{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:50:53Z","timestamp":1760151053838,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,2,10]],"date-time":"2022-02-10T00:00:00Z","timestamp":1644451200000},"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":["61976130"],"award-info":[{"award-number":["61976130"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we study the connection between generalized quasi-left alter BCI-algebra and commutative Clifford semigroup by introducing the concept of an adjoint semigroup. We introduce QM-BCI algebra, in which every element is a quasi-minimal element, and prove that each QM-BCI algebra is equivalent to generalized quasi-left alter BCI-algebra. Then, we introduce the notion of generalized quasi-left alter-hyper BCI-algebra and prove that every generalized quasi-left alter-hyper BCI-algebra is a generalized quasi-left alter BCI-algebra. Next, we propose a new notion of quasi-hyper BCI algebra and discuss the relationship among them. Moreover, we study the subalgebras of quasi-hyper BCI algebra and the relationships between Hv-group and quasi-hyper BCI-algebra, hypergroup and quasi-hyper BCI-algebra. Finally, we propose the concept of a generalized quasi-left alter quasi-hyper BCI algebra and QM-quasi hyper BCI-algebra and discuss the relationships between them and related BCI-algebra.<\/jats:p>","DOI":"10.3390\/axioms11020072","type":"journal-article","created":{"date-parts":[[2022,2,11]],"date-time":"2022-02-11T02:37:46Z","timestamp":1644547066000},"page":"72","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["A Class of BCI-Algebra and Quasi-Hyper BCI-Algebra"],"prefix":"10.3390","volume":"11","author":[{"given":"Xiaohong","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematics & Data Science, Shaanxi University of Science & Technology, Xi\u2019an 710021, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7681-8365","authenticated-orcid":false,"given":"Yudan","family":"Du","sequence":"additional","affiliation":[{"name":"School of Mathematics & Data Science, Shaanxi University of Science & Technology, Xi\u2019an 710021, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,10]]},"reference":[{"key":"ref_1","unstructured":"Meng, J., and Jun, Y.B. 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