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Also, we proved that [Formula: see text] with some operations made a complete distributive bounded lattice, bounded hoop, bounded L-algebra, CKL-algebra, BCK-algebra, commutative integral quantum B-algebra and Boolean algebra. Finally, we presented a congruence relation on [Formula: see text] and we investigated the quotient of it. <\/jats:p>","DOI":"10.1142\/s1793830923501033","type":"journal-article","created":{"date-parts":[[2023,12,12]],"date-time":"2023-12-12T03:04:05Z","timestamp":1702350245000},"source":"Crossref","is-referenced-by-count":0,"title":["Algebraic structures on Soft\ud835\udd08(\ud835\udd43 )"],"prefix":"10.1142","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6416-2151","authenticated-orcid":false,"given":"M.","family":"Shirvani Bourojeni","sequence":"first","affiliation":[{"name":"Department of Mathematics, Payame Noor University, P. O. 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