Lattice Theory for Rough Sets

Järvinen, Jouni

doi:10.1007/978-3-540-71200-8_22

Cited by 105 publications

(54 citation statements)

References 40 publications

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“…The operators and may be viewed as rough approximation operators [13][14][15]28], and the operators and are sometimes interpreted as modifier operators [20,25]. Also other types of definitions for these operators can be found in the literature; see [7] for a survey.…”

Section: Modal-like Operatorsmentioning

confidence: 99%

A unifying study between modal-like operators, topologies and fuzzy sets

Järvinen¹,

Kortelainen²

2007

Fuzzy Sets and Systems

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Section: Modal-like Operatorsmentioning

confidence: 99%

A unifying study between modal-like operators, topologies and fuzzy sets

Järvinen¹,

Kortelainen²

2007

Fuzzy Sets and Systems

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“…The idea of property (A) comes from the concept of a Galois connection [30,56]: let U 1 and U 2 be two universes and f : U 1 → U 2 and g: U 2 → U 1 two mappings between these universes. We call (f, g) a Galois connection in (U 1 , U 2 ) if for all x ∈ U 1 and y ∈ U 2 it holds that…”

Section: Rough Setsmentioning

confidence: 99%

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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“…Basic properties of lower and upper ε-approximations can be found, e.g, in [10,16]. Here we cite only a few among them which will be important in the following.…”

Section: Basics Of Pawlak's Rough Set Theorymentioning

confidence: 99%

“…A natural way of the generalization of Pawlak's idea is that the equivalence relation is replaced by any other type of binary relations on U [10,11,24]. Another generalization is the assumption that the starting point is an arbitrary covering of the universe [1,23,26,27].…”

Section: Introductionmentioning

confidence: 99%

On the Partial Approximation of Sets

2011

AMS

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1 According to Pawlak's classic rough set theory the vagueness of a subset of a finite universe U is defined by the difference of its upper and lower approximations with respect to an equivalence relation on U . A natural way of the generalization of this idea is that the equivalence relation is replaced by either any other type of binary relations on U or an arbitrary covering of the universe. In this paper, our starting point will be an arbitrary family of subsets of an arbitrary universe U . Within this framework, we shall investigate a possible generalization of Pawlak's idea. Both Pawlak's rough set theory and our approach can extensively be applied in medical informatics.

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Lattice Theory for Rough Sets

Cited by 105 publications

References 40 publications

A unifying study between modal-like operators, topologies and fuzzy sets

A unifying study between modal-like operators, topologies and fuzzy sets

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

On the Partial Approximation of Sets

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