Abstract
The current state of the universe is shifting towards multi-polarity, a well-established phenomenon that plays a crucial role across various scientific and technological fields, particularly in information and data domains. In this study, we propose the concept of m-polar quadripartitioned neutrosophic sets and explore their graphical representations, presenting key findings. We introduce novel operations on m-polar quadripartitioned neutrosophic graphs, such as the strong product and direct product. Additionally, we discuss concepts like complement, homomorphism, isomorphism, weak and co-weak isomorphism within the context of m-polar neutrosophic graphs. Furthermore, we elucidate several associated properties and theorems concerning m-polar quadripartitioned neutrosophic graphs. Finally, we demonstrate the practical application of our findings in a supply chain management model.



Similar content being viewed by others
Data availability statement
Not applicable.
References
Akram, M., Waseem, N.: Certain metrics in \(m\)-polar fuzzy graphs. New Math. Nat. Comput. 12(02), 135–155 (2016)
Akram, M., Cecco, D.: \(m\)-Polar Fuzzy Graphs. Springer International Publishing, Cham (2019)
Akram, M., Shahzadi, G.: Operations on single-valued neutrosophic graphs. Uncertain Syst. 11(1), 1–26 (2017)
Belnap, N.D: A useful four-valued logic. In: Modern Uses of Multiple-Valued Logic. Springer. Dordrecht (1977)
Biswas, G., Garai, T., Santra, U.: A possibility-based multi-criteria decision-making approach for artificial recharge structure selection using pentagonal fuzzy numbers. Decis. Anal. 9, 100365 (2023)
Broumi, S., Smarandache, F., Talea, M., Bakali.: “Single-valued neutrosophic graphs: degree, Order and Size. In IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) (2016)
Broumi, S., Mohamed, T., Assia, M., Smarandache, F.: Single-valued neutrosophic graphs. J. New Theory. 10, 86–101 (2016)
Chatterjee, R., Majumdar, P., Samanta, S.K.: On some similarity measures and entropy on quadripartitioned single valued neutrosophic sets. J. Intell. Fuzzy Syst 30(4), 2475–2485 (2016)
Deli, I., Broumi, S.: Neutrosophic soft relations and some properties. AFMI 9(1), 169–182 (2014)
Garai, T., Garg, H., Biswas, G.: Possibilistic index-based multi-criteria decision-making with an unknown weight of air pollution model under bipolar fuzzy environment. Soft Comput. 27(23), 17991–18009 (2023)
Garai, T., Garg, H.: Possibilistic multiattribute decision making for water resource management problem under single valued bipolar neutrosophic environment. Int. J. Intell. Syst. 37(8), 5031–5058 (2022)
Garai, T., Garg, H.: Multi-criteria decision making of water resource management problem (in Agriculture field, Purulia district) based on possibility measures under generalized single valued non-linear bipolar neutrosophic environment. Expert Syst. Appl. 205, 117715 (2022)
Garai, T., Biswas, G., Santra, U.: A novel MCDM method based on possibility mean and its application to water resource management problem under bipolar fuzzy environment. In International Conference on Intelligent and Fuzzy Systems, pp. 405–412, Springer International Publishing, Cham (2022)
Ghorai, G., Pal, M.: Some properties of \(m\)-polar fuzzy graphs. Pac. Sci. Rev. A: Nat. Sci. Eng. 18(1), 38–46 (2016)
Hashmi, M.R., Riaz, M., Smarandache, F.: m-Polar neutrosophic topology with applications to multi-criteria decision-making in medical diagnosis and clustering analysis. Int. J. Fuzzy Syst. 22(1), 273–292 (2020)
Hassan, A., Malik, M.A.: \(m\)-polar neutrosophic graphs. TWMS J. App. Eng. Math. 11(3), 659–680 (2021)
