Rough sets: a new approach to vagueness
Fuzzy logic for the management of uncertainty
Uncertainly measures of rough set prediction
Artificial Intelligence
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets, Fuzzy Sets and Knowledge Discovery
Rough Sets, Fuzzy Sets and Knowledge Discovery
Constraint Based Incremental Learning of Classification Rules
RSCTC '00 Revised Papers from the Second International Conference on Rough Sets and Current Trends in Computing
Fundamenta Informaticae
Peculiarity Oriented Multidatabase Mining
IEEE Transactions on Knowledge and Data Engineering
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
Information Entropy and Granulation Co---Entropy of Partitions and Coverings: A Summary
Transactions on Rough Sets X
Generalized rough sets, entropy, and image ambiguity measures
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics - Special issue on human computing
Information Sciences: an International Journal
MGRS: A multi-granulation rough set
Information Sciences: an International Journal
Information-theoretic measures of uncertainty for rough sets and rough relational databases
Information Sciences: an International Journal
Fuzzy preference based rough sets
Information Sciences: an International Journal
Invertible approximation operators of generalized rough sets and fuzzy rough sets
Information Sciences: an International Journal
Reference points and roughness
Information Sciences: an International Journal
Some improved results on communication between information systems
Information Sciences: an International Journal
Hybrid approaches to attribute reduction based on indiscernibility and discernibility relation
International Journal of Approximate Reasoning
Modeling rough granular computing based on approximation spaces
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
A comparative study of rough sets for hybrid data
Information Sciences: an International Journal
Generalized approximations defined by non-equivalence relations
Information Sciences: an International Journal
Employing rough sets and association rule mining in KANSEI knowledge extraction
Information Sciences: an International Journal
Entropy and co-entropy of a covering approximation space
International Journal of Approximate Reasoning
A parallel method for computing rough set approximations
Information Sciences: an International Journal
Rough set theory applied to lattice theory
Information Sciences: an International Journal
Covering based rough set approximations
Information Sciences: an International Journal
A measurement theory view on the granularity of partitions
Information Sciences: an International Journal
An Axiomatic Approach to the Roughness Measure of Rough Sets
Fundamenta Informaticae
An Improved Axiomatic Definition of Information Granulation
Fundamenta Informaticae
A measurement theory view on the granularity of partitions
Information Sciences: an International Journal
Using one axiom to characterize rough set and fuzzy rough set approximations
Information Sciences: an International Journal
Entropy measures and granularity measures for set-valued information systems
Information Sciences: an International Journal
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In rough set theory, some information-theoretic measures of uncertainty and granularity have been proposed. A common feature of these measures is that they are only dependent on the partitions and the cardinality of a universe, which means that they are independent of the lower and upper approximations of rough sets. This seems somewhat unreasonable since the basic idea of rough set theory is to describe incomplete or inexact concepts by the lower and upper approximations. In light of this, we develop a new pair of information-theoretic entropy and co-entropy functions associated to partitions and approximations in this paper. Such functions are used to measure the uncertainty and granularity of an approximation space. After introducing the novel notions of entropy and co-entropy, we then examine their properties. In particular, we disclose the relationship of co-entropies between different universes. The theoretical development is accompanied by illustrative numerical examples.