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.