Interval Valued Pentapartitioned Neutrosophic Graphs with an Application to MCDM
DOI:
https://doi.org/10.31181/oresta031022031bKeywords:
Neutrosophic Set; Interval valued Pentapartitioned Neutrosophic sets; Neutrosophic Graph; IVPPN-Graph.Abstract
The concept of interval valued pentapartitioned neutrosophic set is the extension of interval-valued neutrosophic set, quadripartitioned neutrosophic set, interval valued quadripartitioned neutrosophic set and pentapartitioned neutrosophic set. The powerful mathematical tool known as the interval valued pentapartitioned neutrosophic set divides indeterminacy into three separate components: unknown, contradiction, and ignorance. There are several applications for graph theory in everyday life, and it is a rapidly growing topic. The concept of an interval valued pentapartitioned neutrosophic set is used in graph theory. A decision-making method ( multicriteria, MCDM) is proposed by using the developed Interval valued Pentapartitioned Neutrosophic set with a numerical illustration. In this paper, as an extension of interval valued neutrosophic graph theory, we introduce the notions of Interval-Valued Pentapartitioned Neutrosophic Graph (IVPPN-graph) with degree, size, and order of an IVPPN-graph.
Downloads
References
Ajay, D., & Chellamani, P. (2020). Pythagorean neutrosophic fuzzy graphs. International Journal of Neutrosophic Science, 11(2), 108-114. DOI: 10.5281/zenodo.4172124
Ajay, D., & Chellamani, P. (2021). Pythagorean neutrosophic soft sets and their application to decision-making scenario. In International Conference on Intelligent and Fuzzy Systems (pp. 552-560). Springer, Cham. https://doi.org/10.1007/978-3- 030-85577-265
Ajay, D., Karthiga, S., & Chellamani, P. (2021a). A study on labelling of pythagorean neutrosophic fuzzy graphs. Journal of Computational Mathematica, 5(1), 105-116. https://doi.org/10.26524/cm97
Ajay, D., Chellamani, P., Rajchakit, G., Boonsatit, N., & Hammachukiattikul, P. (2022). Regularity of Pythagorean neutrosophic graphs with an illustration in MCDM. AIMS Mathematics, 7(5), 9424-9442. doi: 10.3934/math.2022523
Ajay, D., John Borg, S., & Chellamani, P. (2022a). Domination in Pythagorean Neutrosophic Graphs with an Application in Fuzzy Intelligent Decision Making. In International Conference on Intelligent and Fuzzy Systems (pp. 667-675). Springer, Cham. https://doi.org/10.1007/978-3-031-09176-6_74
Al-Hamido, R. K. (2022). A New Neutrosophic Algebraic Structures. Journal of Computational and Cognitive Engineering. https://doi.org/10.47852/bonviewJCCE2202213
Akram, M., & Siddique, S. (2017). Neutrosophic competition graphs with applications. Journal of Intelligent & Fuzzy Systems, 33(2), 921-935. DOI: 10.3233/JIFS-162207
Atanasov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 87-96. https://doi.org/10.1016/S0165-0114(86)80034-3
Broumi, S., Talea, M., Bakali, A., & Smarandache, F. (2016). Single valued neutrosophic graphs. Journal of New theory, (10), 86-101.
Broumi, S., Bakali, A., Talea, M., & Smarandache, F. (2016a). Isolated single valued neutrosophic graphs. Neutrosophic Sets Syst 11:74–78
Broumi, S., Smarandache, F., Talea, M., & Bakali, A. (2016b). An introduction to bipolar single valued neutrosophic graph theory. In Applied Mechanics and Materials, 841, 184-191. DOI:10.4028/www.scientific.net/AMM.841.184
Broumi, S., Talea, M., Bakali, A., & Smarandache, F. (2016c). On bipolar single valued neutrosophic graphs. Journal of New Theory, (11), 84-102.
Broumi, S., Talea, M., Bakali, A., & Smarandache, F. (2016d). Interval valued neutrosophic graphs. Critical Review, XII, 2016, 5-33.
Broumi, S., Talea, M., Bakali, A., Hassan, A., & Smarandache, F. (2017). Generalized Interval valued Neutrosophic graphs of first type. In 2017 IEEE International Conference on Innovations in Intelligent SysTems and Applications (INISTA), Gdynia Maritime University, Gdynia, Poland (Vol. 306). http://doi.org/10.5281/zenodo.888864
Chatterjee, R., Majumdar, 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. DOI: 10.3233/IFS-152017
Chatterjee, R., Majumdar, P., & Samanta, S. K. (2016a). Interval-valued Possibility Quadripartitioned Single Valued Neutrosophic Soft Sets and some uncertainty based measures on them. Neutrosophic Sets Syst Neutrosophic Sets and Systems, vol. 14, , pp. 35-43. doi.org/10.5281/zenodo.570879.
