Rough Fuzzy Sets and Fuzzy Rough Sets*

Dubois, Didier; Prade, Henri

doi:10.1080/03081079008935107

Cited by 2,492 publications

(888 citation statements)

References 21 publications

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“…In (Dubois and Prade, 1990;1992b) we pointed out that indiscernibility and fuzziness are distinct facets of imperfect knowledge. Indiscernibility refers to the granularity of knowledge, which affects the definition of universes of discourse.…”

Section: Examplesmentioning

confidence: 99%

Fuzzy Sets: History and Basic Notions

Dubois¹,

Ostasiewicz

Prade³

2000

The Handbooks of Fuzzy Sets Series

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139

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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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Section: Examplesmentioning

confidence: 99%

Fuzzy Sets: History and Basic Notions

Dubois¹,

Ostasiewicz

Prade³

2000

The Handbooks of Fuzzy Sets Series

Self Cite

139

View full text Add to dashboard Cite

show abstract

“…We next come to the definitions of a rough fuzzy set and allied notions [3], roughness measure of a fuzzy set [2], that shall form the basis of this work. Let A : U → [0, 1] be a fuzzy set in U , A(x), x ∈ U , giving the degree of membership of x in A.…”

Section: Rough Sets and Rough-fuzzy Setsmentioning

confidence: 99%

“…In practice, uncertainties of both the above type appear in nature, and it is apt to characterize both of them. Toward this goal several roughness measures of fuzzy sets (and vice versa) has been defined in literature [2,3]. The objective being to obtain more flexible representation of imprecise objects.…”

Section: Introductionmentioning

confidence: 99%

Object Extraction in Gray-Scale Images by Optimizing Roughness Measure of a Fuzzy Set

Rao

Banerjee

Mitra

2005

Lecture Notes in Computer Science

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Abstract. Object extraction from gray-tone images involve handling of inherent uncertainties in an image. Traditionally fuzzy set theoretic techniques are used for this purpose. However, roughness and limited discernibility of objects is another important aspect of image uncertainty. In this article we propose an algorithm for selection of intensity threshold for object extraction by optimizing a roughness measure of the fuzzy set corresponding to the image object. The rough-fuzzy algorithm is tested on some benchmark images.

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“…Hybridization of both theories has its origin in the early 1990s, when Dubois and Prade [3] presented the first fuzzy rough set model. From then on, research on fuzzy rough set models grows, mainly due to its proven application in machine learning and, in particular, in feature selection.…”

Section: Introductionmentioning

confidence: 99%

Improving the β-Precision and OWA Based Fuzzy Rough Set Models: Definitions, Properties and Robustness Analysis

D'eer

Verbiest

2014

Lecture Notes in Computer Science

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Abstract. Since the early 1990s, many authors have studied fuzzy rough set models and their application in machine learning and data reduction. In this work, we adjust the β-precision and the ordered weighted average based fuzzy rough set models in such a way that the number of theoretical properties increases. Furthermore, we evaluate the robustness of the new models a-β-PREC and a-OWA to noisy data and compare them to a general implicator-conjunctor-based fuzzy rough set model.

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Rough Fuzzy Sets and Fuzzy Rough Sets*

Cited by 2,492 publications

References 21 publications

Fuzzy Sets: History and Basic Notions

Fuzzy Sets: History and Basic Notions

Object Extraction in Gray-Scale Images by Optimizing Roughness Measure of a Fuzzy Set

Improving the β-Precision and OWA Based Fuzzy Rough Set Models: Definitions, Properties and Robustness Analysis

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