{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T21:04:18Z","timestamp":1768683858105,"version":"3.49.0"},"reference-count":33,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,5,18]],"date-time":"2023-05-18T00:00:00Z","timestamp":1684368000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Researchers Supporting Project","award":["PNURSP2023R87"],"award-info":[{"award-number":["PNURSP2023R87"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This study applies the hyperstructure theory to BF-algebra, which is an algebraic structure. In fact, we define hyper-BF-algebras and hyper-BF ideals and investigate several of their related characteristics. BF-algebra and hyper-BF ideal characteristics are taken into account, and supported examples are built. Here, we also develop new concepts known as hyper-B-algebra, hyper-BG-algebra, and hyper-BH algebra as generalizations of other classes of hyper-BCK-\/BCI-algebras. Additionally, we demonstrate that each hyper-BF is a weak hyper-BF in hyper-BF-algebra, but the opposite is not true. It is further established that the intersection of the weak hyper-BF ideal family is weak.<\/jats:p>","DOI":"10.3390\/sym15051106","type":"journal-article","created":{"date-parts":[[2023,5,18]],"date-time":"2023-05-18T06:00:29Z","timestamp":1684389629000},"page":"1106","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Hyperstructure Theory Applied to BF-Algebras"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5596-5841","authenticated-orcid":false,"given":"Ghulam","family":"Muhiuddin","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5529-0565","authenticated-orcid":false,"given":"Nabilah","family":"Abughazalah","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ahsan","family":"Mahboob","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Madanapalle Institute of Technology & Science, Madanapalle 517325, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abdullah G.","family":"Alotaibi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,18]]},"reference":[{"key":"ref_1","first-page":"19","article-title":"On axiom systems of propositional calculi","volume":"42","author":"Imai","year":"1966","journal-title":"Proc. Jpn. Acad."},{"key":"ref_2","first-page":"26","article-title":"An algebra related with a propositional calculus","volume":"42","year":"1966","journal-title":"Proc. Jpn. Acad."},{"key":"ref_3","first-page":"21","article-title":"On B-algebras","volume":"54","author":"Neggers","year":"2002","journal-title":"Math. Vensik"},{"key":"ref_4","first-page":"347","article-title":"On BH-algebras","volume":"1","author":"Jun","year":"1998","journal-title":"Sci. Math. Jpn."},{"key":"ref_5","first-page":"497","article-title":"On BG-algebras","volume":"41","author":"Kim","year":"2008","journal-title":"Demo. 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