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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



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