Relational interpretations of neighborhood operators and rough set approximation operators
Information Sciences—Informatics and Computer Science: 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
Information Sciences—Informatics and Computer Science: An International Journal
Reduction and axiomization of covering generalized rough sets
Information Sciences: an International Journal
An axiomatic characterization of a fuzzy generalization of rough sets
Information Sciences—Informatics and Computer Science: An International Journal
Topological approaches to covering rough sets
Information Sciences: an International Journal
On Three Types of Covering-Based Rough Sets
IEEE Transactions on Knowledge and Data Engineering
Transformation of rough set models
Knowledge-Based Systems
The algebraic structures of generalized rough set theory
Information Sciences: an International Journal
Formal reasoning with rough sets in multiple-source approximation systems
International Journal of Approximate Reasoning
Comparison between different kinds of approximations by using a family of binary relations
Knowledge-Based Systems
Knowledge structure, knowledge granulation and knowledge distance in a knowledge base
International Journal of Approximate Reasoning
MGRS: A multi-granulation rough set
Information Sciences: an International Journal
On the topological properties of fuzzy rough sets
Fuzzy Sets and Systems
Constructive and algebraic methods of the theory of rough sets
Information Sciences: an International Journal
On the structure of generalized rough sets
Information Sciences: an International Journal
Rough set theory based on two universal sets and its applications
Knowledge-Based Systems
Positive approximation: An accelerator for attribute reduction in rough set theory
Artificial Intelligence
Covering rough sets based on neighborhoods: An approach without using neighborhoods
International Journal of Approximate Reasoning
Fuzzy rough set based attribute reduction for information systems with fuzzy decisions
Knowledge-Based Systems
Neighborhood systems-based rough sets in incomplete information system
Knowledge-Based Systems
Topological properties of generalized approximation spaces
Information Sciences: an International Journal
Multi knowledge based rough approximations and applications
Knowledge-Based Systems
Transformation of bipolar fuzzy rough set models
Knowledge-Based Systems
Incomplete Multigranulation Rough Set
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
An Investigation About Rough Set Theory: Some Foundational and Mathematical Aspects
Fundamenta Informaticae - Advances in Rough Set Theory
Tolerance Approximation Spaces
Fundamenta Informaticae
Multigranulation rough sets: From partition to covering
Information Sciences: an International Journal
Multigranulation decision-theoretic rough sets
International Journal of Approximate Reasoning
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The original rough set model, i.e., Pawlak's single-granulation rough set model has been extended to a multigranulation rough set model, where two kinds of multigranulation approximations, i.e., the optimistic and pessimistic approximations were introduced. In this paper, we consider some fundamental properties of the multigranulation rough set model, and show that (i)Both the collection of lower definable sets and that of upper definable sets in the optimistic multigranulation rough set model can form a lattice, such lattices are not distributive, not complemented and pseudo-complemented in the general case. The collection of definable sets in the optimistic multigranulation rough set model does not even form a lattice in general conditions. (ii)The collection of (lower, upper) definable sets in the optimistic multigranulation rough set model forms a topology on the universe if and only the optimistic multigranulation rough set model is equivalent to Pawlak's single-granulation rough set model. (iii)In the context of the pessimistic multigranulation rough set model, the collections of three different kinds of definable sets coincide with each other, and they determine a clopen topology on the universe, furthermore, they form a Boolean algebra under the usual set-theoretic operations.