A Python Framework Enhancement for Neutrosophic Topologies

TL;DR

This paper enhances the Python Neutrosophic Sets framework by adding a class for constructing and analyzing neutrosophic topologies, enabling automated topology generation and verification within neutrosophic modeling.

Contribution

Introduction of the NSfamily class in PYNS for constructing and testing neutrosophic topologies, expanding the framework's capabilities for neutrosophic topology research.

Findings

Automated generation of neutrosophic topologies from families of sets

Verification of closure properties under union and intersection

Practical examples demonstrating enhanced modeling capabilities

Abstract

This paper introduces an extension to the Python Neutrosophic Sets (PYNS) framework, originally detailed in Nordo et al. 2024, with the addition of the NSfamily class for constructing and manipulating neutrosophic topologies. Building on existing classes like NSuniverse and NSset, the NSfamily class enables the definition and testing of neutrosophic families as basis and sub-basis for neutrosophic topological spaces. This extension provides tools for verifying closure properties under union and intersection, and for determining whether a given family constitutes a neutrosophic topology. Through implemented algorithms, the framework automates the generation of topologies from families of neutrosophic sets, offering an efficient tool for advancing research in neutrosophic topology. Practical applications are demonstrated with detailed examples, showcasing how this class enhances the scope and flexibility of neutrosophic modeling within the PYNS framework.