A review of quality evaluation of digital libraries based on users ' perceptions <s> Fuzzy linguistic modelling <s> The aim of this paper is to model the processes of the aggregation of weighted information in a linguistic framework. Three aggregation operators of weighted linguistic information are presented: linguistic weighted disjunction operator, linguistic weighted conjunction operator, and linguistic weighted averaging operator. A study of their axiomatics is presented to demonstrate their rational aggregation. <s> BIB001 </s> A review of quality evaluation of digital libraries based on users ' perceptions <s> Fuzzy linguistic modelling <s> Most group decision making (GDM) problems based on linguistic approaches use symmetrically and uniformly distributed linguistic term sets to express experts' opinions. However, there exist problems whose assessments need to be represented by means of unbalanced linguistic term sets, i.e. using term sets that are not uniformly and symmetrically distributed. The aim of this paper is to present a consensus model for GDM problems with unbalanced fuzzy linguistic information. This consensus model is based on both a fuzzy linguistic methodology to deal with unbalanced linguistic term sets and two consensus criteria, consensus degrees, and proximity measures. To do so, we use a new fuzzy linguistic methodology improving another approach to manage unbalanced fuzzy linguistic information,1 (Int. J. Intell. Syst. 22(11) (2007) 1197–1214), which uses the linguistic 2-tuple model as representation base of unbalanced fuzzy linguistic information. In addition, the consensus model presents a feedback mechanism to help experts for reaching the highest degree of consensus possible. There are two main advantages provided by this consensus model. First, its ability to cope with GDM problems with unbalanced fuzzy linguistic information overcoming the problem of finding different discrimination levels in linguistic term sets. Second, it supports the consensus process automatically, avoiding the possible subjectivity that the moderator can introduce in this phase. <s> BIB002 </s> A review of quality evaluation of digital libraries based on users ' perceptions <s> Fuzzy linguistic modelling <s> In this contribution, we present a new application based on fuzzy linguistic information to evaluate the quality of digital libraries. The quality evaluation of digital libraries is defined using users' perceptions on the quality of digital services provided through their Web sites. We assume a fuzzy linguistic modeling to represent the users' perception and apply automatic tools of fuzzy computing with words based on some weighted aggregation operators to compute global quality evaluations of digital libraries. <s> BIB003 </s> A review of quality evaluation of digital libraries based on users ' perceptions <s> Fuzzy linguistic modelling <s> The aim of this paper is to present a model based on a fuzzy linguistic approach to evaluate the quality of digital libraries. The quality evaluation of digital libraries is defined using users' perceptions on the quality of digital services provided through their Web sites. We assume a fuzzy linguistic modeling to represent the users' perception and apply automatic tools of fuzzy computing with words based on the LOWA and LWA operators to compute global quality evaluations of digital libraries. <s> BIB004 </s> A review of quality evaluation of digital libraries based on users ' perceptions <s> Fuzzy linguistic modelling <s> In group decision making situations, there may be cases in which experts do not have an in-depth knowledge of the problem to be solved and, as a result, they may present incomplete information. In this paper, we present a new selection process to deal with incomplete fuzzy linguistic information. As part of it, we use an iterative procedure to estimate the missing information. This procedure is guided by the additive consistency property and only uses the preference values provided by the experts. In addition, the additive consistency property is also used to measure the level of consistency of the information provided by the experts. The main novelties of this selection process are both the possibility to manage decision situations under incomplete fuzzy linguistic information and the importance of the experts' preferences in the aggregation processes is modeled by means of the experts' consistency. <s> BIB005
In   BIB003 BIB004  , to represent the user's perceptions of the quality of the DL, fuzzy linguistic information  BIB001  BIB002 BIB005  is used instead of numerical values. In particular, ordinal fuzzy linguistic modelling  BIB001 is used to represent the user's perceptions. The ordinal fuzzy linguistic approach is a very useful kind of fuzzy linguistic approach, used for modelling the process of computing with words, as well as the linguistic aspects of problems. It facilitates fuzzy linguistic modelling because it simplifies definition of the semantic and syntactic rules. It is defined by considering a finite and totally ordered label set S = {s i }, i ∈ {0, ., T} in the usual sense, that is, s i ≥ s j if i ≥ j, and with odd cardinality. Typical values of cardinality used in linguistic models are odd values, such as 7 or 9, with an upper limit of granularity of 11 or no more than 13, where the mid-term represents an assessment of 'approximately 0.5', and the rest of the terms are placed symmetrically around it. The semantics of the linguistic term set is established from the ordered structure of the label set by considering that each linguistic term for the pair (s i , s T − i ) is equally informative. For example, we can use the following set of five labels to provide the user's evaluations: VL = very low, L = low, M = medium, H = high, VH = very high. Advantages of the ordinal fuzzy linguistic approach are the simplicity and rapidity of its computational model. It is based on symbolic computation  BIB001 , and acts by direct computation on labels by taking into account the order of such linguistic assessments in the ordered structure of linguistic terms. In order to evaluate the quality of DLs, the two following aggregation operators of linguistic information are used: 1. the linguistic ordered weighted averaging (LOWA) operator  , which is used to combine non-weighted linguistic information; 2. the linguistic weighted averaging (LWA) operator BIB001 , which is used to combine weighted linguistic information, and is proposed as a generalization of the LOWA operator applied to combine linguistic information provided by information sources with different importance. In contrast to the numerical computation of Likert scales presented in Section 4.1, the LOWA and LWA operators compute linguistic labels symbolically, and therefore linguistic approximation processes are unnecessary; this simplifies the processes of computing with words (see Figure 3b) . The behaviour of the LOWA and LWA operators is parameterized by selecting different fuzzy linguistic quantifiers. Table 5 summarizes the results of applying the LOWA operator to our example with the 'most' quantifier, defined as Q(r) = r 1/2 (i.e., it reflects what most of the users think about each criterion). Compared with the analysis of Likert scales, the LOWA operator provides the following benefits: 1. It avoids the simplifying assumption of considering that there is the same distance between all labels. 2. It always produces results contained in the set of linguistic labels. 3. It always generates an intermediate value. In the example, the LOWA result for contact information is LOWA(VL, VL, H)=M. Furthermore, thanks to the LWA operator, it is possible to calculate a total value that blends the assessment of all users and all criteria, taking into account the importance of each criterion. Table 6 summarizes the importance of the subcriteria in our example, expressed with the set S of linguistic labels (e.g. the importance of user satisfaction is Very High). Since LWA(importance, user's opinion) = LWA[(VH, VH), (M, L), (L, M)] = H, it can be concluded that, according to most of the users, the DL satisfies the criterion user opinion solicitation at a high level. 