An Investigation into Bipolar Fuzzy Hoop Algebras and Their Applications
This paper introduces bipolar fuzzy sub-hoops and bipolar fuzzy filters within hoop algebras, extending fuzzy logic to incorporate both positive and negative membership degrees. We define these structures, explore their algebraic properties, and establish their interplay through rigorous theorems. K...
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| Language: | English |
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MDPI AG
2025-04-01
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| Online Access: | https://www.mdpi.com/2075-1680/14/5/338 |
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| author | Tahsin Oner Rajesh Neelamegarajan Ravi Kumar Bandaru Hashem Bordbar |
| author_facet | Tahsin Oner Rajesh Neelamegarajan Ravi Kumar Bandaru Hashem Bordbar |
| author_sort | Tahsin Oner |
| collection | DOAJ |
| description | This paper introduces bipolar fuzzy sub-hoops and bipolar fuzzy filters within hoop algebras, extending fuzzy logic to incorporate both positive and negative membership degrees. We define these structures, explore their algebraic properties, and establish their interplay through rigorous theorems. Key results include characterizations of bipolar fuzzy filters via level sets and conditions under which they become implicative filters. These findings enhance the theoretical framework of many-valued logic and offer practical applications in decision-making, image processing, and spatial reasoning under uncertainty. Our work provides a foundation for advanced fuzzy systems handling complex, contradictory information. |
| format | Article |
| id | doaj-art-37d91ca9eeaa459a9e3d6d89613ce079 |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-37d91ca9eeaa459a9e3d6d89613ce0792025-08-20T03:47:48ZengMDPI AGAxioms2075-16802025-04-0114533810.3390/axioms14050338An Investigation into Bipolar Fuzzy Hoop Algebras and Their ApplicationsTahsin Oner0Rajesh Neelamegarajan1Ravi Kumar Bandaru2Hashem Bordbar3Department of Mathematics, Faculty of Science, Ege University, 35100 Izmir, TürkiyeDepartment of Mathematics, Rajah Serfoji Government College, Thanjavur 613005, Tamil Nadu, IndiaDepartment of Mathematics, School of Advanced Sciences, VIT-AP University, Amaravati 522237, Andhra Pradesh, IndiaCentre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, SloveniaThis paper introduces bipolar fuzzy sub-hoops and bipolar fuzzy filters within hoop algebras, extending fuzzy logic to incorporate both positive and negative membership degrees. We define these structures, explore their algebraic properties, and establish their interplay through rigorous theorems. Key results include characterizations of bipolar fuzzy filters via level sets and conditions under which they become implicative filters. These findings enhance the theoretical framework of many-valued logic and offer practical applications in decision-making, image processing, and spatial reasoning under uncertainty. Our work provides a foundation for advanced fuzzy systems handling complex, contradictory information.https://www.mdpi.com/2075-1680/14/5/338hoopbipolar fuzzy sub-hoopbipolar fuzzy ideal |
| spellingShingle | Tahsin Oner Rajesh Neelamegarajan Ravi Kumar Bandaru Hashem Bordbar An Investigation into Bipolar Fuzzy Hoop Algebras and Their Applications Axioms hoop bipolar fuzzy sub-hoop bipolar fuzzy ideal |
| title | An Investigation into Bipolar Fuzzy Hoop Algebras and Their Applications |
| title_full | An Investigation into Bipolar Fuzzy Hoop Algebras and Their Applications |
| title_fullStr | An Investigation into Bipolar Fuzzy Hoop Algebras and Their Applications |
| title_full_unstemmed | An Investigation into Bipolar Fuzzy Hoop Algebras and Their Applications |
| title_short | An Investigation into Bipolar Fuzzy Hoop Algebras and Their Applications |
| title_sort | investigation into bipolar fuzzy hoop algebras and their applications |
| topic | hoop bipolar fuzzy sub-hoop bipolar fuzzy ideal |
| url | https://www.mdpi.com/2075-1680/14/5/338 |
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