Fuzzy sets, uncertainty, and information
Fuzzy sets, uncertainty, and information
IEEE Transactions on Software Engineering
Extensions and intentions in the rough set theory
Information Sciences: an International Journal
Uncertainly measures of rough set prediction
Artificial Intelligence
Rough set algorithms in classification problem
Rough set methods and applications
Various approaches to reasoning with frequency based decision reducts: a survey
Rough set methods and applications
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets in Knowledge Discovery 2: Applications, Case Studies, and Software Systems
Rough Sets in Knowledge Discovery 2: Applications, Case Studies, and Software Systems
Rough Sets, Fuzzy Sets and Knowledge Discovery
Rough Sets, Fuzzy Sets and Knowledge Discovery
Proceedings of the First International Conference on Rough Sets and Current Trends in Computing
RSCTC '98 Proceedings of the First International Conference on Rough Sets and Current Trends in Computing
Reduction and axiomization of covering generalized rough sets
Information Sciences: an International Journal
Peculiarity Oriented Multidatabase Mining
IEEE Transactions on Knowledge and Data Engineering
Two new operators in rough set theory with applications to fuzzy sets
Information Sciences—Informatics and Computer Science: An International Journal
An improved accuracy measure for rough sets
Journal of Computer and System Sciences
A First Course in Information Theory (Information Technology: Transmission, Processing and Storage)
A First Course in Information Theory (Information Technology: Transmission, Processing and Storage)
The Axiomatization of the Rough Set Upper Approximation Operations
Fundamenta Informaticae
Entropies and Co-Entropies of Coverings with Application to Incomplete Information Systems
Fundamenta Informaticae - New Frontiers in Scientific Discovery - Commemorating the Life and Work of Zdzislaw Pawlak
On Three Types of Covering-Based Rough Sets
IEEE Transactions on Knowledge and Data Engineering
Relationship between generalized rough sets based on binary relation and covering
Information Sciences: an International Journal
A new measure of uncertainty based on knowledge granulation for rough sets
Information Sciences: an International Journal
Relationship among basic concepts in covering-based rough sets
Information Sciences: an International Journal
Attribute selection with fuzzy decision reducts
Information Sciences: an International Journal
On a Criterion of Similarity between Partitions Based on Rough Set Theory
RSFDGrC '09 Proceedings of the 12th International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing
A Rough Sets Approach for Personalized Support of Face Recognition
RSFDGrC '09 Proceedings of the 12th International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing
RSFDGrC '09 Proceedings of the 12th International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing
Constructive and algebraic methods of the theory of rough sets
Information Sciences: an International Journal
Information-theoretic measures of uncertainty for rough sets and rough relational databases
Information Sciences: an International Journal
Covering based granular computing for conflict analysis
ISI'06 Proceedings of the 4th IEEE international conference on Intelligence and Security Informatics
Covering rough sets based on neighborhoods: An approach without using neighborhoods
International Journal of Approximate Reasoning
Entropy and co-entropy of a covering approximation space
International Journal of Approximate Reasoning
Information-theoretic measures associated with rough set approximations
Information Sciences: an International Journal
A measurement theory view on the granularity of partitions
Information Sciences: an International Journal
An Improved Axiomatic Definition of Information Granulation
Fundamenta Informaticae
Matroidal structure of rough sets and its characterization to attribute reduction
Knowledge-Based Systems
Rough matroids based on relations
Information Sciences: an International Journal
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In Pawlak's rough set theory, a set is approximated by a pair of lower and upper approximations. To measure numerically the roughness of an approximation, Pawlak introduced a quantitative measure of roughness by using the ratio of the cardinalities of the lower and upper approximations. Although the roughness measure is effective, it has the drawback of not being strictly monotonic with respect to the standard ordering on partitions. Recently, some improvements have been made by taking into account the granularity of partitions. In this paper, we approach the roughness measure in an axiomatic way. After axiomatically defining roughness measure and partition measure, we provide a unified construction of roughness measure, called strong Pawlak roughness measure, and then explore the properties of this measure. We show that the improved roughness measures in the literature are special instances of our strong Pawlak roughness measure and introduce three more strong Pawlak roughness measures as well. The advantage of our axiomatic approach is that some properties of a roughness measure follow immediately as soon as the measure satisfies the relevant axiomatic definition. (This work was supported by the National Natural Science Foundation of China under Grants 60821001, 60873191, and 60903152. The author would like to thank the anonymous reviewers for their helpful comments.)