Rita De Caluwe

The use of fuzzy set theory in information retrieval and databases: A survey

Due to a rapid expansion of most domains in recent times, there is a constant growing need for information. Together with this phenomenon, there has been an explosive growth of the amount of data needed and the corresponding means of data storage. In order to handle these large amounts of data and to realize a fast processing of the information asked for, more and more institutions and organizations have set up automized information processing and have built up their database. Appearing in all kinds of applications such as economical, social, political, medical, and governmental fields, databases have already proven their ability to reduce time and space with respect to the retrieval as well as to the storage of data and information. In many situations we have to deal with data which are given in imprecise form or which are only partially known or even totally unknown. We may expect that the construction of databases which can represent and manipulate fuzzy data will increase the application areas of database systems and improve the interface between men and machines. In this paper we have made a brief survey of the numerous applications of fuzzy set theory on data representation and information retrieval. The importance of fuzzy set theory with respect to information systems is illustrated by means of an already extensive bibliography containing more than 80 papers describing data systems that are somehow “fuzzy.”

Level-2 fuzzy sets and their usefulness in object-oriented database modelling

Abstract In the real world information is, for the most part, available in an imperfect form. Managing this kind of information with classical database systems brings a disadvantageous loss of data semantics along. Therefore, advanced database modelling techniques are necessary. This paper deals with a uniform and advantageous representation of both perfect and imperfect ‘real world’ information in object-oriented databases. An object-oriented data(base) modelling technique, based on the concept ‘level-2 fuzzy set’, is presented. Hereby, the focus is on the semantic definitions of the structural, as well as on the behavioural aspects of the data. It is shown how level-2 fuzzy sets can be used to generalise the concept ‘type’. Since types are generally recognised to be the basic building blocks of object-oriented database models, generalised types can be used as basic notions of fuzzy object-oriented database models. Finally, it is illustrated and discussed how the ODMG data model can be generalised to handle ‘real world’ data in a more advantageous way.

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.

Null values in fuzzy databases

Since in the real world, it often occurs that information is missing, database systems clearly need some facilities to deal with missing data. With respect to traditional database systems, the most commonly adopted approach to this problem is based on null values and three valued logic. This paper deals with the semantics and the use of null values in fuzzy databases. In dealing with missing information a distinction is made between incompleteness due to unavailability and incompleteness due to inapplicability. Both the database modelling and database querying aspects are described. With respect to attribute values, incompleteness due to unavailability is modelled by possibility distributions, which is a commonly used technique in the fuzzy databases. Domain specific null values, represented by a bottom symbol, are used to model incompleteness due to inapplicability. Extended possibilistic truth values are used to formalize the impact of data manipulation and (flexible) querying operations in the presence of these null values. The different cases of appearances of null values in the handling of selection conditions of flexible database queries are described in detail.

A new approach to information retrieval systems using fuzzy expressions

A fuzzy document retrieval system has been realized that permits a reduction of the time needed for retrieving the set of documents fulfilling a users query, as well as the amount of core space, needed for the document description relations. The method described solves the problems that Radecki-who uses lambda-level fuzzy sets-met with, trying to reduce time, and gives rise to a good working Information Retrieval System, as the examples show. The retrieval process is described by an included algorithm.

A Generalised Object-Oriented Database Model

A new formal framework for a generalised object-oriented database model that is able to cope with fuzzy and uncertain information is presented. The generalised model is obtained as a generalisation of a crisp object-oriented database model that is compliant with the ODMG de facto standard and is built upon an algebraic type system and a constraint system. The novelty of our approach is the integration of (generalised) constraints to enforce integrity rules and to specify the formal semantics of the database model.

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.

Fuzzy time indications in natural languages interfaces

Common observations of the way in which time indications are used in natural language not only show that, very often, time is indicated in an approximative way, but also reveal the context-dependent precision with which time indications are expressed, relative to a kind of natural hierarchical time unit system.

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.

Modelling vague lexical time expressions by means of fuzzy set theory

Abstract On the basis of some large scale inquiries into the nature of time expressions in natural language, in which informants were asked to indicate sharp (crisp) and closed time intervals for a range of linguistic expressions, several models of representing vague lexical time intervals by means of fuzzy set theory are discussed. These models primarily depend on the type of expressions used, and thus take into account the complex heterogeneous semantics of time indications.