Chatterjee, R., Majumdar, P., & Samanta, S. K. (2016b). On some similarity measures and entropy on quadripartitioned single valued neutrosophic sets. Journal of Intelligent & Fuzzy Systems, 30(4), 2475-2485. DOI: 10.3233/IFS-152017
Chatterjee, R., Majumdar, P., & Samanta, S. K. (2020). A multi-criteria group decision making algorithm with quadripartitioned neutrosophic weighted aggregation operators using quadripartitioned neutrosophic numbers in IPQSVNSS environment. Soft Computing, 24(12), 8857-8880. DOI: 10.1007/s00500-019-04417-1
Chellamani, P., & Ajay, D. (2021). Pythagorean neutrosophic Dombi fuzzy graphs with an application to MCDM. Neutrosophic Sets and Systems, 47, 411-431. 10.5281/zenodo.5775162
Chellamani, P., Ajay, D., Broumi, S., & Ligori, T. (2021b). An approach to decision-making via picture fuzzy soft graphs. Granular Computing, 1-22. . https://doi.org/10.1007/s41066-021-00282-2
Das, S., Das, R., & Pramanik, S. (2022). Single valued bipolar pentapartitioned neutrosophic set and its application in MADM strategy. Neutrosophic Sets and Systems, 49, 145-163. DOI: 10.5281/zenodo.6426381
Das, S., Das, R., & Pramanik, S. (2022a). Single Valued Pentapartitioned Neutrosophic Graphs. Neutrosophic Sets and Systems, Vol. 50, pp. 225-238. DOI: 10.5281/zenodo.6774779
Das, K., Samanta, S., & De, K. (2020). Generalized neutrosophic competition graphs. Neutrosophic Sets and Systems, 31, 156-171. 10.5281/zenodo.3639608
Das, S. K., & Edalatpanah, S. A. (2020). A new ranking function of triangular neutrosophic number and its application in integer programming. International Journal of Neutrosophic Science, 4(2), 82-92. DOI: 10.5281/zenodo.3767107
Das, S., Shil, B., & Pramanik, S. (2021). SVPNS-MADM strategy based on GRA in SVPNS Environment. Neutrosophic Sets and Systems, 47, 50-65. DOI: 10.5281/zenodo.5775091
Hussain, S., Hussain, J., Rosyida, I., & Broumi, S. (2022). Quadripartitioned Neutrosophic Soft Graphs. In Handbook of Research on Advances and Applications of Fuzzy Sets and Logic (pp. 771-795). IGI Global. DOI:10.4018/978-1-7998-7979-4.ch034
Hussain, S. S., Durga, N., Hossein, R., Ganesh, G., & Oscar, C. (2022a). New Concepts on Quadripartitioned Single-Valued Neutrosophic Graph with Real-Life Application. International Journal of Fuzzy Systems, 24(3), 1515-1529. https://doi.org/10.1007/s40815-021-01205-8
Kumar, R., Edalatpanah, S. A., Jha, S., & Singh, R. (2019). A novel approach to solve gaussian valued neutrosophic shortest path problems. International Journal of Engineering and Advanced Technology, 2019, 8(3), pp. 347–353. 10.5281/zenodo.3047525
Kauffman A (1973) Introduction a la Theorie des Sous-emsembles Flous, 1, Masson et Cie.
Mao, X., Guoxi, Z., Fallah, M., & Edalatpanah, S. A. (2020). A neutrosophic-based approach in data envelopment analysis with undesirable outputs. Mathematical problems in engineering, 7626102. https://doi.org/10.1155/2020/7626102
Mohamed, S. Y., & Ali, A. M. (2020). Energy of spherical fuzzy graphs. Advances in Mathematics: Scientific Journal, 9(1), 321-332. DOI:10.37418/amsj.9.1.26
Mordeson, J. N., & Chang-Shyh, P. (1994). Operations on fuzzy graphs. Information sciences, 79(3-4), 159-170. https://doi.org/10.1016/0020-0255(94)90116-3
Mallick, R., & Pramanik, S. (2020). Pentapartitioned neutrosophic set and its properties. Neutrosophic Sets and Systems, 36, 184-192. DOI: 10.5281/zenodo.4065431
Majumder, P., Das, S., Das, R., & Tripathy, B. C. (2021). Identification of the most significant risk factor of COVID-19 in economy using cosine similarity measure under SVPNS-environment. Neutrosophic Sets and Systems, Neutrosophic Sets and Systems, vol. 46, 2021, pp. 112-127. DOI: 10.5281/zenodo.5553497
Naz, S., Rashmanlou, H., & Malik, M. A. (2017). Operations on single valued neutrosophic graphs with application. Journal of Intelligent & Fuzzy Systems, 32(3), 2137-2151. DOI: 10.3233/JIFS-161944
Naz, S., Akram, M., & Smarandache, F. (2018). Certain notions of energy in single-valued neutrosophic graphs. Axioms, 7(3), 50. https://doi.org/10.3390/axioms7030050
Pramanik, S. (2022). Interval quadripartitioned neutrosophic set, Neutrosophic Sets and Systems, 50. In press.
