Volume 8 • Issue 2 • PP: 49-61 • 2024
Classification of States for Literal Neutrosophic and Plithogenic Markov Chains
Open Access & Copyright
© 2024 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
View PDF Abstract
In this paper we represent many classifications of neutrosophic and plithogenic Markov Chains states including absorbent states, inessential and essential states, recurrent states and communicated states. We prove that if a state (i) according to a neutrosophic Markov Chain with neutrosophic transition matrix is classified as any of the previous classifications then it is also classified as the same classification in classical scene to two Markov Chains defined with transition matrices respectively. Also, we prove that if a state (i) according to a plithogenic Markov Chain with plithogenic transition matrix is classified as any of the previous classifications then it is also classified as the same classification in classical scene to three Markov Chains defined with transition matrices respectively. Many theorems and solved examples are presented and solved successfully.
Keywords
References
[1] F. Smarandache, “Indeterminacy in neutrosophic theories and their applications,” Int. J. Neutrosophic Sci., vol. 15, no. 2, 2021, doi: 10.5281/zenodo.5295819.
[2] F. Smarandache, “Introduction to Neutrosophic Measure, Neutrosophic Integral, and Neutrosophic Probability,” ArXiv, 2013.
[3] F. Smarandache, “Introduction to Plithogenic Logic as generalization of MultiVariate Logic,” Neutrosophic Sets Syst., vol. 45, 2021.
[4] F. Smarandache, “Plithogenic Set, an Extension of Crisp, Fuzzy, Intuitionistic Fuzzy, and Neutrosophic Sets,” Neutrosophic Sets Syst., vol. 21, pp. 153–166, 2018.
[5] M. Abobala, A. Hatip, N. Olgun, S. Broumi, A. A. Salama, and H. E. Khaled, “The Algebraic Creativity in The Neutrosophic Square Matrices,” Neutrosophic Sets Syst., vol. 40, no. February, pp. 1–11, 2021, doi: 10.5281/zenodo.4549301.
[6] M. Abobala, M. B. Ziena, R. I. Doewes, and Z. Hussein, “The Representation of Refined Neutrosophic Matrices By Refined Neutrosophic Linear Functions,” Int. J. Neutrosophic Sci., vol. 19, no. 1, 2022, doi: 10.54216/IJNS.190131.
[7] D. Zhang, Y. Ma, H. Zhao, and X. Yang, “Neutrosophic Clustering Algorithm Based on Sparse Regular Term Constraint,” Complexity, vol. 2021, 2021, doi: 10.1155/2021/6657849.
[8] R. Alhabib, M. M. Ranna, H. Farah, and A. Salama, “Some Neutrosophic Probability Distributions,” Neutrosophic Sets Syst., vol. 22, pp. 30–38, 2018.
[9] A. Astambli, M. B. Zeina, and Y. Karmouta, “Algebraic Approach to Neutrosophic Confidence Intervals,” J. Neutrosophic Fuzzy Syst., vol. 5, no. 2, pp. 08–22, 2023, doi: 10.54216/JNFS.050201.
[10] R. A. K. Sherwani, T. Arshad, M. Albassam, M. Aslam, and S. Abbas, “Neutrosophic entropy measures for the Weibull distribution: theory and applications,” Complex Intell. Syst., vol. 7, no. 6, 2021, doi: 10.1007/s40747-021-00501-y.
[11] M. B. Zeina, “Erlang Service Queueing Model with Neutrosophic Parameters,” Int. J. Neutrosophic Sci., vol. 6, no. 2, pp. 106–112, 2020, doi: 10.54216/IJNS.060202.
[12] M. B. Zeina, “Linguistic Single Valued Neutrosophic M/M/1 Queue,” Res. J. Aleppo Univ., vol. 144, 2021, Accessed: Feb. 21, 2023. [Online]. Available: https://www.researchgate.net/publication/348945390_Linguistic_Single_Valued_Neutrosophic_MM1_Queue
[13] H. Rashad and M. Mohamed, “Neutrosophic Theory and Its Application in Various Queueing Models: Case Studies,” Neutrosophic Sets Syst., vol. 42, 2021, doi: 10.5281/zenodo.4711516.
