The Cubic Bipolar Neutrosophic Sets theory and Uncertainty Management in Environmental Data Analysis

Environmental data analysis often faces uncertainties in measurements. Cubic Bipolar 
Neutrosophic Sets (CBN Sets) provide a powerful framework to address this challenge. This paper 
explores the mathematical foundations of CBN Sets and highlights their practical applications 
through illustrative examples. We demonstrate how CBN Sets effectively capture varying degrees of 
certainty, possibility, and impermanence in environmental parameters. The concept of inclusion 
relations facilitates comparisons and information fusion. Fundamental set operations (intersection, 
union, complement) are explored for manipulating and analyzing uncertain environmental data. We 
present the application of CBN Sets in water quality assessment, highlighting their ability to analyze 
parameters while accounting for measurement uncertainties. The potential for air quality monitoring 
using CBN Sets is also discussed. Finally, distance measures and similarity coefficients are introduced 
to quantify relationships between air quality characteristics from different stations. By leveraging 
CBN Sets and their associated operations, researchers can gain a more nuanced understanding of 
environmental data, enabling informed decision-making for a healthier planet.