; these subdisci￾plines are codified by six digits. We are going to operate with the first and second levels, because we think the third level sup￾Fig. 2. Linguistic Hierarchy of 3, 5 and 9 labels. Table 1 Linguistic hierarchies Level 1 Level 2 Level 3 lðt; nðtÞÞ l(1, 3) l(2, 5) l(3, 9) lðt; nðtÞÞ l(1, 7) l(2, 13) 5176 C. Porcel et al. / Expert Systems with Applications 36 (2009) 5173–5183