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A dominance-based rough set approach, an extension of rough sets to preferenceordered information systems, was used in [159] to generate preference models for violin quality grading. A set of violins were submitted to a violin-maker s competition and evaluated by a jury according to several assessment criteria. The sound of the instruments was recorded digitally and then processed to obtain sound attributes. These features, along with jury assessments, were analyzed by the rough set method, generating preference models. It was shown that the jury s rankings were well approximated by the automated approach. In [199] an approach to classifying swallowing sound signals is given, utilizing rough set theory. This approach has been developed to facilitate the detection of patients at risk of aspiration, or choking. The waveform dimension is used to describe sound signal complexity and major changes in signal variance. From swallow sound data tables, decision rules were derived, via rough sets. The algorithms yielded a high classi cation accuracy while producing a comparatively small ruleset. A decision system employing rough sets and neural networks is presented in [186]. The aim of the study was to automatically classify musical instrument sounds on the basis of a limited number of parameters, and to test the quality of musical sound parameters that are included in the MPEG-7 standard. The use of wavelet-based parameters led to better audio retrieval ef ciency. The classi cation of musical works is considered in [128], based on the inspection of standard music notations. A decision table is constructed, with features representing various aspects of musical compositions (objects), such as rhythm
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APPLICATIONS I: USE OF RSAR
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disorder, beat characteristics, and harmony. From this table classi cation rules are induced (via rough set rule induction) and used to classify unseen compositions.
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SUMMARY
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This chapter has presented three main applications of rough set attribute reduction, within the very different domains of medical image classi cation, text categorization, and algae population estimation. Classi cation systems for these tasks bene t greatly from the application of RSAR both in terms of induction time speedup and resulting knowledge readability. A brief overview of other applications of rough set theory was presented, showing its utility in a wide range of tasks.
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ROUGH AND FUZZY HYBRIDIZATION
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This chapter provides a broad overview of logical and black box approaches to fuzzy and rough hybridization. The logical approaches include theoretical, supervised learning, feature selection, and unsupervised learning. The black box approaches consist of neural and evolutionary computing. Since both theories originated in the expert system domain, there are a number of research proposals that combine rough and fuzzy concepts in supervised learning. However, continuing developments of rough and fuzzy extensions to clustering, neurocomputing, and genetic algorithms make hybrid approaches in these areas a potentially rewarding research opportunity as well.
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INTRODUCTION
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Fuzzy set theory has entered the fth decade of research and development efforts [408]. Rough set theory celebrates its twenty- fth anniversary this year [260]. The two theories complement each other and as such constitute important components of soft computing. Researchers have explored a variety of different ways in which these two theories interact with each other. The origins of both theories were essentially logical. Hence much of the hybridization between fuzzy and rough set theory is logically based. Moreover rough set theory was proposed for supervised learning. Therefore there is a signi cant body of work that combines supervised classi cation using fuzzy and rough set theory. This chapter begins with a review
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Computational Intelligence and Feature Selection: Rough and Fuzzy Approaches, by Richard Jensen and Qiang Shen Copyright 2008 Institute of Electrical and Electronics Engineers
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of fuzzy and rough hybridization in supervised learning, information retrieval, and feature selection. Both fuzzy and rough set theories are attracting attention among researchers for a more exible representation of clusters. There are various extensions of fuzzy and rough set theory for clustering. These include the fuzzy and rough extensions of popular clustering algorithms including K-means, Kohonen self-organizing maps, evolutionary unsupervised learning, and support vector clustering. In addition to a brief look at these extensions, this chapter looks at attempts to combine fuzzy and rough set theory in unsupervised clustering. These research efforts include truly unsupervised hybridizations as well as semisupervised data-mining techniques that use the rule generation aspect of rough set theory. The two theories have also made forays into black box techniques such as neurocomputing and evolutionary computing. The fuzzy and rough extensions of supervised and unsupervised neural networks have been in existence for more than a decade. Consequently there has also been many fuzzy and rough hybridized neurocomputing work. Moreover some innovative combinations of logical foundations of rough and fuzzy set theory have been integrated into neural networks. The fuzzy and rough evolutionary computing is relatively nascent. There are some examples of hybridization of fuzzy and rough sets in evolutionary computing. In some cases the genetic algorithms are used to aid other hybridization techniques such as rough-fuzzy neural networks.
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