{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T17:39:53Z","timestamp":1776361193371,"version":"3.51.2"},"reference-count":25,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,6,24]],"date-time":"2023-06-24T00:00:00Z","timestamp":1687564800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia","award":["PNURSP2023R87"],"award-info":[{"award-number":["PNURSP2023R87"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this study, by generalizing the notion of fuzzy bi-ideals of ordered semirings, the notion of (\u2208,\u2208\u2228(\u03ba*,q\u03ba))-fuzzy bi-ideals is established. We prove that (\u2208,\u2208\u2228(\u03ba*,q\u03ba))-fuzzy bi-ideals are fuzzy bi-ideals but that the converse is not true, and an example is provided to support this proof. A condition is given under which fuzzy bi-ideals of ordered semirings coincide with (\u2208,\u2208\u2228(\u03ba*,q\u03ba))-fuzzy bi-ideals. An equivalent condition and certain correspondences between bi-ideals and (\u2208,\u2208\u2228(\u03ba*,q\u03ba))-fuzzy bi-ideals are presented. Moreover, the (\u03ba*,\u03ba)-lower part of (\u2208,\u2208\u2228(\u03ba*,q\u03ba))-fuzzy bi-ideals is described and depicted in terms of several classes of ordered semirings. Furthermore, it is shown that the ordered semiring is bi-simple if and only if it is (\u2208,\u2208\u2228(\u03ba*,q\u03ba))-fuzzy bi-simple.<\/jats:p>","DOI":"10.3390\/axioms12070626","type":"journal-article","created":{"date-parts":[[2023,6,26]],"date-time":"2023-06-26T05:28:02Z","timestamp":1687757282000},"page":"626","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A Novel Study of Fuzzy Bi-Ideals in Ordered Semirings"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5596-5841","authenticated-orcid":false,"given":"Ghulam","family":"Muhiuddin","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5529-0565","authenticated-orcid":false,"given":"Nabilah","family":"Abughazalah","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}]},{"given":"Ahsan","family":"Mahboob","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Madanapalle Institute of Technology & Science, Madanapalle 517325, India"}]},{"given":"Deena","family":"Al-Kadi","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistic, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,24]]},"reference":[{"key":"ref_1","first-page":"989","article-title":"On ordered ideals in ordered semirings","volume":"31","author":"Gan","year":"2011","journal-title":"J. Math. Res. Exp."},{"key":"ref_2","first-page":"624","article-title":"Associated groups for a semigroup","volume":"58","author":"Good","year":"1952","journal-title":"Bull. Am. Math. Soc."},{"key":"ref_3","first-page":"505","article-title":"On the bi-ideals in associative rings","volume":"46","author":"Lajos","year":"1970","journal-title":"Proc. Jpn. Acad."},{"key":"ref_4","first-page":"4272451","article-title":"Characterizations of intra-regular ordered semirings by ordered quasi-ideals","volume":"2016","author":"Pibaljommee","year":"2016","journal-title":"Int. J. Math. Math. Sci."},{"key":"ref_5","first-page":"121","article-title":"Prime ordered k-bi-ideals in ordered semirings","volume":"25","author":"Senarat","year":"2017","journal-title":"Quasigroups Relat. Syst."},{"key":"ref_6","first-page":"43","article-title":"Basic notions and properties of ordered semihyperrings","volume":"4","author":"Davvaz","year":"2016","journal-title":"Categ. Gen. Algebr. Struct. Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1083","DOI":"10.1016\/j.jtusci.2016.09.001","article-title":"Contribution to study special kinds of hyperideals in ordered semihyperrings","volume":"11","author":"Omidi","year":"2017","journal-title":"J. Taibah Univ. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"5768","DOI":"10.3934\/math.2020370","article-title":"Characterizations of ordered h-regular semirings by ordered h-ideals","volume":"5","author":"Anjum","year":"2020","journal-title":"AIMS Math."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1750020","DOI":"10.1142\/S1793557117500206","article-title":"Characterizations of ordered k-regular semirings by ordered k-ideals","volume":"10","author":"Patchakhieo","year":"2017","journal-title":"Asian-Eur. J. Math."