Rough sets and fuzzy sets-some remarks on interrelations

Wygralak, Maciej

doi:10.1016/0165-0114(89)90197-8

Cited by 75 publications

(31 citation statements)

References 2 publications

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“…It possesses many features in common (to a certain extent) with the Dempster-Shafer theory of evidence [54] and fuzzy set theory [39], [68]. The rough set itself is the approximation of a vague concept (set) by a pair of precise concepts, called lower and upper approximations, which are a classification of the domain of interest into disjoint categories.…”

Section: Rough Selectionmentioning

confidence: 99%

Semantics-preserving dimensionality reduction: rough and fuzzy-rough-based approaches

Jensen

Shen

2004

IEEE Trans. Knowl. Data Eng.

592

287

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Abstract-Semantics-preserving dimensionality reduction refers to the problem of selecting those input features that are most predictive of a given outcome; a problem encountered in many areas such as machine learning, pattern recognition, and signal processing. This has found successful application in tasks that involve data sets containing huge numbers of features (in the order of tens of thousands), which would be impossible to process further. Recent examples include text processing and Web content classification. One of the many successful applications of rough set theory has been to this feature selection area. This paper reviews those techniques that preserve the underlying semantics of the data, using crisp and fuzzy rough set-based methodologies. Several approaches to feature selection based on rough set theory are experimentally compared. Additionally, a new area in feature selection, feature grouping, is highlighted and a rough set-based feature grouping technique is detailed.

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Section: Rough Selectionmentioning

confidence: 99%

Semantics-preserving dimensionality reduction: rough and fuzzy-rough-based approaches

Jensen

Shen

2004

IEEE Trans. Knowl. Data Eng.

592

287

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show abstract

“…It possesses many features in common (to a certain extent) with the Dempster-Shafer theory of evidence [30] and fuzzy set theory [35]. The rough set itself is the approximation of a vague concept (set) by a pair of precise concepts, called lower and upper approximations, which are a classification of the domain of interest into disjoint categories.…”

Section: VImentioning

confidence: 99%

Performing Feature Selection with ACO

Jensen

2006

Swarm Intelligence in Data Mining

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Summary. The main aim of feature selection is to determine a minimal feature subset from a problem domain while retaining a suitably high accuracy in representing the original features. In real world problems FS is a must due to the abundance of noisy, irrelevant or misleading features. However, current methods are inadequate at finding optimal reductions. This chapter presents a feature selection mechanism based on Ant Colony Optimization in an attempt to combat this. The method is then applied to the problem of finding optimal feature subsets in the fuzzy-rough data reduction process. The present work is applied to two very different challenging tasks, namely web classification and complex systems monitoring.

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“…It is really a 3-uple (A, R*(A), R * (A)), and some constraints relate the two sets in the interval-valued representation. More discussions on the difference between fuzzy sets and rough sets are in Wygralak (1989), Chanas and Kuchta (1992), Lin (1998a).…”

Section: Examplesmentioning

confidence: 99%

Fuzzy Sets: History and Basic Notions

Dubois¹,

Ostasiewicz

Prade³

2000

The Handbooks of Fuzzy Sets Series

138

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Abstract. This paper is an introduction to fuzzy set theory. It has several purposes. First, it tries to explain the emergence of fuzzy sets from an historical perspective. Looking back to the history of sciences, it seems that fuzzy sets were bound to appear at some point in the 20th century. Indeed, Zadeh's works have cristalized and popularized a concern that has appeared in the first half of the century, mainly in philosophical circles. Another purpose of the paper is to scan the basic definitions in the field, that are required for a proper reading of the rest of the volume, as well as the other volumes of the Handbooks of Fuzzy Sets Series. This Chapter also contains a discussion on operational semantics of the generally too abstract notion of membership function. Lastly, a survey of variants of fuzzy sets and related matters is provided.

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Rough sets and fuzzy sets-some remarks on interrelations

Cited by 75 publications

References 2 publications

Semantics-preserving dimensionality reduction: rough and fuzzy-rough-based approaches

Semantics-preserving dimensionality reduction: rough and fuzzy-rough-based approaches

Performing Feature Selection with ACO

Fuzzy Sets: History and Basic Notions

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