Generalized rough sets based on relations
From MaRDI portal
Publication:2456470
DOI10.1016/j.ins.2007.05.037zbMath1129.68088OpenAlexW1983426508MaRDI QIDQ2456470
Publication date: 18 October 2007
Published in: Information Sciences (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.ins.2007.05.037
Knowledge representation (68T30) Reasoning under uncertainty in the context of artificial intelligence (68T37)
Related Items
Probabilistic graded rough set and double relative quantitative decision-theoretic rough set ⋮ Covering-based rough sets and modal logics. I. ⋮ Covering-based rough sets and modal logics. II. ⋮ Multi-granular soft rough covering sets ⋮ Generalized rough sets based on neighborhood systems and topological spaces ⋮ Generalized hesitant fuzzy rough sets (GHFRS) and their application in risk analysis ⋮ Some implicative topological quasi-Boolean algebras and rough set models ⋮ Topological approximations of multisets ⋮ Topological approach to retrieve missing values in incomplete information systems ⋮ On some types of covering rough sets from topological points of view ⋮ On generalizing covering approximation space ⋮ A method of representing rough sets system determined by quasi orders ⋮ On the topological properties of generalized rough sets ⋮ Nullity-based matroid of rough sets and its application to attribute reduction ⋮ Soft sets and soft rough sets ⋮ Topological properties of generalized approximation spaces ⋮ The reduction and fusion of fuzzy covering systems based on the evidence theory ⋮ Generalization of Pawlak's rough approximation spaces by using \(\delta \beta \)-open sets ⋮ Matroidal structure of rough sets based on serial and transitive relations ⋮ Probabilistic rough set over two universes and rough entropy ⋮ On some types of neighborhood-related covering rough sets ⋮ The lattice and matroid representations of definable sets in generalized rough sets based on relations ⋮ Topological structure of generalized rough sets ⋮ The \(\vartheta \)-lower and \(T\)-upper fuzzy rough approximation operators on a semigroup ⋮ A class of rough multiple objective programming and its application to solid transportation problem ⋮ Multiset topologies induced by multiset relations ⋮ Attribute reduction of data with error ranges and test costs ⋮ Comparative studies of covering rough set models ⋮ Decision-making based on q-rung orthopair fuzzy soft rough sets ⋮ The lower and upper approximations in a quotient hypermodule with respect to fuzzy sets. ⋮ Axiomatization of covering-based approximation operators generated by general or irreducible coverings ⋮ Some twin approximation operators on covering approximation spaces ⋮ Picture fuzzy rough set and rough picture fuzzy set on two different universes and their applications ⋮ Generalized fuzzy rough sets determined by a triangular norm ⋮ Communicating between information systems ⋮ A short note on algebraic \(T\)-rough sets ⋮ Neighborhood rough set based heterogeneous feature subset selection ⋮ The lower and upper approximations in a hypergroup ⋮ Multigranulation rough sets: from partition to covering ⋮ On rough approximations via ideal ⋮ On topologies defined by neighbourhood operators of approximation spaces ⋮ Matrix approach to spanning matroids of rough sets and its application to attribute reduction ⋮ Binary relations-based rough sets -- an automated approach ⋮ Mining incomplete data with singleton, subset and concept probabilistic approximations ⋮ Partial order relation for approximation operators in covering based rough sets ⋮ Graph and matrix approaches to rough sets through matroids ⋮ Some minimal axiom sets of rough sets ⋮ Characterizations of coverings for upper approximation operators being closure operators ⋮ The algebraic structures of generalized rough set theory ⋮ Roughness in \(n\)-ary hypergroups. ⋮ The characterizations of upper approximation operators based on special coverings ⋮ Marcus-Wyse topological rough sets and their applications ⋮ A comparison of two types of rough sets induced by coverings ⋮ Concept lattices of fuzzy contexts: formal concept analysis vs. rough set theory ⋮ Homomorphism between ordered decision systems ⋮ Matroidal structure of rough sets from the viewpoint of graph theory ⋮ Covering-based generalized IF rough sets with applications to multi-attribute decision-making ⋮ \(L\)-fuzzifying approximation operators in fuzzy rough sets ⋮ A comparison of