Related Work

Fuzzy logic plays a key role in information retrieval and the need for providing fuzzy/flexible mechanisms to XML querying has recently motivated the investigation of extensions of the XQuery/XPath language. We can distinguish those in which the main goal is the introduction of fuzzy information in data (similarity, proximity, vagueness, etc) [24,25,7,6,14,26,22,23] and the proposals in which the main goal is the handling of crisp information by fuzzy concepts [15,8,9,12,11,18,10]. Our work focuses on the second line of research.

Fuzzy versions of XQuery have been previously studied in some works. The closest to our approach is [15], in which preferences can be described by queries in order to retrieve discriminated answers by user's preferences. FLOWR expressions are extended to cover with fuzzy values and answers. The main aim of their work is to extend XQuery with definition of fuzzy terms: good, cheap, high, young, etc., defined as fuzzy predicates that can be imposed in XPath expressions. They extend XQuery datatypes with xs:truth and incorporate xml:truth as attribute to represent degree of satisfaction. Nevertheless, they lack on an implementation, and therefore we cannot compare our proposal with yours, although we believe that a similar technique we have proposed here can be used. In [24], they also extends the syntax of XQuery, in particular, the expression where to cover with priority and thresholding. Their approach is focused on querying fuzzy XML data, and therefore their proposal is different from our. The have developed an implementation using Java on top of the Exist [19] XQuery processor. A fuzzy query is transformed into standard XQuery to be executed. Fuzzy data querying is also the main aim of the work of [25], in which they propose a fuzzy XML Shema and algebraic operators to handle fuzzy data over an schema. They provide transformations from the algebraic operators to XQuery (and XPath) expressions. Again, their approach is different from our, since they work with fuzzy XML data as input.

Fuzzy versions of XPath have been previously studied in some works. The closest works to our proposal are [8,9] in which authors introduce in XPath flexible matching by means of fuzzy constraints called close and similar for node content, together with below and near for path structure. In addition, they have studied the deep-similar notion for tree matching, and fuzzy versions for not, and and or operators. In order to provide ranked answers they assign a RSV to each item. Our work is similar to the proposed by [8,9]. The below operator of [8,9] is equivalent to our proposed down: both extract elements that are direct descendants of the current node, and the penalization is proportional to the distance. The near operator of [8,9], which is defined as a generalization of below, ranks answers depending on the distance to the required node, in any XPath axis. Our proposed deep ranks answers depending of the distance to the current node, but the considered nodes can be direct and non direct descendants. Therefore our proposed deep combined with down is a particular case of near. To have the same expressivity power as near we could incorporate to our framework a new operator to rank answers from bottom to up. With respect to similar and close operators proposed in [8,9], our framework lacks similarity relations and rather focuses on structural (i.e. path-based) flexibility.

In [12], the authors propose to give a satisfaction degree to XPath expressions based on associating weights to XPath steps. Relaxing XPath expressions when the path does not match the XML schema is the main goal of this work. They have studied how to compute the best answers. In this line, in [11,13] XPath relaxation is studied given some rules for query rewriting: axis relaxation, step deletion and step cloning, among others. The proposed deep-similar notion of [8,9] can be also considered a relaxation technique of XML tree equality. Our work has some similarities with these proposals: deep and down, and also the use of avg operator, are mechanisms for relaxing queries and giving priority to paths and answers. We have also studied in [3] how to introduce axis relaxation, step deletion and step cloning in our approach, but the proposed implementation does not still include these mechanisms. It is considered as future work.

Finally, let us remark that we have previously developed [2,1,3,4] an implementation of our fuzzy XPath using the FLOPER ``Fuzzy LOgic Programming Environment for Research'' toolwhich is based on Multi-Adjoint Logic Programming (MALP) [20,21]. There we made use of the fuzzy logic nature of FLOPER to implement fuzzy XPath by using fuzzy logic rules. Here the implementation has to adapt a Boolean logic based language (i.e., XQuery) to obtain the same behavior as in MALP.