Approximation by filter functions

TL;DR

This paper explores a unifying framework for various estimators like belief functions, rough set approximation, and contextual probability using general filter functions, supported by a simulation study in item response theory.

Contribution

It introduces a general filter function framework that unifies different estimators and compares them through simulation, highlighting their common formal ground.

Findings

Filter functions can unify diverse estimators

Simulation demonstrates the framework's applicability

Comparison reveals similarities among methods

Abstract

In this exploratory article, we draw attention to the common formal ground among various estimators such as the belief functions of evidence theory and their relatives, approximation quality of rough set theory, and contextual probability. The unifying concept will be a general filter function composed of a basic probability and a weighting which varies according to the problem at hand. To compare the various filter functions we conclude with a simulation study with an example from the area of item response theory.