A Note on q-Fractional Neutrosophic Sets and Graphs

Takaaki; Ajoy Kanti; Suman; Sankar Prasad

doi:https://doi.org/10.54216/GJMSA.130204

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Volume 13 • Issue 2 • PP: 17–24 • 2026

A Note on q-Fractional Neutrosophic Sets and Graphs

Takaaki Fujita ^1*

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,

Ajoy Kanti Das ²

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,

Suman Das ³

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,

Sankar Prasad Mondal ⁴

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¹Independent Researcher, Tokyo, Japan

²Department of Mathematics, Tripura University, Agartala-799022, Tripura, India

³Department of Education, National Institute of Technology Calicut, Kozhikode-673601, Kerala, India

⁴Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, Haringhata-741249, West Bengal, India

* Corresponding Author.

DOI https://doi.org/10.54216/GJMSA.130204

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Received: October 07, 2025 Revised: December 10, 2025 Accepted: January 08, 2026

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Abstract

A neutrosophic set assigns to each element three (generally independent) degrees: truth, indeterminacy, and falsity. A q-fractional fuzzy set assigns membership and nonmembership degrees in [0,1] to each element, constrained by (μ +ν)/q ≤ 1 for q ≥ 2. A q-fractional fuzzy graph is a graph whose vertices and edges carry q-fractional fuzzy degrees, with edge membership bounded by endpoints and edge nonmembership dominating them. In this paper, we introduce q-fractional neutrosophic sets and graphs as an extension of q-fractional fuzzy sets and q-fractional fuzzy graphs, and we investigate their fundamental properties.

Keywords

Neutrosophic Graph q-fractional fuzzy set q-fractional fuzzy graph

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Fujita, Takaaki, Das, Ajoy Kanti, Das, Suman, Mondal, Sankar Prasad. "A Note on q-Fractional Neutrosophic Sets and Graphs." Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 13, no. Issue 2, 2026, pp. 17–24. DOI: https://doi.org/10.54216/GJMSA.130204

Fujita, T., Das, A., Das, S., Mondal, S. (2026). A Note on q-Fractional Neutrosophic Sets and Graphs. Galoitica: Journal of Mathematical Structures and Applications, Volume 13(Issue 2), 17–24. DOI: https://doi.org/10.54216/GJMSA.130204

Fujita, Takaaki, Das, Ajoy Kanti, Das, Suman, Mondal, Sankar Prasad. "A Note on q-Fractional Neutrosophic Sets and Graphs." Galoitica: Journal of Mathematical Structures and Applications Volume 13, no. Issue 2 (2026): 17–24. DOI: https://doi.org/10.54216/GJMSA.130204

Fujita, T., Das, A., Das, S., Mondal, S. (2026) 'A Note on q-Fractional Neutrosophic Sets and Graphs', Galoitica: Journal of Mathematical Structures and Applications, Volume 13(Issue 2), pp. 17–24. DOI: https://doi.org/10.54216/GJMSA.130204

Fujita T, Das A, Das S, Mondal S. A Note on q-Fractional Neutrosophic Sets and Graphs. Galoitica: Journal of Mathematical Structures and Applications. 2026;Volume 13(Issue 2):17–24. DOI: https://doi.org/10.54216/GJMSA.130204

T. Fujita, A. Das, S. Das, S. Mondal, "A Note on q-Fractional Neutrosophic Sets and Graphs," Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 13, no. Issue 2, pp. 17–24, 2026. DOI: https://doi.org/10.54216/GJMSA.130204

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