Several rough set models in quotient space

ROUGH SET OVER DUAL-UNIVERSES IN FUZZY APPROXIMATION SPACE

To tackle the problem with inexact, uncertainty and vague knowl- edge, constructive method is utilized to formulate lower and upper approx- imation sets. Rough set model over dual-universes in fuzzy approximation space is constructed. In this paper, we introduce the concept of rough set over dual-universes in fuzzy approximation space by means of cut set. Then, we discuss properties of rough se...

Generalized Rough Set Models

Decision-Theoretic Rough Set Models

Decision-theoretic rough set models are a probabilistic extension of the algebraic rough set model. The required parameters for defining probabilistic lower and upper approximations are calculated based on more familiar notions of costs (risks) through the well-known Bayesian decision procedure. We review and revisit the decision-theoretic models and present new results. It is shown that we nee...

1 a Review of Rough Set Models

Since introduction of the theory of rough set in early eighties, considerable work has been done on the development and application of this new theory. The paper provides a review of the Pawlak rough set model and its extensions, with emphasis on the formulation, characterization, and interpretation of various rough set models.

Four Quotient Set Gems

Our aim in this note is to present four remarkable facts about quotient sets. These observations seem to have been overlooked by the MONTHLY, despite its intense coverage of quotient sets over the years. Introduction If A is a subset of the natural numbers N = {1, 2, . . .}, then we let R(A) = {a/a : a, a ∈ A} denote the corresponding quotient set (sometimes called a ratio set). Our aim in this...