Two fuzzy covering rough set models and their generalizations over fuzzy lattices

Ma, Liwen

doi:10.1016/j.fss.2015.05.002

Cited by 198 publications

(82 citation statements)

References 34 publications

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“…This study mainly develops a novel IF rough set model called IF graded covering rough set using the IF graded neighborhood based on the fuzzy covering rough set models presented by Ma [35] . Many further generalizations can be made concerning the IF covering rough set model.…”

Section: Discussionmentioning

confidence: 99%

“…An IF β-covering (1) If we take β= 1 , 0 , then the IF graded covering degenerates to a crisp covering, the IF β-covering (graded covering) approximation space to a crisp approximation space [74] , and the IF β-neighborhood to a crisp neighborhood [15,19] . (2) If we take β= a, 0 (0 a ≤1) , then the IF graded covering degenerates to a fuzzy β-covering, the IF β-covering (graded covering) approximation space to a fuzzy graded approximation space, and the IF β-neighborhood to a fuzzy β-neighborhood [35] .…”

Section: If Graded Covering and If Graded Neighborhoodmentioning

confidence: 99%

“…Feng et al [17] studied the reduction of a fuzzy covering and the fusion of multi-fuzzy covering systems based on evidence theory and rough set theory. Ma [35] defined two new types of fuzzy covering rough set models, which can be regarded as bridges that link covering rough set theory and fuzzy rough set theory.…”

Section: Introductionmentioning

confidence: 99%

“…[35] Let (U, C ) be a fuzzy covering approximation space with C = { ˜ C 1 , C 2 , · · ·, C m } being a fuzzy β-covering of U for some β ∈ (0, 1]. For each X ∈ F ( U ), one can define the lower approximation C (X ) and the upper approximation C (X ) of X as:…”

Section: Introductionmentioning

confidence: 99%

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An intuitionistic fuzzy graded covering rough set

Huang

Guo

et al. 2016

Knowledge-Based Systems

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Section: Discussionmentioning

confidence: 99%

Section: If Graded Covering and If Graded Neighborhoodmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An intuitionistic fuzzy graded covering rough set

Huang

Guo

et al. 2016

Knowledge-Based Systems

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“…Zhang [109] proposed intuitionistic fuzzy-rough sets based on intuitionistic fuzzy coverings by using intuitionistic fuzzy triangular norms and intuitionistic fuzzy implication operators. Probabilistic rough fuzzy set Proposed Fuzzy-rough sets Introduced a probabilistic rough fuzzy set using the conditional probability of a fuzzy event [119] presented two novel types of fuzzy covering rough set for bridges linking covering rough sets and fuzzy-rough theory. Reference [29] investigated the topological characterizations of generalised fuzzy-rough regarding basic rough equalities.…”

Section: Distribution Of Papers Based On Fuzzy Setmentioning

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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A comprehensive study of upward fuzzy preference relation based fuzzy rough set models: Properties and applications in treatment of coronavirus disease

et al. 2021

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In this paper, we first introduce a new type of rough sets called α ‐upward fuzzified preference rodownward fuzzy preferenceugh sets using upward fuzy preference relation. Thereafter on the basis of α ‐upward fuzzified preference rough sets, we propose approximate precision, rough degree, approximate quality and their mutual relationships. Furthermore, we presented the idea of new types of fuzzy upward β ‐coverings, fuzzy upward β ‐neighborhoods and fuzzy upward complement β ‐neighborhoods and some relavent properties are discussed. Hereby, we formulate a new type of upward lower and upward upper approximations by applying an upward β ‐neighborhoods. After employing the upward β ‐neighborhoods based upward rough set approach to it any times, we can only get the six different sets at most. That is to say, every rough set in a universe can be approximated by only six sets, where the lower and upper approximations of each set in the six sets are still lying among these six sets. The relationships among these six sets are established. Subsequently, we presented the idea to combine the fuzzy implicator and t ‐norm to introduce multigranulation ( MJX-tex-caligraphicnormalℐ , MJX-tex-caligraphicscriptT 0.25em ) ‐fuzzy upward rough set applying fuzzy upward β ‐covering and some relative properties are discussed. Finally we presented a new technique for the selection of medicine for treatment of coronavirus disease (COVID‐19) using multigranulation ( MJX-tex-caligraphicnormalℐ , MJX-tex-caligraphicscriptT 0.25em ) ‐fuzzy upward rough sets.

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Two fuzzy covering rough set models and their generalizations over fuzzy lattices

Cited by 198 publications

References 34 publications

An intuitionistic fuzzy graded covering rough set

An intuitionistic fuzzy graded covering rough set

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

A comprehensive study of upward fuzzy preference relation based fuzzy rough set models: Properties and applications in treatment of coronavirus disease

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