Ali Jaoua

Discovering knowledge from fuzzy concept lattice

Since its inception, association rule mining has become one of the core data mining tasks, and has attracted tremendous interest among researchers and practitioners. Many efficient algorithms have been proposed in the literature, e.g., Apriori, Partition, DIC, for mining association rules in the context of marketbasket analysis. They are all based on apriori methods, i.e., pruning the itemset lattice, and requires multiple database accesses. However, research so far has mainly focused on mining over binary data, i.e., either an item is present in a transaction or not. Little attention was paid to mining over data where the quantity of items is considered. In this paper, we propose to address the problem of mining fuzzy association rules, by considering the quantity of items in the transactions. After the fuzzification of the transaction database, we apply a new efficient algorithm, called FARD (Fuzzy Association Rule Discovery), for mining fuzzy association rules. FARD is based on the pruning of the fuzzy concept lattice, and can be applied equally to classical or fuzzy databases, by scanning the database only once.

An extension of classical functional dependency: dynamic fuzzy functional dependency

Abstract Relational data model has constituted an incontestable success in database history. In this context, a lot of attention has been paid to functional dependencies due to their paramount importance in the design of relational database. For about fifteen years, several attempts to formalize (soft) real world constraints imposed on the data has been made, leading to the emergence of the concept of fuzzy functional dependency. In this paper, an overview of the different proposals of the fuzzy functional dependency is presented. A new extension of classical functional dependency based on the Lukasiewicz implication is presented and called dynamic fuzzy functional dependency. The associated axiomatic system is introduced and proved to be sound.

Using difunctional relations in information organization

Abstract An algorithm for information organization based on rectangular decomposition of a binary relation is introduced. Rectangular decomposition allows a classification of databases presented as a binary relation. This problem, being NP-Complete problem, has been the subject of several previous works. However, we found out necessary the proposition of an approximate polynomial algorithm and to give an improvement to the latest methods. Hence, this work represents a rectangular decomposition approach based on Riguet difunctional relation. The computing of this difunctional results in a set of isolated points allowing us to determine the minimal set of rectangles covering given binary relation.

Completing Missing Values Using Discovered Formal Concepts

Over the past decades there has been a huge increase in the amount of data being stored in databases as well as the number of database applications in business and the scientific domain. This explosion has pointed out the need of techniques or algorithms in order to extract and discover non-trivial, unknown and potentially useful information from large data sets. This extraction of knowledge from large data sets is called Data Mining or Knowledge Discovery in Databases. The extracted knowledge can be used to answer cooperative queries, and facilitate semantic query optimization. Relational databases create new type of problems for knowledge discovery such as missing values for some attributes and a key issue in any discovery system is to ensure the completeness of the discovered knowledge. In this paper, we address the problem of missing values in relational databases. We present an approach to complete or augment a classical relation containing missing values. This is done by exploiting the useful information yielded by the discovered knowledge represented by formal concepts.

Planar Drawing Algorithms of Survivable Telecommunication Networks

Visualizing survivable telecommunication networks on the screen has proven to be useful and helpful for the network designers. In fact, they can easily identify rings, perceive the interaction between rings, and then rapidly spot possible problems. Given a ring cover of survivable telecommunication networks, we provide two techniques for drawing a ring cover. We should mention that all these drawings should respect many criteria in order to preserve the readability of the drawing. These criteria are as follows: Rings must be easily identifiable within the picture, no crossing is acceptable and the resolution rule should be respected. As in most of the graph drawing algorithms, the area used for the drawing is very important. Our proposed algorithms produce drawings that require O(n 2) area, where n is the number of nodes in the ring cover.

At the crossroads of fuzzy Galois lattice and information retrieval

The authors propose a new algorithm for generating a fuzzy Galois lattice from a fuzzy binary relation. As a practical application of the fuzzy Galois lattice, we show that it can be used as an underlying basic structure access, for providing relevant additional information to a user asking queries to an indexed documentary database.

Non-supervised rectangular classification of binary data

Rectangular decomposition [6] has proved to be useful for supervised data classification, for learning, or data organisation, and information extraction [7]. In this paper, we propose an adaptation of rectangular decomposition to non supervised data classification. Initial experiments and comparison with main other classification methods, have given us promising results. The proposed approach is based on successive optimal rectangle selection, from which we extract different classes that give a partition.

Visualizing Algorithms for the Design and Analysis of Survivable Networks

We present algorithms for the drawing of survivable telecommunication networks. The visualization of telecommunication networks is a very important problem. For some specific rings in a network, we may have a high traffic. The network designers may decide to add more equipment to the nodes (sites) of these rings in order to increase the performance of the network. Therefore, one of the most important properties of the survivable telecommunication network, is that rings should be easily recognizable. Given a ring cover of survivable telecommunication networks, we provide three techniques for drawing a ring cover. We should mention that all these drawings should respect many criteria in order to preserve the readability of the drawing. As in most of the graph drawing algorithms, the area used for the drawing is very important, our proposed algorithms produce drawings that require O(n 2 ) area, where n is the number of nodes in the ring cover. These drawings are clear and easy to understand by the network designers.