{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,25]],"date-time":"2025-10-25T14:19:22Z","timestamp":1761401962153,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2018,11,1]],"date-time":"2018-11-01T00:00:00Z","timestamp":1541030400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The concept of quantum B-algebra was introduced by Rump and Yang, that is, unified algebraic semantics for various noncommutative fuzzy logics, quantum logics, and implication logics. In this paper, a new notion of q-filter in quantum B-algebra is proposed, and quotient structures are constructed by q-filters (in contrast, although the notion of filter in quantum B-algebra has been defined before this paper, but corresponding quotient structures cannot be constructed according to the usual methods). Moreover, a new, more general, implication algebra is proposed, which is called basic implication algebra and can be regarded as a unified frame of general fuzzy logics, including nonassociative fuzzy logics (in contrast, quantum B-algebra is not applied to nonassociative fuzzy logics). The filter theory of basic implication algebras is also established.<\/jats:p>","DOI":"10.3390\/sym10110573","type":"journal-article","created":{"date-parts":[[2018,11,1]],"date-time":"2018-11-01T11:31:47Z","timestamp":1541071907000},"page":"573","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["Q-Filters of Quantum B-Algebras and Basic Implication Algebras"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2320-0884","authenticated-orcid":false,"given":"Xiaohong","family":"Zhang","sequence":"first","affiliation":[{"name":"Department of Mathematics, Shaanxi University of Science and Technology, Xi\u2019an 710021, China"},{"name":"Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7538-7885","authenticated-orcid":false,"given":"Rajab Ali","family":"Borzooei","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shahid Beheshti University, Tehran 1983963113, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Young Bae","family":"Jun","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shahid Beheshti University, Tehran 1983963113, Iran"},{"name":"Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,11,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"H\u00e1jek, P. 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