{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,12]],"date-time":"2024-07-12T05:15:57Z","timestamp":1720761357255},"reference-count":15,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2018,10]]},"abstract":"<jats:p> Hyperstructure is the generalized concept of algebraic structure. The study of it and its applications is extremely interesting, offering interesting results to one who is willing to look for structure. This paper deals with hyperstructures associated to the symmetric group [Formula: see text]. First, we define a new hyperoperation [Formula: see text] on [Formula: see text] and study its properties. Next, we prove that [Formula: see text] is a single-power cyclic hypergroup with finite period. Then, we determine the set of all automorphisms of [Formula: see text] and prove that it is a finite group under the operation of function composition. Finally, we construct a sequence of join spaces on [Formula: see text] and find its fuzzy grade. <\/jats:p>","DOI":"10.1142\/s1793830918500702","type":"journal-article","created":{"date-parts":[[2018,9,3]],"date-time":"2018-09-03T02:40:38Z","timestamp":1535942438000},"page":"1850070","source":"Crossref","is-referenced-by-count":1,"title":["The cyclic hypergroup associated with Sn, its automorphism group and its fuzzy grade"],"prefix":"10.1142","volume":"10","author":[{"given":"M.","family":"Al Tahan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Lebanese International University, Lebanon"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"B.","family":"Davvaz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Yazd University, Yazd, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2018,10,11]]},"reference":[{"key":"S1793830918500702BIB002","first-page":"221","volume":"27","author":"Corsini P.","year":"2003","journal-title":"Southeast Asian Bull. Math."},{"key":"S1793830918500702BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3714-1"},{"key":"S1793830918500702BIB004","doi-asserted-by":"crossref","unstructured":"B. Davvaz,  Polygroup Theory and Related Systems  (World Scientific Publishing,  Hackensack, NJ,  2013),  viii+200 pp.","DOI":"10.1142\/8593"},{"issue":"1","key":"S1793830918500702BIB005","first-page":"44","volume":"30","author":"De Salvo M.","year":"1981","journal-title":"Atti Sem. Mat. Fis. Univ. Modena"},{"key":"S1793830918500702BIB006","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511623646"},{"key":"S1793830918500702BIB007","doi-asserted-by":"publisher","DOI":"10.1080\/00927870600936732"},{"key":"S1793830918500702BIB008","first-page":"69","volume":"7","author":"Leoreanu V.","year":"2000","journal-title":"Ital. J. Pure Appl. Math."},{"key":"S1793830918500702BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2007.06.025"},{"key":"S1793830918500702BIB011","first-page":"165","volume":"2","author":"Mittas J.","year":"1972","journal-title":"Math. Balk."},{"key":"S1793830918500702BIB012","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1950-010-7"},{"key":"S1793830918500702BIB013","doi-asserted-by":"crossref","first-page":"v+67","DOI":"10.1080\/00029890.1961.11989823","volume":"68","author":"Prenowitz W.","year":"1961","journal-title":"Amer. Math. Monthly"},{"key":"S1793830918500702BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-9438-9"},{"issue":"1","key":"S1793830918500702BIB015","first-page":"3","volume":"22","author":"Vougiouklis T.","year":"1981","journal-title":"Acta Univ. Carolin. Math. Phys."},{"key":"S1793830918500702BIB016","volume-title":"Hyperstructures and Their Representations","author":"Vougiouklis T.","year":"1994"},{"key":"S1793830918500702BIB017","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830918500702","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T12:40:17Z","timestamp":1565181617000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830918500702"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10]]},"references-count":15,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2018,10,11]]},"published-print":{"date-parts":[[2018,10]]}},"alternative-id":["10.1142\/S1793830918500702"],"URL":"https:\/\/doi.org\/10.1142\/s1793830918500702","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,10]]}}}