{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T22:25:08Z","timestamp":1773872708416,"version":"3.50.1"},"reference-count":13,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,4,28]],"date-time":"2025-04-28T00:00:00Z","timestamp":1745798400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004329","name":"Slovenian Research and Innovation Agency","doi-asserted-by":"publisher","award":["P2-0103"],"award-info":[{"award-number":["P2-0103"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/axioms14050338","type":"journal-article","created":{"date-parts":[[2025,4,28]],"date-time":"2025-04-28T09:39:47Z","timestamp":1745833187000},"page":"338","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["An Investigation into Bipolar Fuzzy Hoop Algebras and Their Applications"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6514-4027","authenticated-orcid":false,"given":"Tahsin","family":"Oner","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Ege University, 35100 Izmir, T\u00fcrkiye"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0921-6054","authenticated-orcid":false,"given":"Rajesh","family":"Neelamegarajan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Rajah Serfoji Government College, Thanjavur 613005, Tamil Nadu, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8661-7914","authenticated-orcid":false,"given":"Ravi Kumar","family":"Bandaru","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Advanced Sciences, VIT-AP University, Amaravati 522237, Andhra Pradesh, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3871-217X","authenticated-orcid":false,"given":"Hashem","family":"Bordbar","sequence":"additional","affiliation":[{"name":"Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"257","DOI":"10.4064\/fm-64-3-257-287","article-title":"Komplement\u00e4re Halbgruppen. 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