aspg-21-4060-1791472329 20261008151209 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2026 27 2 Takaaki Fujita Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan Florentin Smarandache University of New Mexico, Gallup Campus, NM 87301, USA 16.00 Normal false false false EN-US X-NONE AR-SA DefSemiHidden="false" DefQFormat="false" DefPriority="99" LatentStyleCount="371"> UnhideWhenUsed="true" QFormat="true" Name="heading 2"/> UnhideWhenUsed="true" QFormat="true" Name="heading 3"/> UnhideWhenUsed="true" QFormat="true" Name="heading 4"/> UnhideWhenUsed="true" QFormat="true" Name="heading 5"/> UnhideWhenUsed="true" QFormat="true" Name="heading 6"/> UnhideWhenUsed="true" QFormat="true" Name="heading 7"/> UnhideWhenUsed="true" QFormat="true" Name="heading 8"/> UnhideWhenUsed="true" QFormat="true" Name="heading 9"/> Name="index 1"/> Name="index 2"/> Name="index 3"/> 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Table 6 Colorful Accent 4"/> Name="Grid Table 7 Colorful Accent 4"/> Name="Grid Table 1 Light Accent 5"/> Name="Grid Table 6 Colorful Accent 5"/> Name="Grid Table 7 Colorful Accent 5"/> Name="Grid Table 1 Light Accent 6"/> Name="Grid Table 6 Colorful Accent 6"/> Name="Grid Table 7 Colorful Accent 6"/> Name="List Table 1 Light Accent 1"/> Name="List Table 6 Colorful Accent 1"/> Name="List Table 7 Colorful Accent 1"/> Name="List Table 1 Light Accent 2"/> Name="List Table 6 Colorful Accent 2"/> Name="List Table 7 Colorful Accent 2"/> Name="List Table 1 Light Accent 3"/> Name="List Table 6 Colorful Accent 3"/> Name="List Table 7 Colorful Accent 3"/> Name="List Table 1 Light Accent 4"/> Name="List Table 6 Colorful Accent 4"/> Name="List Table 7 Colorful Accent 4"/> Name="List Table 1 Light Accent 5"/> Name="List Table 6 Colorful Accent 5"/> Name="List Table 7 Colorful Accent 5"/> Name="List Table 1 Light Accent 6"/> Name="List Table 6 Colorful Accent 6"/> Name="List Table 7 Colorful Accent 6"/> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin-top:0in; mso-para-margin-right:0in; mso-para-margin-bottom:8.0pt; mso-para-margin-left:0in; line-height:107%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri",sans-serif; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:Arial; mso-bidi-theme-font:minor-bidi;} A variety of mathematical frameworks—such as fuzzy sets, intuitionistic fuzzy sets, neutrosophic sets, soft sets, rough sets, and plithogenic sets—have been developed to model uncertainty, with wide applications in decision making, data analysis, and artificial intelligence. Within soft set theory, extensions like hypersoft sets, indeterm-soft sets, indeterm-hypersoft sets, bipolar soft sets, and bipolar hypersoft sets have further enhanced its expressive power. In this paper, we introduce two new constructs: bipolar indeterm-soft sets and bipolar indeterm-hypersoft sets. We provide their formal definitions, establish key algebraic properties, and demonstrate how they naturally combine bipolar evaluation with inherent indeterminacy. These models offer a versatile toolkit for capturing complex forms of uncertainty and lay the groundwork for future theoretical advances and practical applications in soft set theory. 2026 204 222 4060 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.270218 https://www.americaspg.com/journal/21/article/4060 https://www.americaspg.com/storage/11756830236.pdf