Fuzzy-rough set and fuzzy ID3 decision approaches to knowledge discovery in datasets

Fuzzy rough sets are the generalization of traditional rough sets to deal with both fuzziness and vagueness in data. The existing researches on fuzzy rough sets mainly concentrate on the construction of approximation operators. Less effort has been put on the knowledge discovery in datasets with fuzzy rough sets. This paper mainly focuses on knowledge discovery in datasets with fuzzy rough sets. After analyzing the previous works on knowledge discovery with fuzzy rough sets, we introduce formal concepts of attribute reduction with fuzzy rough sets and completely study the structure of attribute reduction

A scalable approach to fuzzy rough nearest neighbour classification with ordered weighted averaging operators

Fuzzy rough sets have been successfully applied in classification tasks, in particular in combination with OWA operators. There has been a lot of research into adapting algorithms for use with Big Data through parallelisation, but no concrete strategy exists to design a Big Data fuzzy rough sets based classifier. Existing Big Data approaches use fuzzy rough sets for feature and prototype selection, and have often not involved very large datasets. We fill this gap by presenting the first Big Data extension of an algorithm that uses fuzzy rough sets directly to classify test instances, a distributed implementation of FRNN-OWA in Apache Spark. Through a series of systematic tests involving generated datasets, we demonstrate that it can achieve a speedup effectively equal to the number of computing cores used, meaning that it can scale to arbitrarily large datasets

Fuzzy-Rough Sets Assisted Attribute Selection

Attribute selection (AS) refers to the problem of selecting those input attributes or features that are most predictive of a given outcome; a problem encountered in many areas such as machine learning, pattern recognition and signal processing. Unlike other dimensionality reduction methods, attribute selectors preserve the original meaning of the attributes after reduction. This has found application in tasks that involve datasets containing huge numbers of attributes (in the order of tens of thousands) which, for some learning algorithms, might be impossible to process further. Recent examples include text processing and web content classification. AS techniques have also been applied to small and medium-sized datasets in order to locate the most informative attributes for later use. One of the many successful applications of rough set theory has been to this area. The rough set ideology of using only the supplied data and no other information has many benefits in AS, where most other methods require supplementary knowledge. However, the main limitation of rough set-based attribute selection in the literature is the restrictive requirement that all data is discrete. In classical rough set theory, it is not possible to consider real-valued or noisy data. This paper investigates a novel approach based on fuzzy-rough sets, fuzzy rough feature selection (FRFS), that addresses these problems and retains dataset semantics. FRFS is applied to two challenging domains where a feature reducing step is important; namely, web content classification and complex systems monitoring. The utility of this approach is demonstrated and is compared empirically with several dimensionality reducers. In the experimental studies, FRFS is shown to equal or improve classification accuracy when compared to the results from unreduced data. Classifiers that use a lower dimensional set of attributes which are retained by fuzzy-rough reduction outperform those that employ more attributes returned by the existing crisp rough reduction method. In addition, it is shown that FRFS is more powerful than the other AS techniques in the comparative study

Faculty of Sciences

A comprehensive study of fuzzy rough sets and their application in data reductio

Fuzzy Closure Spaces vs. Fuzzy Rough Sets

AbstractThis paper investigates the relationship among fuzzy rough sets, fuzzy closure spaces and fuzzy topology. It is shown that there exists a bijective correspondence between the set of all fuzzy reflexive approximation spaces and the set of all quasi-discrete fuzzy closure spaces satisfying a certain extra condition. Similar correspondence is also obtained between the set of all fuzzy tolerance approximation spaces and the set of all symmetric quasi-discrete fuzzy closure spaces satisfying a certain extra condition

Ordered Weighted Average Based Fuzzy Rough Sets

Traditionally, membership to the fuzzy-rough lower, resp. upper approximation is determined by looking only at the worst, resp. best performing object. Consequently, when applied to data analysis problems, these approximations are sensitive to noisy and/or outlying samples. In this paper, we advocate a mitigated approach, in which membership to the lower and upper approximation is determined by means of an aggregation process using ordered weighted average operators. In comparison to the previously introduced vaguely quantified rough set model, which is based on a similar rationale, our proposal has the advantage that the approximations are monotonous w.r.t. the used fuzzy indiscernibility relation. Initial experiments involving a feature selection application confirm the potential of the OWA-based model

Fuzzy-rough instance selection

Rough set theory provides a useful mathematical foundation for developing automated computational systems that can help understand and make use of imperfect knowledge. Since its introduction, this theory has been successfully utilised to devise mathematically sound and often, computationally efficient techniques for addressing problems such as hidden pattern discovery from data, feature selection and decision rule generation. Fuzzy-rough set theory improves upon this by enabling uncertainty and vagueness to be modeled more effectively. Recently, the value of fuzzy-rough sets for feature selection and rule induction has been established. However, the potential of this theory for instance selection has not been investigated at all. This paper proposes three novel methods for instance selection based on fuzzy-rough sets. The initial experimentation demonstrates that the methods can significantly reduce the number of instances whilst maintaining high classification accuracies