{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:49:42Z","timestamp":1747190982320,"version":"3.40.5"},"reference-count":42,"publisher":"Wiley","license":[{"start":{"date-parts":[[2022,9,23]],"date-time":"2022-09-23T00:00:00Z","timestamp":1663891200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2022,9,23]]},"abstract":"<jats:p>In this study, fuzzy ideals in pseudo-hoop algebras are presented. Also, we investigate fuzzy congruences relations on pseudo-hoop algebras induced by fuzzy ideals. By using fuzzy ideals, we create the fuzzy quotient pseudo-hoop algebras and identify and demonstrate the one-to-one relationship between the set of all normal fuzzy ideals of a pseudo-hoop algebra <jats:inline-formula>\n                     <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\">\n                        <a:mi>H<\/a:mi>\n                     <\/a:math>\n                  <\/jats:inline-formula> with conditions <jats:inline-formula>\n                     <c:math xmlns:c=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\">\n                        <c:mfenced open=\"(\" close=\")\" separators=\"|\">\n                           <c:mrow>\n                              <c:mi>p<\/c:mi>\n                              <c:mtext>\u2009\u2009<\/c:mtext>\n                              <c:mi>D<\/c:mi>\n                              <c:mi>N<\/c:mi>\n                           <\/c:mrow>\n                        <\/c:mfenced>\n                     <\/c:math>\n                  <\/jats:inline-formula> and the set of all fuzzy congruences relation on <jats:inline-formula>\n                     <h:math xmlns:h=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\">\n                        <h:mi>H<\/h:mi>\n                     <\/h:math>\n                  <\/jats:inline-formula>. Additionally, we investigate the relationship between fuzzy ideals and fuzzy filters in pseudo-hoop algebras by considering the set of complement elements of pseudo-hoop algebras. Lastly, we study fuzzy prime ideals and fuzzy <jats:inline-formula>\n                     <j:math xmlns:j=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\">\n                        <j:mo>\u2299<\/j:mo>\n                     <\/j:math>\n                  <\/jats:inline-formula>-prime ideals and their relation.<\/jats:p>","DOI":"10.1155\/2022\/4643252","type":"journal-article","created":{"date-parts":[[2022,9,23]],"date-time":"2022-09-23T19:20:16Z","timestamp":1663960816000},"page":"1-10","source":"Crossref","is-referenced-by-count":0,"title":["Fuzzy Ideals in Pseudo-Hoop Algebras"],"prefix":"10.1155","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9832-9522","authenticated-orcid":true,"given":"Teferi Getachew","family":"Alemayehu","sequence":"first","affiliation":[{"name":"Department of Mathematics, Debre Berhan University, Debre Berhan, Ethiopia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.4064\/fm-64-3-257-287"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.4064\/fm-69-1-1-14"},{"issue":"1-2","key":"3","first-page":"153","article-title":"Pseudo-hoops","volume":"11","author":"G. 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