{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:49:03Z","timestamp":1747190943590,"version":"3.40.5"},"reference-count":15,"publisher":"Wiley","license":[{"start":{"date-parts":[[2022,9,12]],"date-time":"2022-09-12T00:00:00Z","timestamp":1662940800000},"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":[[2022,9,12]]},"abstract":"<jats:p>This paper mainly focuses on building the <jats:inline-formula>\n                     <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\">\n                        <a:mi mathvariant=\"normal\">\u2112<\/a:mi>\n                     <\/a:math>\n                  <\/jats:inline-formula>-fuzzy filter theory of residuated multilattices. Firstly, we introduce the concepts of <jats:inline-formula>\n                     <d:math xmlns:d=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\">\n                        <d:mi mathvariant=\"normal\">\u2112<\/d:mi>\n                     <\/d:math>\n                  <\/jats:inline-formula>-fuzzy filter and <jats:inline-formula>\n                     <g:math xmlns:g=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\">\n                        <g:mi mathvariant=\"normal\">\u2112<\/g:mi>\n                     <\/g:math>\n                  <\/jats:inline-formula>-fuzzy deductive system of residuated multilattices. Then, we highlight their properties and show how they are linked. Secondly, we introduce the concept of prime <jats:inline-formula>\n                     <j:math xmlns:j=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\">\n                        <j:mi mathvariant=\"normal\">\u2112<\/j:mi>\n                     <\/j:math>\n                  <\/jats:inline-formula>-fuzzy filter and propose some illustrative examples. Then, we bring out their properties and show how they are related to the concept of <jats:inline-formula>\n                     <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\">\n                        <m:mi mathvariant=\"normal\">\u2112<\/m:mi>\n                     <\/m:math>\n                  <\/jats:inline-formula>-fuzzy prime filter. Thirdly, we characterize <jats:inline-formula>\n                     <p:math xmlns:p=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\">\n                        <p:mi mathvariant=\"normal\">\u2112<\/p:mi>\n                     <\/p:math>\n                  <\/jats:inline-formula>-fuzzy maximal filter and maximal <jats:inline-formula>\n                     <s:math xmlns:s=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\">\n                        <s:mi mathvariant=\"normal\">\u2112<\/s:mi>\n                     <\/s:math>\n                  <\/jats:inline-formula>-fuzzy filter by atoms and coatoms. In the case where <jats:inline-formula>\n                     <v:math xmlns:v=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M10\">\n                        <v:mi mathvariant=\"normal\">\u2112<\/v:mi>\n                     <\/v:math>\n                  <\/jats:inline-formula> is a distributive lattice, we prove that maximal <jats:inline-formula>\n                     <y:math xmlns:y=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M11\">\n                        <y:mi mathvariant=\"normal\">\u2112<\/y:mi>\n                     <\/y:math>\n                  <\/jats:inline-formula>-fuzzy filters are prime. Finally, we are interested in <jats:inline-formula>\n                     <bb:math xmlns:bb=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M12\">\n                        <bb:mi mathvariant=\"normal\">\u2112<\/bb:mi>\n                     <\/bb:math>\n                  <\/jats:inline-formula>-fuzzy cosets of an <jats:inline-formula>\n                     <eb:math xmlns:eb=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M13\">\n                        <eb:mi mathvariant=\"normal\">\u2112<\/eb:mi>\n                     <\/eb:math>\n                  <\/jats:inline-formula>-fuzzy filter, and we prove that the set of all <jats:inline-formula>\n                     <hb:math xmlns:hb=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M14\">\n                        <hb:mi mathvariant=\"normal\">\u2112<\/hb:mi>\n                     <\/hb:math>\n                  <\/jats:inline-formula>-fuzzy cosets of any <jats:inline-formula>\n                     <kb:math xmlns:kb=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M15\">\n                        <kb:mi mathvariant=\"normal\">\u2112<\/kb:mi>\n                     <\/kb:math>\n                  <\/jats:inline-formula>-fuzzy filter of a residuated multilattice is a residuated multilattice.<\/jats:p>","DOI":"10.1155\/2022\/6833943","type":"journal-article","created":{"date-parts":[[2022,9,12]],"date-time":"2022-09-12T21:05:18Z","timestamp":1663016718000},"page":"1-14","source":"Crossref","is-referenced-by-count":0,"title":["<a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\">\n                     <a:mi mathvariant=\"normal\">\u2112<\/a:mi>\n                  <\/a:math>-Fuzzy Cosets of <d:math xmlns:d=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\">\n                     <d:mi mathvariant=\"normal\">\u2112<\/d:mi>\n                  <\/d:math>-Fuzzy Filters of Residuated Multilattices"],"prefix":"10.1155","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3132-6874","authenticated-orcid":true,"given":"Pierre Carole","family":"Kengne","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, P.O. Box 67, Dschang, Cameroon"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9035-6753","authenticated-orcid":true,"given":"Blaise Bleriot","family":"Koguep Njionou","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, P.O. Box 67, Dschang, Cameroon"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8756-3487","authenticated-orcid":true,"given":"Daquin C\u00e8dric","family":"Awouafack","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, P.O. Box 67, Dschang, Cameroon"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5260-7686","authenticated-orcid":true,"given":"Luc Em\u00e9ry","family":"Di\u00e9kouam Fotso","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Higher Teacher\u2019s Training College, University of Maroua, Maroua, Cameroon"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.21136\/cmj.1954.100103"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2013.04.002"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365x(81)90263-6"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/s0019-9958(65)90241-x"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247x(67)90189-8"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1007\/s13370-011-0009-y"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-016-2113-2"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1007\/s10472-009-9146-5"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1142\/9789812799470_0023"},{"key":"10","first-page":"2287","article-title":"Fuzzy setting of residuated multilattices","volume":"10","author":"L. N. Maffeu Nzoda","year":"2015","journal-title":"Annals of Fuzzy Mathematics and Informatics"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2006.11.006"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2011.10.081"},{"issue":"2","key":"13","first-page":"221","article-title":"A new connection between hypergroups and fuzzy sets","volume":"27","author":"P. Corsini","year":"2003","journal-title":"Southeast Asian Bulletin of Mathematics"},{"issue":"1","key":"14","first-page":"53","article-title":"Some results on congruences on semihypergroups","volume":"23","author":"B. Davvaz","year":"2000","journal-title":"Bulletin of Malaysian Mathematical Sciences Society"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.12988\/imf.2006.06048"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2022\/6833943.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2022\/6833943.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2022\/6833943.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,12]],"date-time":"2022-09-12T21:05:22Z","timestamp":1663016722000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/ijmms\/2022\/6833943\/"}},"subtitle":[],"editor":[{"given":"Frederic","family":"Mynard","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2022,9,12]]},"references-count":15,"alternative-id":["6833943","6833943"],"URL":"https:\/\/doi.org\/10.1155\/2022\/6833943","relation":{},"ISSN":["1687-0425","0161-1712"],"issn-type":[{"type":"electronic","value":"1687-0425"},{"type":"print","value":"0161-1712"}],"subject":[],"published":{"date-parts":[[2022,9,12]]}}}