Some properties of the interval quadripartitioned neutrosophic sets
Some properties of the interval quadripartitioned neutrosophic sets
Résumé
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.
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Références
References
[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.
[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.
Publiée
2026-04-17
Rubrique
Special Issue: Global Assembly for Mathematical Modeling and Analysis
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