{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:53:08Z","timestamp":1747191188114,"version":"3.40.5"},"reference-count":40,"publisher":"Wiley","license":[{"start":{"date-parts":[[2022,1,17]],"date-time":"2022-01-17T00:00:00Z","timestamp":1642377600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Fuzzy Systems"],"published-print":{"date-parts":[[2022,1,17]]},"abstract":"<jats:p>The notions of an <jats:inline-formula>\n                     <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\">\n                        <a:mi mathvariant=\"normal\">inf<\/a:mi>\n                     <\/a:math>\n                  <\/jats:inline-formula>-hesitant fuzzy <jats:inline-formula>\n                     <d:math xmlns:d=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\">\n                        <d:mi mathvariant=\"normal\">\u0393<\/d:mi>\n                     <\/d:math>\n                  <\/jats:inline-formula>-ideal and a <jats:inline-formula>\n                     <g:math xmlns:g=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\">\n                        <g:mfenced open=\"(\" close=\")\" separators=\"|\">\n                           <g:mrow>\n                              <g:mi mathvariant=\"normal\">sup<\/g:mi>\n                              <g:mo>,<\/g:mo>\n                              <g:mi mathvariant=\"normal\">inf<\/g:mi>\n                           <\/g:mrow>\n                        <\/g:mfenced>\n                     <\/g:math>\n                  <\/jats:inline-formula>-hesitant fuzzy <jats:inline-formula>\n                     <n:math xmlns:n=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\">\n                        <n:mi mathvariant=\"normal\">\u0393<\/n:mi>\n                     <\/n:math>\n                  <\/jats:inline-formula>-ideal, which are a generalization of an interval-valued fuzzy <jats:inline-formula>\n                     <q:math xmlns:q=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\">\n                        <q:mi mathvariant=\"normal\">\u0393<\/q:mi>\n                     <\/q:math>\n                  <\/jats:inline-formula>-ideal, of a <jats:inline-formula>\n                     <t:math xmlns:t=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\">\n                        <t:mi mathvariant=\"normal\">\u0393<\/t:mi>\n                     <\/t:math>\n                  <\/jats:inline-formula>-semigroup are introduced and some properties are investigated. Characterizations of the notions are provided in terms of sets, fuzzy sets, intuitionistic fuzzy sets, interval-valued fuzzy sets, and hesitant fuzzy sets. Furthermore, characterizations of a <jats:inline-formula>\n                     <w:math xmlns:w=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M10\">\n                        <w:mi mathvariant=\"normal\">\u0393<\/w:mi>\n                     <\/w:math>\n                  <\/jats:inline-formula>-ideal of a <jats:inline-formula>\n                     <z:math xmlns:z=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M11\">\n                        <z:mi mathvariant=\"normal\">\u0393<\/z:mi>\n                     <\/z:math>\n                  <\/jats:inline-formula>-semigroup are given in terms of <jats:inline-formula>\n                     <cb:math xmlns:cb=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M12\">\n                        <cb:mi mathvariant=\"normal\">inf<\/cb:mi>\n                     <\/cb:math>\n                  <\/jats:inline-formula>-hesitant and <jats:inline-formula>\n                     <fb:math xmlns:fb=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M13\">\n                        <fb:mfenced open=\"(\" close=\")\" separators=\"|\">\n                           <fb:mrow>\n                              <fb:mi mathvariant=\"normal\">sup<\/fb:mi>\n                              <fb:mo>,<\/fb:mo>\n                              <fb:mi mathvariant=\"normal\">inf<\/fb:mi>\n                           <\/fb:mrow>\n                        <\/fb:mfenced>\n                     <\/fb:math>\n                  <\/jats:inline-formula>-hesitant fuzzy <jats:inline-formula>\n                     <mb:math xmlns:mb=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M14\">\n                        <mb:mi mathvariant=\"normal\">\u0393<\/mb:mi>\n                     <\/mb:math>\n                  <\/jats:inline-formula>-ideals.<\/jats:p>","DOI":"10.1155\/2022\/9755894","type":"journal-article","created":{"date-parts":[[2022,1,17]],"date-time":"2022-01-17T18:20:07Z","timestamp":1642443607000},"page":"1-8","source":"Crossref","is-referenced-by-count":0,"title":["On <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\">\n                     <a:mi mathvariant=\"normal\">inf<\/a:mi>\n                  <\/a:math>-Hesitant Fuzzy <d:math xmlns:d=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\">\n                     <d:mi mathvariant=\"normal\">\u0393<\/d:mi>\n                  <\/d:math>-Ideals of <g:math xmlns:g=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\">\n                     <g:mi mathvariant=\"normal\">\u0393<\/g:mi>\n                  <\/g:math>-Semigroups"],"prefix":"10.1155","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2565-1948","authenticated-orcid":true,"given":"Pongpun","family":"Julatha","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phlai Chumphon, Mueang, Phitsanulok 65000, Thailand"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0475-3320","authenticated-orcid":true,"given":"Aiyared","family":"Iampan","sequence":"additional","affiliation":[{"name":"Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/s0019-9958(65)90241-x"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-37125-0_5"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1109\/fuzzy.2009.5276884"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1002\/int.20418"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2012.04.031"},{"issue":"1","key":"6","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1109\/TFUZZ.2011.2170076","article-title":"Hesitant fuzzy linguistic term sets for decision making","volume":"20","author":"R. 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