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We give the main theorem which characterizes the bi-hyperideals in terms of fuzzy bi-hyperideals. Then, we characterize the left and right simple, the completely regular, and the strongly regular ordered semihypergroups by means of fuzzy bi-hyperideals.<\/jats:p>","DOI":"10.3233\/ifs-141494","type":"journal-article","created":{"date-parts":[[2015,7,1]],"date-time":"2015-07-01T11:36:19Z","timestamp":1435750579000},"page":"2141-2148","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":15,"title":["Characterizations of (fuzzy) bi-hyperideals in ordered semihypergroups"],"prefix":"10.1177","volume":"28","author":[{"given":"Bundit","family":"Pibaljommee","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bijan","family":"Davvaz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Yazd University, Yazd, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2015,6,23]]},"reference":[{"key":"e_1_3_1_2_1","first-page":"569","article-title":"On ordered semigroups","volume":"14","author":"Alimov NG","year":"1950","unstructured":"AlimovNG1950On ordered semigroupsIzvestiya Akad Nauk SSSR14569576","journal-title":"Izvestiya Akad Nauk SSSR"},{"issue":"1","key":"e_1_3_1_3_1","first-page":"717","article-title":"On semihypergroup and hypergroup homomorphisms","volume":"6","author":"Bonansinga P","year":"1982","unstructured":"BonansingaPCorsiniP1982On semihypergroup and hypergroup homomorphismsBoll Un Mat Ital B61(2)717727","journal-title":"Boll Un Mat Ital B"},{"key":"e_1_3_1_4_1","first-page":"19","article-title":"Commutative hypergroups in the sense of Marty and ordered sets","author":"Chvalina J","year":"1994","unstructured":"ChvalinaJ1994Commutative hypergroups in the sense of Marty and ordered setsProceedings Summer School General Algebra and Ordered Sets1930Horni Lipova","journal-title":"Proceedings Summer School General Algebra and Ordered Sets"},{"key":"e_1_3_1_5_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1958-10221-9"},{"key":"e_1_3_1_6_1","author":"Corsini P","year":"1993","unstructured":"CorsiniP1993Prolegomena of hypergroup theoryAviani Editore","journal-title":"Prolegomena of hypergroup theory"},{"key":"e_1_3_1_7_1","unstructured":"CorsiniPLeoreanuV2003Applications of hyperstructure theoryKluwer Academic PublishersDordrecht Hardbound"},{"key":"e_1_3_1_8_1","first-page":"95","article-title":"semisimple ihypergroups in terms of hyperideals and fuzzy hyperideals","volume":"8","author":"Corsini P","year":"2011","unstructured":"CorsiniPShabirMMahmoodT2011semisimple ihypergroups in terms of hyperideals and fuzzy hyperidealsIran J Fuzzy Syst895111","journal-title":"Iran J Fuzzy Syst"},{"key":"e_1_3_1_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10114-012-0314-x"},{"key":"e_1_3_1_10_1","first-page":"67","article-title":"Fuzzy hyperideals in semihypergroups","volume":"8","author":"Davvaz B","year":"2000","unstructured":"DavvazB2000Fuzzy hyperideals in semihypergroupsItalian J Pure Appl Math86774","journal-title":"Italian J Pure Appl Math"},{"issue":"2","key":"e_1_3_1_11_1","first-page":"110","article-title":"More general forms of interval valued fuzzy filters of ordered semigroups","volume":"15","author":"Davvaz B","year":"2013","unstructured":"DavvazBKhanASarminNHKhanH2013More general forms of interval valued fuzzy filters of ordered semigroupsInt J Fuzzy Syst152110126","journal-title":"Int J Fuzzy Syst"},{"issue":"2","key":"e_1_3_1_12_1","first-page":"53","article-title":"Some results on congruences in semihypergroups","volume":"23","author":"Davvaz B","year":"2000","unstructured":"DavvazB2000Some results on congruences in semihypergroupsB Malays Math Sci So2325358","journal-title":"B Malays Math Sci So"},{"key":"e_1_3_1_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10587-005-0076-z"},{"key":"e_1_3_1_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF03009938"},{"issue":"29","key":"e_1_3_1_15_1","first-page":"203","article-title":"Intuitionistic hyperideals of semihypergroups","volume":"2","author":"Davvaz B","year":"2006","unstructured":"DavvazB2006Intuitionistic hyperideals of semihypergroupsB Malays Math Sci So229(1)203207","journal-title":"B Malays Math Sci So"},{"key":"e_1_3_1_16_1","first-page":"55","article-title":"Nezhad and A. 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