Roughness based on fuzzy ideals

DOI10.1016/j.ins.2005.10.001zbMath1112.03049OpenAlexW2006571464MaRDI QIDQ855699

Bijan Davvaz

Publication date: 7 December 2006

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

Full work available at URL: https://doi.org/10.1016/j.ins.2005.10.001

zbMATH Keywords

ringfuzzy setrough setfuzzy ideallower approximationupper approximation

Mathematics Subject Classification ID

Theory of fuzzy sets, etc. (03E72) Nonclassical and second-order set theories (03E70) Ideals in associative algebras (16D25) Generalizations (16Y99)

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Cites Work

• Roughness in rings.
• Roughness in modules.
• Operations on fuzzy ideals
• Fuzzy invariant subgroups and fuzzy ideals
• The concept of a linguistic variable and its application to approximate reasoning. III
• Rough ideals in semigroups
• Interpretations of belief functions in the theory of rough sets
• Extensions and intensions in the rough set theory
• Rough sets in a fundamental ring
• The lower and upper approximations in a fuzzy group
• Roughness of a fuzzy set
• Approximations in \(H_v\)-modules.
• Rough set analysis of a general type of fuzzy data using transitive aggregations of fuzzy similarity relations.
• Reduction and axiomization of covering generalized rough sets.
• An axiomatic characterization of a fuzzy generalization of rough sets.
• A comparative study of fuzzy rough sets
• On the topological properties of fuzzy rough sets
• Rough mereology: A new paradigm for approximate reasoning
• Relational interpretations of neighborhood operators and rough set approximation operators
• On fuzzy ideals of a ring. I
• Neighborhood operator systems and approximations
• Rough--fuzzy functions in classification
• Generalized rough sets
• Two new operators in rough set theory with applications to fuzzy sets
• Fuzziness in rough sets
• \(\alpha\)-RST: A generalization of rough set theory
• Rough prime ideals and rough fuzzy prime ideals in semigroups.
• On the structure of generalized rough sets
• Fuzzy groups
• Modules with decompositions that complement direct summands
• Fuzzy sets and join spaces associated with rough sets
• ROUGH FUZZY SETS AND FUZZY ROUGH SETS*
• Rough sets
• ROUGHNESS OF GAMMA-SUBSEMIGROUPS/IDEALS IN GAMMA-SEMIGROUPS
• Fuzzy sets
• Rough set theory applied to (fuzzy) ideal theory
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item