two kinds of definitions of rough approximations based on a similarity relation ⋮ Covering rough sets based on neighborhoods: an approach without using neighborhoods ⋮ Generalized lower and upper approximations in a ring. ⋮ A new methodology for fuzzification of rough sets based on \(\alpha\)-indiscernibility ⋮ Topological characterizations of generalized fuzzy rough sets ⋮ Textural approach to generalized rough sets based on relations ⋮ On fuzzy rough sets based on tolerance relations ⋮ Roughness in MV-algebras ⋮ Axiomatic systems for rough sets and fuzzy rough sets ⋮ Generalized intuitionistic fuzzy rough sets based on intuitionistic fuzzy coverings ⋮ The fourth type of covering-based rough sets ⋮ An application of rough sets to graph theory ⋮ Topological characterizations of covering for special covering-based upper approximation operators ⋮ Relationships among generalized rough sets in six coverings and pure reflexive neighborhood system ⋮ Invertible approximation operators of generalized rough sets and fuzzy rough sets ⋮ Rough sets based on Galois connections ⋮ Soft covering based rough graphs and corresponding decision making ⋮ Algebraic aspects of generalized approximation spaces ⋮ Reference points and roughness ⋮ Roughness in Cayley graphs ⋮ Some improved results on communication between information systems ⋮ The further investigation of covering-based rough sets: uncertainty characterization, similarity measure and generalized models ⋮ Boundary region-based rough sets and uncertainty measures in the approximation space ⋮ Roughness and fuzziness in quantales. ⋮ On \((\odot, \operatorname{\&})\)-fuzzy rough sets based on residuated and co-residuated lattices ⋮ Generalized rough set models determined by multiple neighborhoods generated from a similarity relation ⋮ Note on ``Generalized rough sets based on reflexive and transitive relations ⋮ Relationship between generalized rough sets based on binary relation and covering ⋮ The relationships between topologies and generalized rough sets ⋮ Maps between covering approximation spaces and the product space of two covering approximation spaces ⋮ Formal development of rough inclusion functions ⋮ Characteristic numbers and approximation operators in generalized rough approximation system ⋮ Formalizing two generalized approximation operators ⋮ Rough multisets and information multisystems ⋮ Uncertainty measurement for neighborhood based soft covering rough graphs with applications ⋮ Novel soft fuzzy rough rings (ideals) of rings and their application in decision making ⋮ The characterizations of upper approximation operators based on coverings ⋮ The comparative study of covering rough sets and multi-granulation rough sets ⋮ Belief functions and rough sets: survey and new insights ⋮ \(L\)-fuzzy rough approximation operators via three new types of \(L\)-fuzzy relations ⋮ Topological properties of locally finite covering rough sets and \(K\)-topological rough set structures ⋮ Generalized multigranulation fuzzy rough sets based on upward additive consistency ⋮ Rough approximation operators based on quantale-valued fuzzy generalized neighborhood systems ⋮ The rough membership function based on C 10 ¯ and its applications ⋮ Covering-based multigranulation decision-theoretic rough sets ⋮ Generalization of Pawlak's approximations in hypermodules by set-valued homomorphisms ⋮ Approximations in a module by using set-valued homomorphisms ⋮ Relations arising from coverings and their topological structures ⋮ Cost-sensitive feature selection of numeric data with measurement errors ⋮ Relationship among basic concepts in covering-based rough sets ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Rough approximations via ideal on a complete completely distributive lattice ⋮ Computer Certification of Generalized Rough Sets Based on Relations ⋮ Developing complementary rough inclusion functions ⋮ Test-cost-sensitive attribute reduction on heterogeneous data for adaptive neighborhood model ⋮ Applications of rough soft sets to Krasner (m,n)-hyperrings and corresponding decision making methods ⋮ Novel matrix-based approaches to computing minimal and maximal descriptions in covering-based rough sets ⋮ Approximate Reduction for the Interval-Valued Decision Table ⋮ Reductions of a covering approximation space from algebraic points of view ⋮ A textural view of soft fuzzy rough sets ⋮ Decidability in Pre-rough Algebras: