A novel variable precision <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mo stretchy="false">(</mml:mo><mml:mi>θ</mml:mi><mml:mo>,</mml:mo><mml:mi>σ</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>-fuzzy rough set model based on fuzzy granules

Yao, Yanqing; Mi, Jin‐Xiao; Li, Zhoujun

doi:10.1016/j.fss.2013.06.012

Cited by 86 publications

(25 citation statements)

References 27 publications

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“…Zhang and Miao [221] and Zhang and Miao [222] proposed the double-quantitative approximation space for presenting two double-quantitative rough set theories. Yao et al [101] suggested the variable precision ( , )-fuzzyrough sets theory regarding fuzzy granules. Liu et al [223] investigated logistic regression for classification based on decision-theoretic rough sets theory.…”

Section: Related Workmentioning

confidence: 99%

Recent Fuzzy Generalisations of Rough Sets Theory: A Systematic Review and Methodological Critique of the Literature

et al. 2017

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Rough set theory has been used extensively in fields of complexity, cognitive sciences, and artificial intelligence, especially in numerous fields such as expert systems, knowledge discovery, information system, inductive reasoning, intelligent systems, data mining, pattern recognition, decision-making, and machine learning. Rough sets models, which have been recently proposed, are developed applying the different fuzzy generalisations. Currently, there is not a systematic literature review and classification of these new generalisations about rough set models. Therefore, in this review study, the attempt is made to provide a comprehensive systematic review of methodologies and applications of recent generalisations discussed in the area of fuzzy-rough set theory. On this subject, the Web of Science database has been chosen to select the relevant papers. Accordingly, the systematic and metaanalysis approach, which is called "PRISMA," has been proposed and the selected articles were classified based on the author and year of publication, author nationalities, application field, type of study, study category, study contribution, and journal in which the articles have appeared. Based on the results of this review, we found that there are many challenging issues related to the different application area of fuzzy-rough set theory which can motivate future research studies.

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Section: Related Workmentioning

confidence: 99%

Recent Fuzzy Generalisations of Rough Sets Theory: A Systematic Review and Methodological Critique of the Literature

et al. 2017

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“…There are models which are frequency-based, analogous to the VPRS model of Ziarko [5,24,25,42,43,65]. Another model adjusts the set which is approximated [69].…”

Section: Robust Fuzzy Rough Set Modelsmentioning

confidence: 99%

“…Moreover, some models use other aggregation operators than the infimum and supremum operators [7,18]. To the best of our knowledge, the seven models we discuss here are the most widely used robust fuzzy rough set models [27,65].…”

Section: Robust Fuzzy Rough Set Modelsmentioning

confidence: 99%

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A comprehensive study of implicator–conjunctor-based and noise-tolerant fuzzy rough sets: Definitions, properties and robustness analysis

D'eer

Verbiest

Cornelis

et al. 2015

Fuzzy Sets and Systems

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Both rough and fuzzy set theories offer interesting tools for dealing with imperfect data: while the former allows us to work with uncertain and incomplete information, the latter provides a formal setting for vague concepts. The two theories are highly compatible, and since the late 1980s many researchers have studied their hybridization. In this paper, we critically evaluate most relevant fuzzy rough set models proposed in the literature. To this end, we establish a formally correct and unified mathematical framework for them. Both implicator-conjunctor-based definitions and noise-tolerant models are studied. We evaluate these models on two different fronts: firstly, we discuss which properties of the original rough set model can be maintained and secondly, we examine how robust they are against both class and attribute noise. By highlighting the benefits and drawbacks of the different fuzzy rough set models, this study appears a necessary first step to propose and develop new models in future research.

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“…In literature, many robust fuzzy rough set models are defined. A first group of robust models is based on frequency: these models only take a subset of U into account when computing the lower and upper approximation [10,11,12]. Furthermore, there are robust models that use vague quantifiers to compute the approximation operators [13] or that modify the fuzzy set A which is approximated [14].…”

Section: Robust Fuzzy Rough Set Modelsmentioning

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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A novel variable precision (θ,σ)-fuzzy rough set model based on fuzzy granules

Cited by 86 publications

References 27 publications

Recent Fuzzy Generalisations of Rough Sets Theory: A Systematic Review and Methodological Critique of the Literature

Recent Fuzzy Generalisations of Rough Sets Theory: A Systematic Review and Methodological Critique of the Literature

A comprehensive study of implicator–conjunctor-based and noise-tolerant fuzzy rough sets: Definitions, properties and robustness analysis

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

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