B-Boundary in Pythagorean Neutrosophic Fuzzy

Mathematics

In this paper, we explore the structure and behavior of Pythagorean Neutrosophic Fuzzy Topological Spaces (PNFTS), which generalize and fuzzy topologies by incorporating the concepts of indeterminacy and hesitation though the Neutrosophic and Pythagorean frameworks. We introduce and study the concept of b-boundary within this context and investigate its fundamental properties. The b-boundary operator plays a critical role in describing the topological boundaries of sets in uncertain environments and offers a deeper understanding of topological separation in neutrosophic fuzzy space. We provide a set of examples to illustrate and validate the theoretical findings. Furthermore, we examine several theorems related to the behavior of b-boundaries under various set operations. The results obtained demonstrate that the b-boundary in Pythagorean Neutrosophic Fuzzy topological space maintains desirable topological characteristics while offering greater flexibility in dealing with imprecise, vague, or inconsistent information. This work not only extends existing topological concepts to the neutrosophic domain but also opens the door to future application in areas where uncertainty and indeterminacy.

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