Helga Naessens

Algorithms for the computation of T-transitive closures

We present two weight-driven algorithms for the computation of the T-transitive closure of a symmetric binary fuzzy relation on a finite universe X with cardinality n (or, equivalently, of a symmetric (n/spl times/n)-matrix with elements in [0, 1]), with T a triangular norm. The first algorithm is proven to be valid for any triangular norm T, whereas the second algorithm is shown to be valid when T is either the minimum operator or an Archimedean triangular norm. Furthermore, we investigate how these algorithms can be appropriately adapted to generate the T-transitive closure of nonsymmetric binary fuzzy relations (or matrices) as well.

A class of rational cardinality-based similarity measures

A systematic way of generating similarity measures for ordinary sets is presented in the form of a rational expression solely based on cardinalities of the sets involved. Twenty-eight measures are examined carefully and completely classified on the basis of their boundary behaviour and properties of reflexivity and monotonicity. Two types of reflexivity (reflexivity and local reflexivity) and three types of monotonicity (involving, respectively, two, three and four sets) are considered. In addition, 17 of these measures are shown to be T-transitive, with the t-norm T ranging from the drastic product Z to the minimum operator M. The given class of rational cardinality-based measures covers some well-known similarity measures.

Algorithms for computing the min-transitive closure and associated partition tree of a symmetric fuzzy relation

Abstract Based on a previously derived weight-driven algorithm for the computation of the T -transitive closure of an arbitrary binary fuzzy relation on a finite universe, with T a triangular norm, we establish three algorithms for the computation of the min-transitive closure of a symmetric matrix with elements in [0,1]. As a by-product, these algorithms enable to generate the partition tree associated with the min-transitive closure of the given matrix in descending order of the cutting parameter.

On rational cardinality-based inclusion measures

In order to express the degree to which a subset of a finite universe is contained into another subset, the concept of inclusion measure (or subsethood measure) of ordinary sets is introduced. A distinction is made between three types of inclusion measures. The first type yields reflexive inclusion measures, whereas the second and third type both give rise to locally reflexive inclusion measures, the latter ones simply being complementary to the former ones.Furthermore, a systematic way of generating inclusion measures for ordinary sets is presented in the form of a rational expression solely based on cardinalities of the sets involved. Various properties of the obtained rational inclusion measures, such as monotonicity and transitivity, are investigated.

A top-down algorithm for generating the Hasse tree of a fuzzy preorder closure

This paper describes a new top-down algorithm for the stepwise generation of the different levels or Hasse diagrams of the Hasse tree associated to the fuzzy preorder closure (min-transitive closure) of a given reflexive binary fuzzy relation. The algorithm is based upon a recently established weight-driven method for computing the min-transitive closure of a reflexive binary fuzzy relation. The way in which this method gradually establishes the fuzzy preorder closure implies that for the generation of a specific level of the Hasse tree, the newly proposed algorithm does not require the complete computation of this closure.

Metadata impact on research paper similarity

While collaborative filtering and citation analysis have been well studied for research paper recommender systems, content-based approaches typically restrict themselves to straightforward application of the vector space model. However, various types of metadata containing potentially useful information are usually available as well. Our work explores several methods to exploit this information in combination with different similarity measures.

An Exploratory Study on Content-Based Filtering of Call for Papers

Due to the increasing number of conferences, researchers need to spend more and more time browsing through the respective calls for papers CFPs to identify those conferences which might be of interest to them. In this paper we study several content-based techniques to filter CFPs retrieved from the web. To this end, we explore how to exploit the information available in a typical CFP: a short introductory text, topics in the scope of the conference, and the names of the people in the program committee. While the introductory text and the topics can be directly used to model the document e.g. to derive a tf-idf weighted vector, the names of the members of the program committee can be used in several indirect ways. One strategy we pursue in particular is to take into account the papers that these people have recently written. Along similar lines, to find out the research interests of the users, and thus to decide which CFPs to select, we look at the abstracts of the papers that they have recently written. We compare and contrast a number of approaches based on the vector space model and on generative language models.