aspg-24-989-1791482204 20261008175644 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Journal of Neutrosophic and Fuzzy Systems JNFS 2771-6430 2771-6449 2022 2 1 Mikail Bal Gaziantep University, Turkey Mohammad Abobala Tishreen University, Syria In this paper, we show that for a finite game with two players A , B: Each winning strategy of the first player A can be represented by a neutrosophic subgroup of the neutrosophic group ( style='font-size:12.0pt;mso-ansi-font-size:12.0pt;mso-bidi-font-size:12.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-hansi-font-family:"Times New Roman";mso-hansi-theme-font:major-bidi; mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi; mso-bidi-language:AR-SY;font-style:italic;mso-bidi-font-style:normal'> style='mso-bidi-font-style:normal'> 115%;font-family:"Cambria Math",serif;mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:major-bidi;mso-bidi-language:AR-SY'>Z style='mso-bidi-font-style:normal'> 115%;font-family:"Cambria Math",serif;mso-hansi-font-family:"Times New Roman"; mso-hansi-theme-font:major-bidi;mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:major-bidi;mso-bidi-language:AR-SY'>2 dir=RTL> 12.0pt;line-height:115%;font-family:"Times New Roman",serif;mso-ascii-theme-font: major-bidi;mso-hansi-theme-font:major-bidi;mso-bidi-theme-font:major-bidi; mso-bidi-language:AR-SY;mso-ansi-font-style:italic'> dir=RTL>× style='mso-bidi-font-style:normal'> 115%;font-family:"Cambria Math",serif;mso-hansi-font-family:"Times New Roman"; mso-hansi-theme-font:major-bidi;mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:major-bidi;mso-bidi-language:AR-SY'> dir=LTR>.. style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman",serif; mso-ascii-theme-font:major-bidi;mso-hansi-theme-font:major-bidi;mso-bidi-theme-font: major-bidi;mso-bidi-language:AR-SY'>× style='font-size:12.0pt;mso-ansi-font-size:12.0pt;mso-bidi-font-size:12.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-hansi-font-family:"Times New Roman";mso-hansi-theme-font:major-bidi; mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi; mso-bidi-language:AR-SY;font-style:italic;mso-bidi-font-style:normal'> style='mso-bidi-font-style:normal'> 115%;font-family:"Cambria Math",serif;mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:major-bidi;mso-bidi-language:AR-SY'>Z style='mso-bidi-font-style:normal'> 115%;font-family:"Cambria Math",serif;mso-hansi-font-family:"Times New Roman"; mso-hansi-theme-font:major-bidi;mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:major-bidi;mso-bidi-language:AR-SY'>2 style='mso-bidi-font-style:normal'> 115%;font-family:"Cambria Math",serif;mso-hansi-font-family:"Times New Roman"; mso-hansi-theme-font:major-bidi;mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:major-bidi;mso-bidi-language:AR-SY'>)( style='mso-bidi-font-style:normal'> 115%;font-family:"Cambria Math",serif;mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:major-bidi;mso-bidi-language:AR-SY'>I style='mso-bidi-font-style:normal'> 115%;font-family:"Cambria Math",serif;mso-hansi-font-family:"Times New Roman"; mso-hansi-theme-font:major-bidi;mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:major-bidi;mso-bidi-language:AR-SY'>) , and each winning strategy of the second player B can be represented by an elementary abelian group style='font-size:12.0pt;mso-ansi-font-size:12.0pt;mso-bidi-font-size:12.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-hansi-font-family:"Times New Roman";mso-hansi-theme-font:major-bidi; mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi; mso-bidi-language:AR-SY;font-style:italic;mso-bidi-font-style:normal'> style='mso-bidi-font-style:normal'> 115%;font-family:"Cambria Math",serif;mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:major-bidi;mso-bidi-language:AR-SY'>Z style='mso-bidi-font-style:normal'> 115%;font-family:"Cambria Math",serif;mso-hansi-font-family:"Times New Roman"; mso-hansi-theme-font:major-bidi;mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:major-bidi;mso-bidi-language:AR-SY'>2 dir=RTL> 12.0pt;line-height:115%;font-family:"Times New Roman",serif;mso-ascii-theme-font: major-bidi;mso-hansi-theme-font:major-bidi;mso-bidi-theme-font:major-bidi; mso-bidi-language:AR-SY;mso-ansi-font-style:italic'> dir=RTL>× style='mso-bidi-font-style:normal'> 115%;font-family:"Cambria Math",serif;mso-hansi-font-family:"Times New Roman"; mso-hansi-theme-font:major-bidi;mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:major-bidi;mso-bidi-language:AR-SY'> dir=LTR>.. style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman",serif; mso-ascii-theme-font:major-bidi;mso-hansi-theme-font:major-bidi;mso-bidi-theme-font: major-bidi;mso-bidi-language:AR-SY'>× style='font-size:12.0pt;mso-ansi-font-size:12.0pt;mso-bidi-font-size:12.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-hansi-font-family:"Times New Roman";mso-hansi-theme-font:major-bidi; mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi; mso-bidi-language:AR-SY;font-style:italic;mso-bidi-font-style:normal'> style='mso-bidi-font-style:normal'> 115%;font-family:"Cambria Math",serif;mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:major-bidi;mso-bidi-language:AR-SY'>Z style='mso-bidi-font-style:normal'> 115%;font-family:"Cambria Math",serif;mso-hansi-font-family:"Times New Roman"; mso-hansi-theme-font:major-bidi;mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:major-bidi;mso-bidi-language:AR-SY'>2 . Also, we introduce the concept of algebraically relative games and present some examples on it. 2022 8 13 989 https://creativecommons.org/licenses/by/4.0/ 10.54216/JNFS.020101 https://www.americaspg.com/journal/24/article/989 https://www.americaspg.com/storage/7623.pdf