Construction of rough approximations in fuzzy setting

Chen, Xueyou; Li, Qingguo

doi:10.1016/j.fss.2007.05.016

Cited by 53 publications

(20 citation statements)

References 15 publications

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“…∇ . Note that the four set operators have been also considered in qualitative data analysis by Gediga and Düntsch (2002) and can be related to crisp rough set theory (Yao and Chen 2006), and fuzzy rough set theory over residuated lattice (Chen and Li 2007) or over general fuzzy lattice (Liu 2008). We recall the three new operators: -X is the set of properties that are satisfied by at least one object in X :…”

Section: Possibility-theoretic View Of Formal Concept Analysismentioning

confidence: 99%

Possibility-theoretic extension of derivation operators in formal concept analysis over fuzzy lattices

Djouadi

Prade

2011

Fuzzy Optim Decis Making

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Formal concept analysis (FCA) associates a binary relation between a set of objects and a set of properties to a lattice of formal concepts defined through a Galois connection. This relation is called a formal context, and a formal concept is then defined by a pair made of a subset of objects and a subset of properties that are put in mutual correspondence by the connection. Several fuzzy logic approaches have been proposed for inducing fuzzy formal concepts from L-contexts based on antitone L−Galois connections. Besides, a possibility-theoretic reading of FCA which has been recently proposed allows us to consider four derivation powerset operators, namely sufficiency, possibility, necessity and dual sufficiency (rather than one in standard FCA). Classically, fuzzy FCA uses a residuated algebra for maintaining the closure property of the composition of sufficiency operators. In this paper, we enlarge this framework and provide sound minimal requirements of a fuzzy algebra w.r.t. the closure and opening properties of antitone L−Galois connections as well as the closure and opening properties of isotone L−Galois connections. We apply these results to particular compositions of the four derivation operators. We also give some noticeable properties which may be useful for building the corresponding associated lattices.

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Section: Possibility-theoretic View Of Formal Concept Analysismentioning

confidence: 99%

Possibility-theoretic extension of derivation operators in formal concept analysis over fuzzy lattices

Djouadi

Prade

2011

Fuzzy Optim Decis Making

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“…They also suggested some possible real world applications of these measures in pattern recognition and image analysis problems. Some results of these generalisations are obtained about rough sets and fuzzy sets in Chakrabarty et al (2000), Chen and Li (2007), Gong et al (2008), Li et al (2008), Liu (2008b), Nakamura (1988) and Nanda and Majumda (1992). Rough set theory is a recent approach for reasoning about data.…”

Section: Introductionmentioning

confidence: 99%

Multi topological approximations of rough set theory

Salama

Elbarbary

2013

IJGCRSIS

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In this paper, we generalise Pawlak's approximation spaces to topological approximation spaces. These topological approximation spaces are generated using many topological notions such as regular open sets, semi-open sets, pre-open sets, γ-open sets, α-open sets and β-open sets and others. Thebasic definitions and properties of these topological approximation spaces are introduced and sufficiently illustrated. We put all topological generalisations in one generalisation called m-generalisation spaces. include rough set, fuzzy set, information system, information retrieval, natural language processing and document processing. 2 pre-open set (Levine, 1963) if A ⊆ int(cl(A)) and it is called a pre-closed set if cl(int(A)) ⊆ A 3 α-open set (Liu, 2008b) if A ⊆ int(cl(int(A))) and it is called a α-closed set if cl(int(cl(A))) ⊆ A 4 semi-pre-open set (Abu-Donia, 2008) (β-open; Pawlak, 1982) if A ⊆ cl(int(cl(A))) and it is called a semi-pre-closed set (Abu-Donia, 2008) (β-closed; Abu-Donia, 2008) if int(cl(int(A))) ⊆ A 5 regular-open set if A ⊆ int(cl(A)) and it is called a regular-closed set if cl(int(A)) ⊆ A 6 semi-regular set (Bryniaski, 1998) if it both semi-open and semi-closed in (U, τ)7 δ-closed set (Liu and Sai, 2009) The semi-closure (resp. α-closure, semi-pre-closure) of a subset A of (U, τ) is the intersection of all semi-closed (resp. α-closed, semi-pre-closed) sets that contains A and

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“…After nearly 20 years since the introduction of fuzzy sets, Pawlak [50] introduced the notion of a rough set as a new mathematical tool to deal with the approximation of a concept in the context of inexact, or incomplete information [5,30]. Since the introduction of rough set theory, many attempts to establish the relationships between the two theories, to compare each to the other, and to simultaneously hybridize them have been made, the aim being to develop a model of uncertainty stronger than both of them [13,18,19,38,43,52,67,68]. For example, Dubois and Prade were one of the first who investigated the problem of fuzzification of a rough set, and presented a kind of fuzzy rough set theory based on a fuzzy similarity relation (i.e., reflexive, symmetric and transitive fuzzy relation) [18].…”

Section: Introductionmentioning

confidence: 99%

Reasoning within expressive fuzzy rough description logics

Jiang

Wang

Pei-min

et al. 2009

Fuzzy Sets and Systems

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It is generally accepted that the management of imprecision and vagueness will yield more intelligent and realistic knowledgebased applications. Description Logics (DLs) are suitable, well-known logics for managing structured knowledge that have gained considerable attention the last decade. The current research progress and the existing problems of uncertain or imprecise knowledge representation and reasoning in DLs are analyzed in this paper. An integration between the theories of fuzzy DLs and rough DLs has been attempted by providing fuzzy rough DLs based on fuzzy rough set theory. The syntax, semantics and properties of fuzzy rough DLs are given. It is proved that the satisfiability, subsumption, entailment and ABox consistency reasoning in fuzzy rough DLs may be reduced to the ABox consistency reasoning in the corresponding fuzzy DLs.

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Construction of rough approximations in fuzzy setting

Cited by 53 publications

References 15 publications

Possibility-theoretic extension of derivation operators in formal concept analysis over fuzzy lattices

Possibility-theoretic extension of derivation operators in formal concept analysis over fuzzy lattices

Multi topological approximations of rough set theory

Reasoning within expressive fuzzy rough description logics

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