M. Dolores Ruiz

Fuzzy quantification: a state of the art

Abstract Quantified sentences are a very powerful notion for modelling statements in Natural Language (NL), but in practice they have been used to solve several problems. This paper is intended to offer a global view of the development on this branch until now, focusing in the different approaches dealing with quantification, specially those involving imprecision, called fuzzy quantification. We put attention to the different mechanisms for defining them, the evaluation methods for measuring their fulfilment, as well as the properties they should satisfy.

STUDYING INTEREST MEASURES FOR ASSOCIATION RULES THROUGH A LOGICAL MODEL

Many papers have addressed the task of proposing a set of convenient axioms that a good rule interestingness measure should fulfil. We provide a new study of the principles proposed until now by means of the logic model proposed by Hajek et al.14 In this model association rules can be viewed as general relations of two itemsets quantified by means of a convenient quantifier.28 Moreover, we propose and justify the addition of two new principles to the three proposed by Piatetsky-Shapiro.27 We also use the logic approach for studying the relation between the different classes of quantifiers and these axioms. We define new classes of quantifiers according to the notions of strong and very strong rules, and we present a quantifier based on the certainty factor measure,317 studying its most salient features.

NEW APPROACHES FOR DISCOVERING EXCEPTION AND ANOMALOUS RULES

Mining association rules is a well known framework for extracting useful knowledge from databases. Despite their proven applicability there exist other approaches that also search for novel and useful information such us peculiarities, infrequent rules, exceptions or anomalous rules. The common feature of these proposals is the low support of such type of rules. So there is a necessity of finding efficient algorithms for extracting them. The principal objective of this paper is providing a unified framework for dealing with such kind of rules. In our case, we take advantage of an existing logic approach called GUHA. This model was first presented in the middle sixties by Hajek et al. and then has been developed by Rauch and others in the last decade. Following this line, this paper also offers some interesting issues. First, it provides a deep analysis of semantics and formulation of exception and anomalous rules. Second, we define the so called double rules as a new type of rules which in conjunction with exceptions and anomalies will describe in more detail the relationship between two sets of items. Third, we give new approaches for mining them and we propose an algorithm with reasonably good performance.

A formal and empirical analysis of the fuzzy gamma rank correlation coefficient

The so-called gamma coefficient is a well-known rank correlation measure frequently used to quantify the strength of dependence between two variables with ordered domains. To increase the robustness of this measure toward noise in the data, a generalization of the gamma coefficient has recently been developed on the basis of fuzzy order relations. The goal of this paper is threefold. First, we analyze some formal properties of the fuzzy gamma coefficient. Second, we complement the original experiments, which have been conducted on a simple artificial data set, by a more extensive empirical evaluation using real-world data. On the basis of these empirical results, we provide some basic insights and offer an explanation for the effectiveness of the fuzzy gamma coefficient. Third, we propose an alternative motivation for the measure, based on the idea of (fuzzy) equivalence relations induced by limited precision in the perception of measurements.

Anomaly detection using fuzzy association rules

Data mining techniques are a very important tool for extracting useful knowledge from databases. Recently, some approaches have been developed for mining novel kinds of useful information, such as anomalous rules. These kinds of rules are a good technique for the recognition of normal and anomalous behaviour, that can be of interest in several area domains such as security systems, financial data analysis, network traffic flow, etc. The aim of this paper is to propose an association rule mining process for extracting the common and anomalous patterns in data that is affected by some kind of imprecision or uncertainty, obtaining information that will be meaningful and interesting for the user. This is done by mining fuzzy anomalous rules. We present a new approach for mining such rules, and we apply it to the case of detecting normal and anomalous patterns on credit data.

PATTERN EXTRACTION FROM BAG DATABASES

Many databases in real life involve pairs of the form (item,quantity). This kind of data can be characterized using the theory of bags. We present a general framework for extracting useful knowledge from bag databases using different types of patterns. Here we present different approaches for the task of discovering fuzzy association rules and gradual dependencies in bag databases.

Discovering Fuzzy Exception and Anomalous Rules

Nowadays, searching for specific kind of knowledge that deviates from the usual standards is very useful in several domains such as network traffic anomalies, fraud detection, economic analysis, or medical diagnosis. Fuzzy association rules have been developed as a powerful tool for dealing with imprecision in databases (that may come from the source, i.e., imprecise measures taken by the machine, or from the human understanding of a concept) and offering a comprehensive representation of found knowledge. In this paper, we introduce the notion of fuzzy exception and fuzzy anomalous rule for the recognition of these types of deviations. The deviations are associated with the common patterns, which usually are hidden in data affected by some kind of fuzziness. We present a new approach for mining such rules based on a recently proposed model for representing and evaluating fuzzy rules. Important advantages are to obtain more understandable results and that the mining process can be parallelized. An algorithm following the proposed model is developed, and some experiments are performed in data where some numerical attributes have been fuzzified and also in some real fuzzy transactional datasets for testing the proposed algorithm. From experimentation, we have seen that the proposed fuzzy rules give some insights on the exception and anomaly detection in credit payments.

RL-bags: A conceptual, level-based approach to fuzzy bags

In this paper we claim that, though algebraically well-defined, bags are not well suited for representing and reasoning with real-world information, and we propose suitable alternatives. We extend the same discussion to the fuzzy case, in which membership of elements to bags is gradual, extending the proposed alternatives. There are two main ideas behind our approach. The first is that in general the elements of a bag can be identified and are distinguishable in the real world and, when this is not the case, we are facing a problem of representation of partial knowledge, i.e., we have a lack of information. Under this consideration, we discuss and criticize the usual operations for bags. The second is to manage the fuzziness by levels using a recent level-based representation approach that extends that of fuzzy sets and keeps all the properties of the crisp case. The classical notion of bag can be seen in our approach as a bag summary. We propose a new model that generalizes the existing approach, defining new operations from this new perspective. We also propose how to deal with fuzziness and incompleteness following our approach, doing a review of the existing approaches and applications concerning bags.

Summarizing Structured Documents through a Fractal Technique

Every day we search new information in the web, and we found a lot of documents which contain pages with a great amount of information. There is a big demand for automatic summarization in a rapid and precise way. Many methods have been used in automatic extraction but most of them do not take into account the hierarchical structure of the documents. A novel method using the structure of the document was introduced by Yang and Wang in 2004. It is based in a fractal view method for controlling the information displayed. We explain its drawbacks and we solve them using the new concept of fractal dimension of a text document to achieve a better diversification of the extracted sentences improving the performance of the method.

Extraction of association rules using big data technologies

The large amount of information stored by companies and the rise of social networks and the Internet of Things are producing exponential growth in the amount of data being produced. Data analysis techniques must therefore be improved to enable all this information to be processed. One of the most commonly used techniques for extracting information in the data mining field is that of association rules, which accurately represent the frequent co-occurrence of items in a dataset. Although several methods have been proposed for mining association rules, these methods do not perform well in very large databases due to high computational costs and lack of memory problems. In this article, we address these problems by studying the current technologies for processing Big Data to propose a parallelization of the association rule mining process using Big Data technologies which implements an efficient algorithm that can handle massive amounts of data. This new algorithm is then compared with traditional association rule mining algorithms.