{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T08:17:04Z","timestamp":1760170624272,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,12,9]],"date-time":"2021-12-09T00:00:00Z","timestamp":1639008000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61632002"],"award-info":[{"award-number":["61632002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Key R&amp;D Program of China","award":["2018YFB1005100"],"award-info":[{"award-number":["2018YFB1005100"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this work, we study the notion of w-pseudo-order on an ordered (semi)hyperring and give some explicit examples. In addition, we give some examples to compare weak pseudo-order relations with pseudo-order relations. Finally, we construct ordered (semi)hyperrings using regular relations.<\/jats:p>","DOI":"10.3390\/sym13122371","type":"journal-article","created":{"date-parts":[[2021,12,10]],"date-time":"2021-12-10T02:07:18Z","timestamp":1639102038000},"page":"2371","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Note on the w-Pseudo-Orders in Ordered (Semi)Hyperrings"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9328-0774","authenticated-orcid":false,"given":"Xiaoli","family":"Qiang","sequence":"first","affiliation":[{"name":"Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7859-5409","authenticated-orcid":false,"given":"Hao","family":"Guan","sequence":"additional","affiliation":[{"name":"Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8717-9530","authenticated-orcid":false,"given":"Hossein","family":"Rashmanlou","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Mazandaran, Babolsar 47415, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,9]]},"reference":[{"key":"ref_1","unstructured":"Marty, F. (1934). Sur une Generalization de la Notion de Groupe, Congres Math. Scandinaves. [8th ed.]."},{"key":"ref_2","unstructured":"Davvaz, B., and Leoreanu-Fotea, V. (2007). Hyperring Theory and Applications, International Academic Press."},{"key":"ref_3","first-page":"85","article-title":"On ordered hyperstructures","volume":"73","author":"Heidari","year":"2011","journal-title":"Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/BF02573514","article-title":"On subdirectly irreducible ordered semigroups","volume":"50","author":"Kehayopulu","year":"1995","journal-title":"Semigroup Forum"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1007\/BF02573534","article-title":"Pseudoorder in ordered semigroups","volume":"50","author":"Kehayopulu","year":"1995","journal-title":"Semigroup Forum"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1016\/j.ejc.2014.08.006","article-title":"Relationship between ordered semihypergroups and ordered semigroups by using pseudoorder","volume":"44","author":"Davvaz","year":"2015","journal-title":"Eur. J. Combin."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1155\/2021\/6683910","article-title":"A study on A-I-\u0393-hyperideals and (m,n)-\u0393-hyperfilters in ordered \u0393-Semihypergroups","volume":"2021","author":"Rao","year":"2021","journal-title":"Discrete Dyn. Nat. Soc."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1016\/j.jalgebra.2015.11.026","article-title":"Ordered regular equivalence relations on ordered semihypergroups","volume":"450","author":"Gu","year":"2016","journal-title":"J. Algebra"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1515\/math-2018-0016","article-title":"A further study on ordered regular equivalence relations in ordered semihypergroups","volume":"16","author":"Tang","year":"2018","journal-title":"Open Math."},{"key":"ref_10","first-page":"35","article-title":"Ordered Krasner hyperrings","volume":"12","author":"Omidi","year":"2017","journal-title":"Iran. J. Math. Sci. Inform."},{"key":"ref_11","first-page":"131","article-title":"Foundations of ordered (semi)hyperrings","volume":"22","author":"Omidi","year":"2016","journal-title":"J. Indones. Math. Soc."},{"key":"ref_12","first-page":"601","article-title":"Construction of ordered regular equivalence relations on ordered semihyperrings","volume":"40","author":"Omidi","year":"2018","journal-title":"Honam Math. J."},{"key":"ref_13","first-page":"87","article-title":"Some properties of derivations and m-k-hyperideals in ordered semihyperrings","volume":"83","author":"Rao","year":"2021","journal-title":"Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys."},{"key":"ref_14","first-page":"125","article-title":"Left k-bi-quasi hyperideals in ordered semihyperrings","volume":"83","author":"Rao","year":"2021","journal-title":"Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"413","DOI":"10.3389\/fphy.2020.555573","article-title":"Some properties of relative bi-(int-)\u0393-hyperideals in ordered \u0393-semihypergroups","volume":"8","author":"Rao","year":"2020","journal-title":"Front. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1155\/S0161171283000265","article-title":"A class of hyperrings and hyperfields","volume":"6","author":"Krasner","year":"1983","journal-title":"Int. J. Math. Math Sci."},{"key":"ref_17","first-page":"21","article-title":"On some representation of hypergroups","volume":"26","author":"Vougiouklis","year":"1990","journal-title":"Ann. Sci. Univ. Clermont-Ferrand II Math."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Kou, Z., Kosari, S., Monemrad, M., Akhoundi, M., and Omidi, S. (2021). A note on the connection between ordered semihyperrings. 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