Polymenis, A. (2021). A neutrosophic Student’st–type of statistic for AR (1) random processes. Journal of Fuzzy Extension and Applications, 2(4), 388-393. 10.22105/JFEA.2021.287294.1149
Quek, S. G., Broumi, S., Selvachandran, G., Bakali, A., Talea, M., & Smarandache, F. (2018). Some results on the graph theory for complex neutrosophic sets. Symmetry, 10(6), 190. https://doi.org/10.3390/sym10060190
Quek, S. G., Selvachandran, G., Ajay, D., Chellamani, P., Taniar, D., Fujita, H., ... & Giang, N. L. (2022). New concepts of pentapartitioned neutrosophic graphs and applications for determining safest paths and towns in response to COVID-19. Computational and Applied Mathematics, 41(4), 1-27. https://doi.org/10.1007/s40314-022-01823-4
Radha, R., & Arul Mary, A. S. (2021). Quadripartitioned neutrosophic pythagorean lie subalgebra. Journal of Fuzzy Extension and Applications, 2(3), 283-296. https://doi.org/10.22105/jfea.2021.293069.1157
Saha, P., Majumder, P., Das, S., Das, P. K., & Tripathy, B. C. (2022). Single-valued pentapartitioned neutrosophic dice similarity measure and its application in the selection of suitable metal oxide nano-additive for biodiesel blend on environmental aspect. Neutrosophic Sets and Systems, Vol. 48, 2022, pp. 154-171, DOI: 10.5281/zenodo.6041439.
Rosenfeld, A. (1975). Fuzzy graphs. In Fuzzy Sets and Their Applications to Cognitive and Decision Processes, Zadeh, L.A., Fu, K.S., Shimura, M., Eds.; Academic Press: Cambridge, MA, USA, 77–95. . https://doi.org/10.1016/B978-0-12-775260- 0.50008-6
Smarandache, F. (2013). n-Valued refined neutrosophic logic and its applications to physics. Infinite Study, 4, 143-146. DOI: 10.5281/zenodo.49149
Smarandache, F. (1999). A unifying field in logics, neutrosophy: neutrosophic probability, set and logic. American Research Press, Rehobooth.
Smarandache, F. (2022). Plithogeny, Plithogenic Set, Logic, Probability and Statistics: A Short Review. Journal of Computational and Cognitive Engineering, 47-50. https://doi.org/10.47852/bonviewJCCE2202213
Tan, R. P., & Zhang, W. D. (2021). Decision-making method based on new entropy and refined single-valued neutrosophic sets and its application in typhoon disaster assessment. Applied Intelligence, 51(1), 283-307. https://doi.org/10.1007/s10489-020-01706-3
Voskoglou, M., & Broumi, S. (2022). A hybrid method for the assessment of analogical reasoning skills. Journal of fuzzy extension and applications, 3(2), 152-157. 10.22105/JFEA.2022.342139.1220
Vellapandi, R., & Gunasekaran, S. (2020). A new decision making approach for winning strategy based on muti soft set logic. Journal of fuzzy extension and applications, 1(2), 119-129. 10.22105/JFEA.2020.249373.1013
Wang, H., Smarandache, F., Zhang, Y. Q., & Sunderraman, R. (2010). Single valued neutrosophic sets. Multispace Multistructure 4:410–413
Yager, R.R. (2013). Pythagorean fuzzy subsets. In Proceedings of the 2013 Joint IFSAWorld Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), Edmonton, AB, Canada, 57–61. . https://doi.org/10.1109/IFSANAFIPS.2013.6608375
Zhang, K., Xie, Y., Noorkhah, S. A., Imeni, M., & Das, S. K. (2022). Neutrosophic management evaluation of insurance companies by a hybrid TODIM-BSC method: a case study in private insurance companies. Management Decision. https://doi.org/10.1108/MD-01-2022-0120
Zadeh, L. A. (1965). Fuzzy sets. Inf Control 8, 38–353. https://doi.org/10.2307/2272014
Zadeh, L. A. (2020). Similarity relations and fuzzy orderings. Inf. Sci., vol. 3, 177 – 200. https://doi.org/10.1016/S0020-0255(71)80005-1
