Axel Hallez

Field Based Methods for the Modeling of Fuzzy Spatial Data

In this chapter, two different field based techniques for the modeling of fuzzy information spread over a geographic region, are presented and are compared regarding their applicability. The first one is a vector-mode approach, using triangulated irregular networks (or TINs), the second one is a raster (bitmapmode) approach. Appropriate aggregation operators are defined in both approaches and illustrated by means of examples. The feasibility of the implementation of the operators (by approximation whenever required) is studied. Attention has been paid to the applicability, advantages and disadvantages of both methods in flexible querying.

Fuzzy Regions: Theory and Applications

Traditionally, information in geographic information systems (GIS) is represented as crisp information. While for many applications, this is a good enough approximation of reality, some models would benefit from having the inherent imprecision or uncertainty incorporated in the model. In literature, several ideas and concepts to improve on the crisp models have been considered. In the past, we have presented different models to represent and to work with the concept of regions, defined using fuzzy set theory in GIS systems. For such fuzzy regions, a number of approaches already have been described in detail. In this paper, we will elaborate on a fuzzy set approach and practical implementations of the concept. Apart from the concept, two developed techniques (one based on triangulated networks, one based on bitmap models) are presented along with some of the operators. An overview of application fields is provided to illustrate where and how the techniques can be used.

A Hierarchical Approach to Object Comparison

Comparing objects is a very general problem domain. The way objects are compared can differ a lot, in the way objects are related to each other as well as in the meaning that is attributed to the result of a comparison. In this paper we develop a theoretical framework for comparing objects. This framework can be tailored to the specific needs of an application through the choice of appropriate operators and evaluation domain (i.e. the domain in which the comparison results are expressed).

Conjunctive Aggregation of Extended Possibilistic Truth Values and Flexible Database Querying

Extended possibilistic truth values are a flexible means to model the linguistic (un)certainty about the truth value of a proposition. With respect to flexible database querying, they are suited to express the extent to which a database instance satisfies a query condition. Since a query can impose several conditions, aggregation is necessary. In this paper, three definitions of conjunctive aggregation operators for extended possibilistic truth values are presented and compared with each other on the basis of their capability to rank the possible alternatives in the result of a (flexible) database query.

COMPARISON OF SETS AND MULTISETS

The comparison of sets of objects is a research topic with applications in diverse fields such as computer science, biology and psychology. Since the introduction of the Jaccard index, many techniques have been proposed. This paper aims at extending an existing framework of comparison indices for sets. Firstly, the novel indices account for similarities between elements, rather than identity of elements as is the case for existing techniques. As a result, a richer framework of comparison indices is obtained. The use of fuzzy quantifiers in this framework is shown. Secondly, the machinery for sets is extended to the case of multisets, which results in two classes of comparison indices. The first class considers each element instance as a separate element, while the second class considers groups of elements instances as an atomic entity. The number of instances is then a property of this group, that is taken into account when calculating similarity between element groups.

Similarity between multi-valued thesaurus attributes: theory and application in multimedia systems

In this paper, the theoretical aspects of calculating the similarity between sets, and its generalizations multisets, fuzzy sets and fuzzy multisets, is presented. Afterwards, this theory is applied to enhance the facilities for accessing a multimedia system, namely when searching for correspondence between multi-valued attributes, which are coupled with a thesaurus. Furthermore, to allow flexibility in this search, thesauri with similarities defined between the thesaurus terms are considered. As a possible application, the DEKKMMA project is introduced, a project about an audio archive of African music.

A framework for flexible querying and mining of musical audio archives

In this paper the outline of a framework for the handling of flexible querying and mining of musical audio archives is presented. This framework has been designed within the scope of the DEKKMMA-project, which aims to build a digital musical audio archive for the ethnomusicological department of the Belgian Royal Museum for Central Africa. This museum holds one of the largest and world wide most important collections of music from Central Africa. Beside the digitizing and recording aspects, efficient access facilities for both specialized and nonspecialized users are required. In order to achieve this, the framework supports and integrates flexible querying, classification and object comparison mechanisms.

Modelling of fuzzy and uncertain spatio-temporal information in databases : a constraint-based approach

A constraint-based generalized object-oriented database model is adapted to manage spatio-temporal information. The presented adaptation is based on the definition of a new data type, which is suited to handle both temporal and spatial information. Generalized constraints are used to describe spatio-temporal data, to enforce integrity rules on databases, to specify the semantics of a database scheme and to impose selection criteria in flexible database querying.

Weighted Conjunctive and Disjunctive Aggregation of Possibilistic Truth Values

In this paper, weighted aggregation of extended possibilistic truth values will be presented. The impact of the weights on both conjunctive and disjunctive aggregation will be handled, and special care will be given to the case where both conjunctive and disjunctive aggregation are mixed together. The problems that can arise will be illustrated and solutions will be proposed.

The Applicability of Generalized Constraints in Spatio-Temporal Database Modelling and Querying

From a formal point of view, a constraint can be seen as a relationship that has to be satisfied. With respect to data and information modelling, constraints provide a declarative and elegant means to represent data in an efficient way. Moreover, constraints support the definition of data semantics. For example, the set of valid temperatures t on earth can be defined as ranging from a high of 57 degrees Celcius to -70 degrees Celcius, which can be described by the constraint t ∈ [-70°C, 57°C] or, using linear arithmetic, by (t ≥ -70°C) ∧ (t ≤ 57°C).