Relational interpretations of neighborhood operators and rough set approximation operators
Information Sciences—Informatics and Computer Science: An International Journal
Rules in incomplete information systems
Information Sciences: an International Journal
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets: Theoretical Aspects of Reasoning about Data
A Generalized Definition of Rough Approximations Based on Similarity
IEEE Transactions on Knowledge and Data Engineering
On the Extension of Rough Sets under Incomplete Information
RSFDGrC '99 Proceedings of the 7th International Workshop on New Directions in Rough Sets, Data Mining, and Granular-Soft Computing
On the Unknown Attribute Values in Learning from Examples
ISMIS '91 Proceedings of the 6th International Symposium on Methodologies for Intelligent Systems
On generalizing rough set theory
RSFDGrC'03 Proceedings of the 9th international conference on Rough sets, fuzzy sets, data mining, and granular computing
RSEISP '07 Proceedings of the international conference on Rough Sets and Intelligent Systems Paradigms
Approximation Space and LEM2-like Algorithms for Computing Local Coverings
Fundamenta Informaticae - Concurrency Specification and Programming (CS&P)
Lower and upper approximations in data tables containing possibilistic information
Transactions on rough sets VII
Local and global approximations for incomplete data
Transactions on rough sets VIII
A Local Version of the MLEM2 Algorithm for Rule Induction
Fundamenta Informaticae - Understanding Computers' Intelligence Celebrating the 100th Volume of Fundamenta Informaticae in Honour of Helena Rasiowa
A comparison of some rough set approaches to mining symbolic data with missing attribute values
ISMIS'11 Proceedings of the 19th international conference on Foundations of intelligent systems
Mining incomplete data: a rough set approach
RSKT'11 Proceedings of the 6th international conference on Rough sets and knowledge technology
Definability and other properties of approximations for generalized indiscernibility relations
Transactions on Rough Sets XI
Approximations and uncertainty measures in incomplete information systems
Information Sciences: an International Journal
Approximation Space and LEM2-like Algorithms for Computing Local Coverings
Fundamenta Informaticae - Concurrency Specification and Programming (CS&P)
Local probabilistic approximations for incomplete data
ISMIS'12 Proceedings of the 20th international conference on Foundations of Intelligent Systems
A novel feature selection method and its application
Journal of Intelligent Information Systems
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For completely specified decision tables, where lower and upper approximations are unique, the lower approximation is the largest definable set contained in the approximated set X and the upper approximation of X is the smallest definable set containing X. For incomplete decision tables the existing definitions of upper approximations provide sets that, in general, are not minimal definable sets. The same is true for approximations based on relations that are generalizations of the equivalence relation. In this paper we introduce two definitions of approximations, local and global, such that the corresponding upper approximations are minimal. Local approximations are more precise than global approximations. Global lower approximations may be determined by a polynomial algorithm. However, algorithms to find both local approximations and global upper approximations are NP-hard.