{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:52:08Z","timestamp":1760151128735,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,2,24]],"date-time":"2022-02-24T00:00:00Z","timestamp":1645660800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"publisher","award":["62081240416"],"award-info":[{"award-number":["62081240416"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>BZ-algebra, as the common generalization of BCI-algebra and BCC-algebra, is a kind of important logic algebra. Herein, the new concepts of QM-BZ-algebra and quasi-hyper BZ-algebra are proposed and their structures and constructions are studied. First, the definition of QM-BZ-algebra is presented, and the structure of QM-BZ-algebra is obtained: Each QM-BZ-algebra is KG-union of quasi-alter BCK-algebra and anti-grouped BZ-algebra. Second, the new concepts of generalized quasi-left alter (hyper) BZ-algebras and QM-hyper BZ-algebra are introduced, and some characterizations of them are investigated. Third, the definition of quasi-hyper BZ-algebra is proposed, and the relationships among BZ-algebra, hyper BZ-algebra, quasi-hyper BCI-algebra, and quasi-hyper BZ-algebra are discussed. Finally, several special classes of quasi-hyper BZ-algebras are studied in depth and the following important results are proved: (1) an anti-grouped quasi-hyper BZ-algebra is an anti-grouped BZ-algebra; (2) every generalized anti-grouped quasi-hyper BZ-algebra corresponds to a semihypergroup.<\/jats:p>","DOI":"10.3390\/axioms11030093","type":"journal-article","created":{"date-parts":[[2022,2,24]],"date-time":"2022-02-24T07:22:35Z","timestamp":1645687355000},"page":"93","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["QM-BZ-Algebras and Quasi-Hyper BZ-Algebras"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7681-8365","authenticated-orcid":false,"given":"Yudan","family":"Du","sequence":"first","affiliation":[{"name":"School of Mathematics & Data Science, Shaanxi University of Science & Technology, Xi\u2019an 710021, China"}]},{"given":"Xiaohong","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics & Data Science, Shaanxi University of Science & Technology, Xi\u2019an 710021, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,24]]},"reference":[{"key":"ref_1","unstructured":"Meng, J., and Jun, Y.B. 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