Rough set theory and its Applications: Course Outline (MAT 618)
Rough set theory proposes a new mathematical approach to imperfect. knowledge, i.e. to vagueness (or imprecision). In this approach, vagueness is expressed by a boundary region of a set.
Course Outline
 Introduction to the course
 Basic knowledge about different types of binary relations
 Equivalence classes and equivalence relations
 Knowledge and classification knowledge base
 Rough sets, approximations of the set
 Properties of approximations
 Approximations and membership relation
 Numerical characterization of imprecision
 Topological characterization of imprecision
 Approximation of classifications
 Rough equality and rough inclusion of sets
 Reduct and core of knowledge
 Relative reduct and relative core
 Reduction of categories
 Relative reduct and core of categories
 Dependencies in knowledge: Dependency of knowledge
 Partial dependency of knowledge
 Significance of attributes and discernibility matrix
 Applications of Rough sets in Algebra: roughness in Rings
 Generalizations of rough set: Rough sets with covers
 Rough sets based on similarity and tolerance relations
Text Books
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