In modeling multiagent systems for real-life problems, techniques for approximate reasoning about vague concepts and dependencies (ARVCD) are necessary. We discuss an approach to approximate reasoning based on rough sets. In particular, we present a number of basic concepts such as approximation spaces, concept approximation, rough inclusion, construction of information granules in calculi of i...

The approximation space definition has evolved in rough set theory over the last 15 years. The aim was to build a unified framework for concept approximations. We present an overview of this evolution together with some operations on approximation spaces that are used in searching for relevant approximation spaces. Among such operations are inductive extensions and granulations of approximation...

The formal concept analysis gives a mathematical definition of a formal concept. However, in many real-life applications, the problem under investigation cannot be described by formal concepts. Such concepts are called the non-definable concepts (Saquer and Deogun, 2000a). The process of finding formal concepts that best describe non-definable concepts is called the concept approximation. In th...

We consider linear divergence-form scalar elliptic equations and vectorial equations for elasticity with rough (L∞(Ω), Ω ⊂ R) coefficients a(x) that, in particular, model media with non-separated scales and high contrast in material properties. While the homogenization of PDEs with periodic or ergodic coefficients and well separated scales is now well understood, we consider here the most gener...

We consider linear divergence-form scalar elliptic equations and vectorial equations for elasticity with rough (L ∞ (Ω), Ω ⊂ R d) coefficients a(x) that, in particular, model media with non-separated scales and high contrast in material properties. While the homogenization of PDEs with periodic or ergodic coefficients and well separated scales is now well understood, we consider here the most g...

We consider divergence-form scalar elliptic equations and vectorial equations for elasticity with rough (L ∞ (Ω), Ω ⊂ R d) coefficients a(x) that, in particular, model media with non-separated scales and high contrast in material properties. While the homogenization of PDEs with periodic or ergodic coefficients and well separated scales is now well understood, we consider here the most general ...

We present eecient techniques for the numerical approximation of complicated dynamical behavior. In particular, we develop numerical methods which allow to approximate SBR-measures as well as (almost) cyclic behavior of a dynamical system. The methods are based on an appropriate discretization of the Frobenius-Perron operator, and two essentially diierent mathematical concepts are used: the ide...