Review Article

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

Table 4

Distribution papers based on approximation operators.

Author and referenceApplication fieldType of studyStudy categoryStudy contribution

 Fan et al. [68]Approximate reasoningProposedFuzzy-rough setsProposed a new dominance-based fuzzy-rough set model for decision analysis
 Cheng [69]ApproximationsProposedFuzzy-rough setsSuggested two incremental approaches for fast computing of the rough fuzzy approximation including cut sets of fuzzy sets and boundary sets
 Yang et al. [70]Approximate reasoningProposedFuzzy probabilistic rough setsSuggested a new fuzzy probabilistic rough set approach
 Wu et al. [71]Approximate reasoningProposedFuzzy-rough approximationExamined the problem related to construct rough approximations of a vague set in fuzzy approximation space
 Fan et al. [72]Approximation reasoningProposedFuzzy-rough set and decision-theoretic rough setsProposed the quantitative decision-theoretic rough fuzzy set approaches based on logical disjunction and logical conjunction
 Sun et al. [73]Approximate reasoningDevelopedRough set and fuzzy-rough setsProposed the upper and lower approximations of fuzzy sets based on a hybrid indiscernibility relation
 Estaji et al. [74]Approximate reasoningProposedFuzzy-rough setsIntroduced the notion of a -lower and -upper approximations of a fuzzy subset of
 Li and Yin [75]Approximate reasoningProposedFuzzy-rough setsIntroduced a novel fuzzy algebraic structure which was a named TL-fuzzy-rough semigroup based on a -upper fuzzy-rough approximation and -lower and operators
 Zhang et al. [76]Approximation operatorsDevelopedFuzzy-rough setsDiscussed an approximation set of a vague set in Pawlak’s approximation space
 Li and Cui [77]Approximation operatorsProposedFuzzy-rough setsIntroduced and investigated fuzzy topologies induced by fuzzy-rough approximation operators and the concept of similarity of fuzzy relations
 Wu et al. [78]Approximation operatorsDevelopedFuzzy-rough setsInvestigated the axiomatic characterizations of relation-based -fuzzy-rough approximation operators
 Hao and Li [79]L-fuzzy-rough approximation spaceDevelopedFuzzy-rough setsDiscussed the relationship between -topologies and -fuzzy-rough sets in an arbitrary universe
 Cheng [80]ApproximationProposedFuzzy-rough setsProposed two algorithms based on forward and backward approximations which were called mine rules based on the backward approximation and mine rules based on the forward approximation
 Feng et al. [81]Fuzzy approximation operatorsDevelopedFuzzy-rough setsProposed the approximation of a soft set based on a Pawlak approximation space
 Sun et al. [82]Probabilistic rough fuzzy setProposedFuzzy-rough setsIntroduced a probabilistic rough fuzzy set using the conditional probability of a fuzzy event