Descriptive Unions. A Fibre Bundle Characterization of the Union of Descriptively Near Sets

TL;DR

This paper introduces a fibre bundle framework for descriptive unions of sets, establishing their properties and equivalence to set intersection, with applications in convex unions and digital image analysis.

Contribution

It presents a novel fibre bundle approach to characterize descriptive unions and their properties, extending the concept of descriptive intersection.

Findings

Descriptive unions are equivalent to set intersection under certain conditions.

The framework applies to convex unions and digital image analysis.

Four forms of descriptive unions are characterized and analyzed.

Abstract

This paper introduces an extension of descriptive intersection and provides a framework for descriptive unions of nonempty sets. Fibre bundles provide structures that characterize spatially near as well as descriptively near sets, their descriptive intersection and their unions. The properties of four different forms of descriptive unions are given. A main result given in this paper is the equivalence between ordinary set intersection and a descriptive union. Applications of descriptive unions are given with respect to Jeffs-Novik convex unions and descriptive unions in digital images.