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Title: :  B-Boundary in Pythagorean Neutrosophic Fuzzy
PaperId: :  27097
Published in:   International Journal Of Advance Research And Innovative Ideas In Education
Publisher:   IJARIIE
e-ISSN:   2395-4396
Volume/Issue:    Volume 11 Issue 4 2025
DUI:    16.0415/IJARIIE-27097
Licence: :   IJARIIE is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Author NameAuthor Institute
Ameerah Abu SurrahAbu-Isa Faculty of Education, Zawia University
Fatimah AlhawuyilAbu-Isa Faculty of Education, Zawia University

Abstract

Mathematics
Pythagorean Neutrosophic Sets, Pythagorean Neutrosophic Fuzzy Topological Spaces, b-Boundary in Pythagorean Neutrosophic Fuzzy topological space
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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IJARIIE Ameerah Abu Surrah, and Fatimah Alhawuyil. "B-Boundary in Pythagorean Neutrosophic Fuzzy" International Journal Of Advance Research And Innovative Ideas In Education Volume 11 Issue 4 2025 Page 614-618
MLA Ameerah Abu Surrah, and Fatimah Alhawuyil. "B-Boundary in Pythagorean Neutrosophic Fuzzy." International Journal Of Advance Research And Innovative Ideas In Education 11.4(2025) : 614-618.
APA Ameerah Abu Surrah, & Fatimah Alhawuyil. (2025). B-Boundary in Pythagorean Neutrosophic Fuzzy. International Journal Of Advance Research And Innovative Ideas In Education, 11(4), 614-618.
Chicago Ameerah Abu Surrah, and Fatimah Alhawuyil. "B-Boundary in Pythagorean Neutrosophic Fuzzy." International Journal Of Advance Research And Innovative Ideas In Education 11, no. 4 (2025) : 614-618.
Oxford Ameerah Abu Surrah, and Fatimah Alhawuyil. 'B-Boundary in Pythagorean Neutrosophic Fuzzy', International Journal Of Advance Research And Innovative Ideas In Education, vol. 11, no. 4, 2025, p. 614-618. Available from IJARIIE, http://ijariie.com/AdminUploadPdf/B_Boundary_in_Pythagorean_Neutrosophic_Fuzzy_ijariie27097.pdf (Accessed : ).
Harvard Ameerah Abu Surrah, and Fatimah Alhawuyil. (2025) 'B-Boundary in Pythagorean Neutrosophic Fuzzy', International Journal Of Advance Research And Innovative Ideas In Education, 11(4), pp. 614-618IJARIIE [Online]. Available at: http://ijariie.com/AdminUploadPdf/B_Boundary_in_Pythagorean_Neutrosophic_Fuzzy_ijariie27097.pdf (Accessed : )
IEEE Ameerah Abu Surrah, and Fatimah Alhawuyil, "B-Boundary in Pythagorean Neutrosophic Fuzzy," International Journal Of Advance Research And Innovative Ideas In Education, vol. 11, no. 4, pp. 614-618, Jul-Aug 2025. [Online]. Available: http://ijariie.com/AdminUploadPdf/B_Boundary_in_Pythagorean_Neutrosophic_Fuzzy_ijariie27097.pdf [Accessed : ].
Turabian Ameerah Abu Surrah, and Fatimah Alhawuyil. "B-Boundary in Pythagorean Neutrosophic Fuzzy." International Journal Of Advance Research And Innovative Ideas In Education [Online]. volume 11 number 4 ().
Vancouver Ameerah Abu Surrah, and Fatimah Alhawuyil. B-Boundary in Pythagorean Neutrosophic Fuzzy. International Journal Of Advance Research And Innovative Ideas In Education [Internet]. 2025 [Cited : ]; 11(4) : 614-618. Available from: http://ijariie.com/AdminUploadPdf/B_Boundary_in_Pythagorean_Neutrosophic_Fuzzy_ijariie27097.pdf
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