Some properties of the interval quadripartitioned neutrosophic sets
Some properties of the interval quadripartitioned neutrosophic sets
DOI:
https://doi.org/10.5269/bspm.77944Abstract
The Interval Quadripartitioned Neutrosophic Set (IQNS) is the combination of the quadripartitioned neutrosophic set and interval neutrosophic set. IQNS plays an important role as a mathematical tool to deal with real-life problems involving uncertainty and indeterminacy. We define some set-theoretic operations of IQNSs namely, the symmetric difference and prove some of their properties. We also define the convexity criteria of IQNSs and explore their properties.
References
References
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Rehoboth: American Research Press.
[2] Wang, H., Smarandache, F., Zhang, Y., & Sunderraman, R. (2010). Single valued neutrosophic sets. Review
of Air Force Academy, 1, 10-14.
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[6] Mallick, R., & Pramanik, S. (2020). Pentapartitioned neutrosophic set and its properties. Neutrosophic
Sets and Systems, 36, 184-192.
Ullaskar Bag, and Surapati Paramanik, Some properties of the interval quadripartitioned
neutrosophic sets
Bol. Soc. Paran. Mat., Vol. xx, 20xx 15 of 15
[7] Wang, H., Madiraju, P., Zhang, Y. Q., & Sunderraman, R. (2005). Interval neutrosophic sets. International
Journal of Applied Mathematics & Statistics, 3, 1-18.
[8] Pramanik, S. (2022). Interval quadripartitioned neutrosophic sets. Neutrosophic Sets and Systems, 51,
2022, 146-156 .
[9] Pramanik, S. (2023). Interval pentapartitioned neutrosophic sets. Neutrosophic Sets and Systems, 55, 232-
246.
[10] Broumi, S., Bakali, A., Talea, M., Smarandache, F., Ulucay, V., Sahin, S., Dey, A., Dhar, M., Tan, R. P.,
de Oliveira, A., & Pramanik, S. (2018). Neutrosophic sets: An overview. In F. Smarandache, S. Pramanik
(Edn., vol.2), New trends in neutrosophic theory and applications (pp.403-434). Brussels: Pons Editions.
[11] Smarandache, F. & Pramanik, S. (Eds.). (2016). New trends in neutrosophic theory and applications.
Brussels: Pons Editions.
[12] Smarandache, F. & Pramanik, S. (Eds.). (2018). New trends in neutrosophic theory and application (Vol.2).
Brussels: Pons Editions.
[13] Pramanik, S., Mallick, R., & Dasgupta, A. (2018). Contributions of selected Indian researchs to
multi-attribute decision making in neutrosophic environment. Neutrosophic Sets and Systems, 20, 108-
131.http://doi.org/10.5281/zenodo.1284870
[14] Khan, M., Son, L. H., Ali, M., Chau, H. T. M., Na, N. T. N., & Smarandache, F. (2018). Systematic review
of decision making algorithms in extended neutrosophic Sets. Symmetry, 10(8), 314.
[15] Peng, X., & Dai, J. (2020). A bibliometric analysis of neutrosophic sets: Two decades review from 1998 to
2017. Artificial Intelligence Review, 53(1), 199-255.
[16] Pramanik, S. (2022). Single-valued neutrosophic sets: An overview . In: N. Rezaei (Eds.) Transdiciplinarity.
Integrated Science, vol 5(pp.563-608). Springer, Cham.
[17] Pramanik, S. (2020). Rough neutrosophic set: An overview. In F. Smarandache, & S. Broumi(Eds.),
Neutrosophic theories in communication, management and information technology (pp.275-311). New York.
Nova Science Publishers.
[1] Smarandache, F. (1986). A unifying field in logics, Neutrosophy: Neutrosophic probability, set and logic.
Rehoboth: American Research Press.
[2] Wang, H., Smarandache, F., Zhang, Y., & Sunderraman, R. (2010). Single valued neutrosophic sets. Review
of Air Force Academy, 1, 10-14.
[3] Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 5, 338-353.
[4] Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and System, 20(1), 87-96.
[5] Chatterjee, R., Majumder, P., & Samanta, S. K.(2016). On some similarity measures and entropy on
quadripartitioned single valued neutrosophic sets Journal of Intelligent & Fuzzy Systems, 30(4), 2475-2485.
[6] Mallick, R., & Pramanik, S. (2020). Pentapartitioned neutrosophic set and its properties. Neutrosophic
Sets and Systems, 36, 184-192.
Ullaskar Bag, and Surapati Paramanik, Some properties of the interval quadripartitioned
neutrosophic sets
Bol. Soc. Paran. Mat., Vol. xx, 20xx 15 of 15
[7] Wang, H., Madiraju, P., Zhang, Y. Q., & Sunderraman, R. (2005). Interval neutrosophic sets. International
Journal of Applied Mathematics & Statistics, 3, 1-18.
[8] Pramanik, S. (2022). Interval quadripartitioned neutrosophic sets. Neutrosophic Sets and Systems, 51,
2022, 146-156 .
[9] Pramanik, S. (2023). Interval pentapartitioned neutrosophic sets. Neutrosophic Sets and Systems, 55, 232-
246.
[10] Broumi, S., Bakali, A., Talea, M., Smarandache, F., Ulucay, V., Sahin, S., Dey, A., Dhar, M., Tan, R. P.,
de Oliveira, A., & Pramanik, S. (2018). Neutrosophic sets: An overview. In F. Smarandache, S. Pramanik
(Edn., vol.2), New trends in neutrosophic theory and applications (pp.403-434). Brussels: Pons Editions.
[11] Smarandache, F. & Pramanik, S. (Eds.). (2016). New trends in neutrosophic theory and applications.
Brussels: Pons Editions.
[12] Smarandache, F. & Pramanik, S. (Eds.). (2018). New trends in neutrosophic theory and application (Vol.2).
Brussels: Pons Editions.
[13] Pramanik, S., Mallick, R., & Dasgupta, A. (2018). Contributions of selected Indian researchs to
multi-attribute decision making in neutrosophic environment. Neutrosophic Sets and Systems, 20, 108-
131.http://doi.org/10.5281/zenodo.1284870
[14] Khan, M., Son, L. H., Ali, M., Chau, H. T. M., Na, N. T. N., & Smarandache, F. (2018). Systematic review
of decision making algorithms in extended neutrosophic Sets. Symmetry, 10(8), 314.
[15] Peng, X., & Dai, J. (2020). A bibliometric analysis of neutrosophic sets: Two decades review from 1998 to
2017. Artificial Intelligence Review, 53(1), 199-255.
[16] Pramanik, S. (2022). Single-valued neutrosophic sets: An overview . In: N. Rezaei (Eds.) Transdiciplinarity.
Integrated Science, vol 5(pp.563-608). Springer, Cham.
[17] Pramanik, S. (2020). Rough neutrosophic set: An overview. In F. Smarandache, & S. Broumi(Eds.),
Neutrosophic theories in communication, management and information technology (pp.275-311). New York.
Nova Science Publishers.
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Published
2026-04-17
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Conf. Issue: Global Assembly for Mathematical Modeling and Analysis
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