Discrete mathematics for computer science
Discrete mathematics for computer science
Tolerance approximation spaces
Fundamenta Informaticae - Special issue: rough sets
Relational interpretations of neighborhood operators and rough set approximation operators
Information Sciences—Informatics and Computer Science: An International Journal
Optimizations of rough set model
Fundamenta Informaticae
Rough set approach to incomplete information systems
Information Sciences: 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
A New Rough Set Approach to Multicriteria and Multiattribute Classification
RSCTC '98 Proceedings of the First International Conference on Rough Sets and Current Trends in Computing
RSFDGrC '99 Proceedings of the 7th International Workshop on New Directions in Rough Sets, Data Mining, and Granular-Soft Computing
Reduction and axiomization of covering generalized rough sets
Information Sciences: an International Journal
Dominance relation and rules in an incomplete ordered information system
International Journal of Intelligent Systems
Information-preserving hybrid data reduction based on fuzzy-rough techniques
Pattern Recognition Letters
Topological approaches to covering rough sets
Information Sciences: an International Journal
Expert Systems with Applications: An International Journal
Similarity, Boolean Reasoning and Rule Induction
IITA '08 Proceedings of the 2008 Second International Symposium on Intelligent Information Technology Application - Volume 01
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
Information Sciences: an International Journal
Distance: A more comprehensible perspective for measures in rough set theory
Knowledge-Based Systems
Dominance-based rough set model in intuitionistic fuzzy information systems
Knowledge-Based Systems
Graded rough set model based on two universes and its properties
Knowledge-Based Systems
On interval type-2 rough fuzzy sets
Knowledge-Based Systems
On the structure of the multigranulation rough set model
Knowledge-Based Systems
A novel soft set approach in selecting clustering attribute
Knowledge-Based Systems
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Rough sets theory has proved to be a useful mathematical tool for dealing with the vagueness and granularity in information tables. Classical definitions of lower and upper approximations were originally introduced with reference to an indiscernibility relation. However, indiscernibility relation is still restrictive for many applications. Many real-world problems deal with assignment of some objects to some preference-ordered decision classes. And, the objects are described by a finite set of qualitative attributes and quantitative attributes. In this paper, we construct the indiscernibility relation for the subset of nominal attributes, the outranking relation for the subset of ordinal attributes, and the similarity relation for the subset of quantitative attributes. Then the global binary relation is generated by the intersection of indiscernibility relation, outranking relation and similarity relation. New definitions of lower and upper approximations of the upward and downward unions of decision classes are proposed based on the global relation. We also prove that the lower and upper approximation operations satisfy the properties of rough inclusion, complementarity, identity of boundaries, and monotonicity.