aspg-24-2879-1791482589 20261008180309 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Journal of Neutrosophic and Fuzzy Systems JNFS 2771-6430 2771-6449 2024 8 2 Suhar Massassati Faculty of Science, Department of Mathematical Statistics, University of Aleppo, Aleppo, Syria Mohamed Bisher Zeina Faculty of Science, Department of Mathematical Statistics, University of Aleppo, Aleppo, Syria Yasin Karmouta Faculty of Science, Department of Mathematical Statistics, University of Aleppo, Aleppo, Syria 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 style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-fareast-font-family:"Times New Roman";mso-hansi-font-family:"Cambria Math"; mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi; color:black;mso-fareast-language:DE;mso-bidi-language:EN-US;mso-bidi-font-weight: bold;font-style:italic;mso-bidi-font-style:normal'> style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi;color:black;mso-fareast-language: DE;mso-bidi-language:EN-US'>M style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi;color:black;mso-fareast-language: DE;mso-bidi-language:EN-US'>N style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi;color:black;mso-fareast-language: DE;mso-bidi-language:EN-US'>=A+BI 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 style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi;color:black;mso-fareast-language: DE;mso-bidi-language:EN-US'>A,A+B respectively. Also, we prove that if a state (i) according to a plithogenic Markov Chain with plithogenic transition matrix style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-fareast-font-family:"Times New Roman";mso-hansi-font-family:"Cambria Math"; mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi; color:black;mso-fareast-language:DE;mso-bidi-language:EN-US;mso-bidi-font-weight: bold;font-style:italic;mso-bidi-font-style:normal'> style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi;color:black;mso-fareast-language: DE;mso-bidi-language:EN-US'>M style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi;color:black;mso-fareast-language: DE;mso-bidi-language:EN-US'>P style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi;color:black;mso-fareast-language: DE;mso-bidi-language:EN-US'>=A+B style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-fareast-font-family:"Times New Roman";mso-hansi-font-family:"Cambria Math"; mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi; color:black;mso-fareast-language:DE;mso-bidi-language:EN-US;mso-bidi-font-weight: bold;font-style:italic;mso-bidi-font-style:normal'> style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi;color:black;mso-fareast-language: DE;mso-bidi-language:EN-US'>P style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi;color:black;mso-fareast-language: DE;mso-bidi-language:EN-US'>1 style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi;color:black;mso-fareast-language: DE;mso-bidi-language:EN-US'>+C style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-fareast-font-family:"Times New Roman";mso-hansi-font-family:"Cambria Math"; mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi; color:black;mso-fareast-language:DE;mso-bidi-language:EN-US;mso-bidi-font-weight: bold;font-style:italic;mso-bidi-font-style:normal'> style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi;color:black;mso-fareast-language: DE;mso-bidi-language:EN-US'>P style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi;color:black;mso-fareast-language: DE;mso-bidi-language:EN-US'>2 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 style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi;color:black;mso-fareast-language: DE;mso-bidi-language:EN-US'>A,A+B,A+B+C respectively. Many theorems and solved examples are presented and solved successfully. 2024 49 61 2879 https://creativecommons.org/licenses/by/4.0/ 10.54216/JNFS.080206 https://www.americaspg.com/journal/24/article/2879 https://www.americaspg.com/storage/31717962191.pdf