},{"key":"ref_10","first-page":"1","article-title":"Characterizationsof ordered intra-k-regular semirings by ordered k-ideals","volume":"3","author":"Pibaljommee","year":"2018","journal-title":"Commun. Korean Math. Soc."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/0165-0114(93)90441-J","article-title":"Fuzzy semirings","volume":"60","author":"Ahsan","year":"1993","journal-title":"Fuzzy Sets Syst."},{"key":"ref_12","first-page":"17","article-title":"Fuzzy bi-ideals in semigroups","volume":"28","author":"Kuroki","year":"1979","journal-title":"Comment. Math. Univ. St. Pauli"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.fiae.2014.06.008","article-title":"Fuzzy ideals and fuzzy interior ideals in ordered semirings","volume":"6","author":"Mandal","year":"2014","journal-title":"Fuzzy Inf. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"60","DOI":"10.56947\/gjom.v2i4.208","article-title":"Fuzzy bi-ideals and fuzzy quasi-ideals in ordered semirings","volume":"2","author":"Mandal","year":"2014","journal-title":"Gulf J. Math."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"6443","DOI":"10.3233\/JIFS-18278","article-title":"Fuzzy Orders and Pseudo-fuzzy Orders on Semirings","volume":"36","author":"Gao","year":"2019","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_16","first-page":"1211","article-title":"Single valued neutrosophic (m,n)-ideals of ordered semirings","volume":"7","author":"Davvaz","year":"2022","journal-title":"AIMS Math."},{"key":"ref_17","first-page":"391","article-title":"Ordered semigroup characterized by their (\u2208,\u2208\u2228q)-fuzzy bi-ideals","volume":"32","author":"Jun","year":"2009","journal-title":"Bull. Malays. Math. Soc."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1219","DOI":"10.1007\/s00521-011-0569-7","article-title":"Fuzzy ideals of semirings","volume":"20","author":"Hedayati","year":"2011","journal-title":"Neural Comput. Appl."},{"key":"ref_19","first-page":"283","article-title":"A new type fuzzy quasi-ideals of Ordered Semigrouops","volume":"34","author":"Cristea","year":"2020","journal-title":"J. Mult.-Valued Log. Soft Comput."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"4195","DOI":"10.3233\/JIFS-190293","article-title":"A new type of fuzzy semiprime subsets in ordered semigroups","volume":"37","author":"Muhiuddin","year":"2019","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2412","DOI":"10.3934\/math.2020159","article-title":"Int-soft Ideals over the soft sets in ordered semigroups","volume":"5","author":"Muhiuddin","year":"2020","journal-title":"AIMS Math."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1014","DOI":"10.2991\/ijcis.d.210223.003","article-title":"Interval valued m-polar fuzzy BCK\/BCI-algebras","volume":"14","author":"Muhiuddin","year":"2021","journal-title":"Int. J. Comput. Intell. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/s44196-021-00006-z","article-title":"Generalized fuzzy ideals of BCI-algebras based on interval valued m-polar fuzzy structures","volume":"14","author":"Muhiuddin","year":"2021","journal-title":"Int. J. Comput. Intell. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"110519","DOI":"10.1016\/j.knosys.2023.110519","article-title":"A comparative study of evaluating and benchmarking sign language recognition system-based wearable sensory devices using a single fuzzy set","volume":"269","author":"Qahtan","year":"2023","journal-title":"Knowl.-Based Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"119958","DOI":"10.1016\/j.eswa.2023.119958","article-title":"Performance assessment of sustainable transportation in the shipping industry using a q-rung orthopair fuzzy rough sets-based decision-making methodology","volume":"223","author":"Qahtan","year":"2023","journal-title":"Expert Syst. Appl."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/7\/626\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:59:54Z","timestamp":1760126394000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/7\/626"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,24]]},"references-count":25,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2023,7]]}},"alternative-id":["axioms12070626"],"URL":"https:\/\/doi.org\/10.3390\/axioms12070626","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,6,24]]}}}