Dual Mathematical Models Based on Rough Approximations

Rough Approximations on Preordered Sets

In this paper, we investigate the properties of rough approximations defined by preordered sets. We study the relations among the lower and upper rough approximations, closure and interior systems, and closure and interior operators.

Exponential Models: Approximations for Probabilities

Welch & Peers (1963) used a root-information prior to obtain posterior probabilities for a scalar parameter exponential model and showed that these Bayes probabilities had the confidence property to second order asymptotically. An important undercurrent of this indicates that the constant information reparameterization provides location model structure, for which the confidence property ...

A Uniform Framework for Rough Approximations Based on Generalized Quantifiers

Concept Approximations Based on Rough Sets and Similarity Measures

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...

On the Structure of Rough Approximations

We study rough approximations based on indiscernibility relations which are not necessarily reflexive, symmetric or transitive. For this, we define in a lattice-theoretical setting two maps which mimic the rough approximation operators and note that this setting is suitable also for other operators based on binary relations. Properties of the ordered sets of the upper and the lower approximatio...