Frederick E. Petry

A fuzzy representation of data for relational databases

A structure for representing inexact information in the form of a relational database is presented. The structure differs from ordinary relational databases in two important respects: Components of tuples need not be single values and a similarity relation is required for each domain set of the database. Two critical properties possessed by ordinary relational databases are proven to exist in the fuzzy relational structure. These properties are (1) no two tuples have identical interpretations, and (2) each relational operation has a unique result.

Information-theoretic measures of uncertainty for rough sets and rough relational databases

Rough set theory has become well-established as a mechanism for uncertainty management in a wide variety of applications including databases. This paper addresses the measurement of uncertainty in rough sets and rough relational databases by introducing a measurement based on information theory. This rough entropy is discussed as it applies to rough sets in general, and in particular to aspects of the rough relational database model.

A variable-length genetic algorithm for clustering and classification

Pattern clustering and classification can be viewed as a search for, and labeling of a set of inherent clusters in any given data set. This approach can be divided broadly into two types namely supervised and unsupervised clustering. Motivated by human perception and Kohonens method, we present a novel method of supervised clustering and classification using genetic algorithms. Clusters in the pattern space can be approximated by ellipses or sets of ellipses in two dimensions and ellipsoids in general, and the search for clusters can be approximated as the search for ellipsoids or sets of ellipsoids. By assigning fuzzy membership values to points in the pattern space a fuzzy ellipsoid is obtained. The process of thresholding which follows can be thought of as warping the contour of the ellipse to include and exclude certain points in pattern space and in effect producing an arbitrarily shaped cluster. Here we examine the use of genetic algorithms in generating fuzzy ellipsoids for learning the separation of the classes. Our evaluation function drives the genetic search towards the smallest ellipsoid or set of ellipsoids, which maximizes the number of correctly classified examples, and minimizes the number of misclassified examples.

Uncertainty management issues in the object-oriented data model

This paper fully develops a previous approach by George et al. (1993) to modeling uncertainty in class hierarchies. The model utilizes fuzzy logic to generalize equality to similarity which permitted impreciseness in data to be represented by uncertainty in classification. In this paper, the data model is formally defined and a nonredundancy preserving primitive operator, the merge, is described. It is proven that nonredundancy is always preserved in the model. An object algebra is proposed, and transformations that preserve query equality are discussed.

Scene recognition using genetic algorithms with semantic nets

Abstract A model for genetic algorithms with semantic nets is derived for which the relationships between concepts is depicted as a semantic net. An organism represents the manner in which objects in a scene are attached to concepts in the net. Predicates between object pairs are continuous valued truth functions in the form of an inverse exponential function (e − β | x | ). 1 : n relationships are combined via the fuzzy OR (Max[…]). Finally, predicates between pairs of concepts are resolved by taking the average of the combined predicate values of the objects attached to the concept at the tail of the arc representing the predicate in the semantic net. The method is illustrated by applying it to the identification of oceanic features in the North Atlantic.

EXTENSION OF THE RELATIONAL DATABASE AND ITS ALGEBRA WITH ROUGH SET TECHNIQUES

This paper describes a database model based on the original rough sets theory. Its rough relations permit the representation of a rough set of tuples not definable in terms of the elementary classes, except through use of lower and upper approximations. The rough relational database model also incorporates indiscernibility in the representation and in all the operators of the rough relational algebra. This indiscernibility is based strictly on equivalence classes which must be defined for every attribute domain.

Extending the fuzzy database with fuzzy numbers

Abstract The fuzzy relational database model originated by the authors permits fuzzy domain values from a discrete, finite universe. The model is extended here by demonstrating that fuzzy numbers may be employed as domain values without loss of consistency with respect to representation or the relational algebra. Where equivalence is required in an ordinary relational database, similarity is employed in a fuzzy relational database. For discrete, finite universes, similarity between atomic elements is described via a fuzzy similarity relation with max-min transitivity. Two or more fuzzy numbers are defined to be α-similar if their union forms a continuous α-level set over the real line. This convention effects the partitioning of fuzzy number domains that is necessary to assure the well-definedness of the fuzzy relational algebra.

Fuzzy sets in database and information systems: Status and opportunities

Fuzzy set approaches have been applied in the database and information retrieval areas for nearly 30years. Here we give consideration to aspects of these areas that seem to afford the greatest potential for further development. This includes among others database design, preferences for flexible queries and fuzzy functional dependencies and redundancy. Applications to areas such as data mining and geographical information systems are described. Fuzzy information retrieval topics such as multi-media, digital libraries and web retrieval are also discussed.

Modelling class hierarchies in the fuzzy object-oriented data model

Abstract In this paper we describe a fuzzy logic based approach to modelling uncertainty in class hierarchies. It is shown that the traditional view of class hierarchies is subsumed in this model as a special case. The problem of multiple inheritance in class hierarchies is discussed and analyzed. The membership value derivations in the inheritance hierarchy reflects the degree of fuzziness existing in the data values and the semantics of the situation being modelled. Thus a more realistic modelling of the universe of discourse is possible through this approach. This model is compatible with existing object-oriented data models.

Uncertainty models in information and database systems

Information systems have evolved to the point where it is desirable to capture the vagueness and uncertainty of data that occurs in actuality. Approaches have been taken using various fuzzy set concepts such as degree of membership, similarity relations and possibility distributions. This leads to the concept of generalized information systems which are typically char acterized by heterogeneous data representations, weakly typed data domains and the requirement for semantic knowledge during query interpretation. A generalized information system is more likely to have a direct representation for larger classes of information at the cost of more complex data management and query processing. In general the various fuzzy database approaches that have been developed are overviewed in the paper and characterized with respect to the concept of a generalized information system.