Generalized fuzzy rough sets determined by a triangular norm

DOI10.1016/j.ins.2008.03.013zbMath1151.03344OpenAlexW2006138243MaRDI QIDQ942307

B. E. Eshmatov

Publication date: 5 September 2008

Published in: Information Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ins.2008.03.013

zbMATH Keywords

uncertaintyrough setsfuzzy setsfuzzy relationtriangular normapproximation operatorsminimal sets of axioms

Mathematics Subject Classification ID

Theory of fuzzy sets, etc. (03E72) Reasoning under uncertainty in the context of artificial intelligence (68T37) Measures of information, entropy (94A17)

Related Items

Topological structures of a type of granule based covering rough sets, On \((O,G)\)-fuzzy rough sets based on overlap and grouping functions over complete lattices, Attribute selection with fuzzy decision reducts, On axiomatic characterizations of three pairs of covering based approximation operators, Fuzzy approximations of fuzzy relational structures, Single axioms for \((S,T)\)-fuzzy rough approximation operators with fuzzy product operations, APPROXIMATION OPERATORS AND FUZZY ROUGH SETS IN CO-RESIDUATED LATTICES, Axiomatic characterizations of \((S, T)\)-fuzzy rough approximation operators, Attribute reduction with fuzzy rough self-information measures, A comprehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets: definitions, properties and robustness analysis, Granular variable precision fuzzy rough sets with general fuzzy relations, \(T\)-similarity of fuzzy relations and related algebraic structures, Two fuzzy covering rough set models and their generalizations over fuzzy lattices, Notes on a comprehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets: definitions, properties and robustness analysis, Distance spaces, Alexandrov pretopologies and join-meet operators, Feature selection in mixed data: a method using a novel fuzzy rough set-based information entropy, Generalized Dominance-Based Rough Set Model for the Dominance Intuitionistic Fuzzy Information Systems, New results on granular variable precision fuzzy rough sets based on fuzzy (co)implications, Unsupervised attribute reduction for mixed data based on fuzzy rough sets, Fuzzy rough granular self-organizing map and fuzzy rough entropy, Fuzzy rough set models over two universes using textures, Constructive and axiomatic approaches to hesitant fuzzy rough set, On generalised interval-valued fuzzy soft sets, Axiomatic characterizations of \(L\)-valued rough sets using a single axiom, Granular computing based on fuzzy similarity relations, On intuitionistic fuzzy topologies based on intuitionistic fuzzy reflexive and transitive relations, Parameterized attribute reduction with Gaussian kernel based fuzzy rough sets, Fuzzy rough granular neural networks, fuzzy granules, and classification, A class of rough multiple objective programming and its application to solid transportation problem, Characterization of rough set approximations in atanassov intuitionistic fuzzy set theory, A graph approach for fuzzy-rough feature selection, A kind of new rough set: Rough soft sets and rough soft rings, Belief and plausibility functions of type-2 fuzzy rough sets, On \((I_O,O)\)-fuzzy rough sets based on overlap functions, New topological approach of rough set generalizations, Topological structures induced by L-fuzzifying approximation operators, Some properties of \( L\)-fuzzy approximation spaces based on bounded integral residuated lattices, Labeled fuzzy approximations based on bisimulations, Relationships between generalized rough sets based on covering and reflexive neighborhood system, NEIGHBORHOOD SYSTEM BASED ROUGH SET: MODELS AND ATTRIBUTE REDUCTIONS, Topological structures of \(L\)-fuzzy rough sets and similarity sets of \(L\)-fuzzy relations, \(L\)-fuzzifying approximation operators in fuzzy rough sets, On minimization of axiom sets characterizing covering-based approximation operators, Generalized lower and upper approximations in a ring., Topological characterizations of generalized fuzzy rough sets, Rough set theory applied to lattice theory, Unnamed Item, The further investigation of covering-based rough sets: uncertainty characterization, similarity measure and generalized models, On \((\odot, \operatorname{\&})\)-fuzzy rough sets based on residuated and co-residuated lattices, Using one axiom to characterize \(L\)-fuzzy rough approximation operators based on residuated lattices, Single axioms for lower fuzzy rough approximation operators determined by fuzzy implications, Granular variable precision \(L\)-fuzzy rough sets based on residuated lattices, New results on single axioms for \(L\)-fuzzy rough approximation operators, On characterization of intuitionistic fuzzy rough sets based on intuitionistic fuzzy implicators, Fuzzy variable precision rough sets based on residuated lattices, Generalized interval-valued fuzzy variable precision rough sets determined by fuzzy logical operators, Reasoning with rough description logics: An approximate concepts approach, On characterizations of a pair of covering-based approximation operators, \(L\)-fuzzy rough approximation operators via three new types of \(L\)-fuzzy relations, Uncertainty Problem Processing with Covering Generalized Rough Sets, A comparative study of variable precision fuzzy rough sets based on residuated lattices, Single axiomatic characterization of a hesitant fuzzy generalization of rough approximation operators, Notes on ``On \((O,G)\)-fuzzy rough sets based on overlap and grouping functions over complete lattices, Topological properties of a pair of relation-based approximation operators, A novel variable precision \((\theta ,\sigma )\)-fuzzy rough set model based on fuzzy granules, On Bijective Correspondence between Fuzzy Reflexive Approximation Spaces and Fuzzy Transformation Systems, Generalized fuzzy rough approximation operators determined by fuzzy implicators, Representations of typical hesitant fuzzy rough sets

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Mathematical Theory of Communication
• The minimization of axiom sets characterizing generalized approximation operators
• A rough logic formalism for fuzzy controllers: A hard and soft computing view
• Fuzzy rough sets
• Variable precision rough set model
• Constructive and algebraic methods of the theory of rough sets
• Fuzzy closure operators. II: Induced relations, representation, and examples
• Constructive and axiomatic approaches of fuzzy approximation operators.
• An axiomatic characterization of a fuzzy generalization of rough sets.
• A comparative study of fuzzy rough sets
• Two views of the theory of rough sets in finite universes
• Generalized fuzzy rough sets
• Relational interpretations of neighborhood operators and rough set approximation operators
• Axiomatics for fuzzy rough sets
• Fuzziness in rough sets
• Minimization of axiom sets on fuzzy approximation operators
• (\(\vartheta, T\))-fuzzy rough approximation operators and the \(TL\)-fuzzy rough ideals on a ring
• On characterizations of \((\mathcal J,\mathcal T)\)-fuzzy rough approximation operators
• Generalized rough sets based on relations
• Rough fuzzy approximations on two universes of discourse
• A weighted rough set based method developed for class imbalance learning
• Roughian: Rough information analysis
• A new method for measuring uncertainty and fuzziness in rough set theory
• ROUGH FUZZY SETS AND FUZZY ROUGH SETS*
• Rough sets
• UPPER AND LOWER APPROXIMATIONS OF FUZZY SETS
• MEASURING UNCERTAINTY IN ROUGH SET THEORY
• An uncertainty measure in partition-based fuzzy rough sets
• On axiomatic characterisations of crisp approximation operators
• Rough set theory applied to (fuzzy) ideal theory