Extended Abstract ⋮ Fuzzy approximation based on \(\tau\)-\(\mathfrak{K}\) fuzzy open (closed) sets ⋮ An efficient feature selection algorithm based on the description vector and hypergraph ⋮ Axiomatic characterizations of \(L\)-valued rough sets using a single axiom ⋮ On the Relationship Between L-fuzzy Closure Spaces and L-fuzzy Rough Sets ⋮ An Application on an Information System via Nano Ordered Topology ⋮ Generalized \(\mathcal TL\)-fuzzy rough rings via \(\mathcal TL\)-fuzzy relational morphisms. ⋮ Unnamed Item ⋮ Formal concept analysis based on the topology for attributes of a formal context ⋮ Covering-based fuzzy rough sets ⋮ Roughness in n-ary semigroups based on fuzzy ideals ⋮ Covering-based multi-granulation fuzzy rough sets ⋮ A kind of new rough set: Rough soft sets and rough soft rings ⋮ Generalized rough multiset via multiset ideals ⋮ Rough and rough fuzzy sets on two universes via covering approach ⋮ On multi-granulation covering rough sets ⋮ A New Subsystem-Based Definition of Generalized Rough Set Model ⋮ A Further Investigation to Relative Reducts of Decision Information Systems ⋮ Formalizing Lattice-Theoretical Aspects of Rough and Fuzzy Sets ⋮ A multiview approach for intelligent data analysis based on data operators ⋮ Rough Multiset and Its Multiset Topology ⋮ New Approach in Defining Rough Approximations ⋮ On the structure of rough prime (primary) ideals and rough fuzzy prime (primary) ideals in commutative rings. ⋮ Generalized rough sets over fuzzy lattices ⋮ Automated Comparative Study of Some Generalized Rough Approximations ⋮ Residuated Algebraic Structures in the Vicinity of Pre-rough Algebra and Decidability ⋮ A Review on Rough Sets and Possible World Semantics for Modal Logics ⋮ A roughness measure of fuzzy sets from the perspective of distance ⋮ Novel classes of fuzzy soft \(\beta\)-coverings-based fuzzy rough sets with applications to multi-criteria fuzzy group decision making ⋮ The structures and the connections on four types of covering rough sets ⋮ Relational Formal Characterization of Rough Sets ⋮ Four operators of rough sets generalized to matroids and a matroidal method for attribute reduction ⋮ Bitopological approximation space with application to data reduction in multi-valued information systems
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The minimization of axiom sets characterizing generalized approximation operators
- Topological approaches to covering rough sets
- Rudiments of rough sets
- Rough sets: some extensions
- Rough sets and Boolean reasoning
- Regranulation: a granular algorithm enabling communication between granular worlds
- The concept of a linguistic variable and its application to approximate reasoning. I
- The concept of a linguistic variable and its application to approximate reasoning. II
- The concept of a linguistic variable and its application to approximate reasoning. III
- Rough sets in knowledge discovery 1. Methodology and applications
- Extensions and intensions in the rough set theory
- Constructive and algebraic methods of the theory of rough sets
- A comparative study of fuzzy sets and rough sets
- Rough sets and current trends in computing. 1st international conference, RSCTC '98, Warsaw, Poland, June 22--26, 1998. Proceedings
- Reduction and axiomization of covering generalized rough sets.
- Fuzzy fractal dimensions and fuzzy modeling.
- Constructive and axiomatic approaches of fuzzy approximation operators.
- On the topological properties of fuzzy rough sets
- Generalized fuzzy rough sets
- Relational interpretations of neighborhood operators and rough set approximation operators
- Rough set approach to incomplete information systems
- Rules in incomplete information systems
- On characterizations of \((\mathcal J,\mathcal T)\)-fuzzy rough approximation operators
- On the abstraction of conventional dynamic systems: from numerical analysis to linguistic analysis
- On the structure of generalized rough sets
- Knowledge acquisition in incomplete information systems: a rough set approach
- Toward a generalized theory of uncertainty (GTU) -- an outline
- ROUGH FUZZY SETS AND FUZZY ROUGH SETS*
- Transactions on Rough Sets II
- Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing
- Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing
- Subsystem Based Generalizations of Rough Set Approximations
- Fuzzy sets
- Axiomatic Systems of Generalized Rough Sets