Hussain, S.S., Durga, N., Hossein, R., Ganesh, G., Oscar, C.: New concepts on quadripartitioned single-valued neutrosophic graph with real-life application. Int. J. Fuzzy Syst. 24(3), 1515–1529 (2022)
Hussain, S.S., Muhiuddin, G., Durga, N., Al-Kadi, D.: New concepts on quadripartitioned bipolar single valued neutrosophic graph. CMES Comput. Model. 130(1), 559–580 (2022)
Hussain, S.S., Hussain, J., Rosyida, I., Broumi, S.: Quadripartitioned neutrosophic soft graphs. In Handbook of Research on Advances and Applications of Fuzzy Sets and Logi. pp. 771–795 (2022). IGI Global
Hussain, S.S., Rosyida, I., Rashmanlou, H., Mofidnakhaei, F.: Interval intuitionistic neutrosophic sets with its applications to interval intuitionistic neutrosophic graphs and climatic analysis. Comput. Appl. Math. 40(4), 1–20 (2022)
Karadayi-Usta, S.: A novel neutrosophic set based hierarchical challenge analysis approach for servicizing business models: a case study of car share service network. Comput. Ind. Eng. 163, 107795 (2022)
Mohanta, K., Dey, A., Pal, A., Long, H.V., Son, L.H.: A study of \(m\)-polar neutrosophic graph with applications. J. Intell. Inf. Syst 38(4), 4809–4828 (2020)
Naeem, K., Divvaz, B.: Information measures for MADM under \(m\)-polar neutrosophic environment. Granul. Comput 8(3), 597–616 (2023)
Roy, S., Lee, J.G., Pal, A., Samanta, S.K.: Similarity measures of quadripartitioned single valued bipolar neutrosophic sets and its application in multi-criteria decision making problems. Symmetry 12(6), 1012 (2020)
Riaz, M., Almalki, Y., Batool, S., Tanveer, S.: Topological structure of single-valued neutrosophic hesitant fuzzy sets and data analysis for uncertain supply chains. Symmetry 14(7), 1382 (2022)
Saeed, M., Saqlain, M., Mehmood, A.: Application of similarity measure on m-polar interval-valued neutrosophic set in decision making in sports. Infinite Study, vol. 38 (2020)
Saeed, M., Basit, A.M., Rahman, A.U., Yasir, H.M.: A multi-attribute decision making context for supply chain management using possibility single-valued neutrosophic soft settings. Yugosl. J. Oper. Res. 00, 33–33 (2024)
Shao, Z., Kosari, S., Rashmanlou, H., Shoaib, M.: New concepts in intuitionistic fuzzy graph with application in water supplier systems. Mathematics 8, 1241 (2020)
Smarandache, F.: A Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set and Logic, Rehoboth: American Research Press, (1999). ISBN 9781599738925
Smarandache, F.: \(n-\)valued Refined Neutrosophic Logic and its Applications to Physics. arXiv (2014), arXiv:1407.1041
Smarandache, F.: “Neutrosophic Graphs, in his Book Symbolic Neutrosophic Theory. Europa, Nova (2015)
Wang, H., Smarandache, F., Zhang, Y., Sunderraman, R.: Single-valued neutrosophic sets. Multispace and Multistructure. 4, 410–413 (2010)
Zulqarnain, R.M., Siddique, I., Iampan, A., Bonyah, E.: Algorithms for Multipolar Interval-Valued Neutrosophic Soft Set with Information Measures to Solve Multicriteria Decision-Making Problem. COMPUT INTEL NEUROSC, 7211399 (2021)
Acknowledgements
The authors would like to thank the anonymous reviewer and editor for improving the quality of this paper.
Funding
No funding.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no Conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Satham Hussain, S., Nagarajan, D., Rashmanlou, H. et al. Novel supply chain decision making model under m-polar quadripartitioned neutrosophic environment. J. Appl. Math. Comput. 71, 1051–1076 (2025). https://doi.org/10.1007/s12190-024-02256-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12190-024-02256-4
Keywords
- m-polar quadripartitioned neutrosophic set
- m-polar quadripartitioned neutrosophic graph
- m-polar quadripartitioned neutrosophic topology
- m-polar quadripartitioned neutrosophic products
- Supply chain management