[14] S. Broumi, M. B. Zeina, M. Lathamaheswari, A. Bakali, and M. Talea, “A Maple Code to Perform Operations on Single Valued Neutrosophic Matrices,” Neutrosophic Sets Syst., vol. 49, 2022.
[15] M. Miari, M. T. Anan, and M. B. Zeina, “Neutrosophic Two Way ANOVA,” Int. J. Neutrosophic Sci., vol. 18, no. 3, 2022, doi: 10.54216/IJNS.180306.
[16] F. Smarandache, “Symbolic Neutrosophic Theory,” ArXiv, 2015, doi: 10.5281/ZENODO.32078.
[17] M. B. Zeina and A. Hatip, “Neutrosophic Random Variables,” Neutrosophic Sets Syst., vol. 39, 2021, doi: 10.5281/zenodo.4444987.
[18] C. Granados, “New Notions On Neutrosophic Random Variables,” Neutrosophic Sets Syst., vol. 47, 2021.
[19] C. Granados and J. Sanabria, “On Independence Neutrosophic Random Variables,” Neutrosophic Sets Syst., vol. 47, 2021.
[20] C. N. Bouza-Herrera and M. Subzar, “Estimating the Ratio of a Crisp Variable and a Neutrosophic Variable,” Int. J. Neutrosophic Sci., vol. 11, no. 1, 2020, doi: 10.5281/zenodo.4030309.
[21] M. B. Zeina and M. Abobala, “A novel approach of neutrosophic continuous probability distributions using AH-isometry with applications in medicine,” Cogn. Intell. with Neutrosophic Stat. Bioinforma., pp. 267–286, Jan. 2023, doi: 10.1016/B978-0-323-99456-9.00014-3.
[22] D. Dham, M. B. Zeina, and R. K. Al-hamido, “Symbolic Neutrosophic and Plithogenic Marshall-Olkin Type I Class of Distributions,” Neutrosophic Sets Syst., vol. 59, pp. 234–252, 2023.
[23] D. Danyah, M. B. Zeina, and R. K. Al Al-Hamido, “Literal Neutrosophic and Plithogenic Marshall-Olkin Type II Class of Distributions with Application to Exponential Distribution,” J. Neutrosophic Fuzzy Syst., vol. 8, no. 1, pp. 46–64, 2024, doi: 10.54216/jnfs.080106.
[24] M. B. Zeina, M. Abobala, A. Hatip, S. Broumi, and S. Jalal Mosa, “Algebraic Approach to Literal Neutrosophic Kumaraswamy Probability Distribution,” Neutrosophic Sets Syst., vol. 54, pp. 124–138, 2023.
[25] M. B. Zeina, S. Hemeda, M. Koreny, and M. Abobala, “On Symbolic n-Plithogenic Random Variables Using a Generalized Isomorphism,” vol. 59, 2023, doi: 10.5281/zenodo.10031266.
[26] M. B. Zeina, N. Altounji, M. Abobala, and Y. Karmouta, “Introduction to Symbolic 2-Plithogenic Probability Theory,” Galoitica J. Math. Struct. Appl., vol. 7, no. 1, 2023.
[27] N. Sets, N. Altounji, M. M. Ranneh, and M. B. Zeina, “Foundation of 2-Symbolic Plithogenic Maximum a Posteriori Estimation,” Neutrosophic Sets Syst., vol. 59, pp. 59–74, 2023.
[28] N. Sets, S. Massassati, M. B. Zeina, and Y. Karmouta, “Plithogenic and Neutrosophic Markov Chains : Modeling Uncertainty and Ambiguity in Stochastic Processes,” Neutrosophic Sets Syst., vol. 59, pp. 119–138, 2023.
Cite This Article
Choose your preferred format
Publisher's Note
The statements, opinions, and data presented in this article are solely those of the author(s) and do not necessarily represent those of ASPG, the journal, or its editors. ASPG and the editors disclaim responsibility for any harm arising from the use of any ideas, methods, instructions, or products described in this article, to the fullest extent permitted by applicable law.