{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,9]],"date-time":"2025-09-09T22:25:57Z","timestamp":1757456757863,"version":"3.40.5"},"reference-count":17,"publisher":"Wiley","license":[{"start":{"date-parts":[[2022,6,13]],"date-time":"2022-06-13T00:00:00Z","timestamp":1655078400000},"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":[[2022,6,13]]},"abstract":"<jats:p>In this paper, a new notion of fuzzy local function called <jats:inline-formula>\n                     <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\">\n                        <a:mi>r<\/a:mi>\n                     <\/a:math>\n                  <\/jats:inline-formula>-fuzzy local function is introduced, and some properties are given in a fuzzy ideal topological space <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>X<\/c:mi>\n                              <c:mo>,<\/c:mo>\n                              <c:mi>\u03c4<\/c:mi>\n                              <c:mo>,<\/c:mo>\n                              <c:mi>\u2113<\/c:mi>\n                           <\/c:mrow>\n                        <\/c:mfenced>\n                     <\/c:math>\n                  <\/jats:inline-formula> in \u0160ostak sense. After that, the concepts of fuzzy upper (resp., lower) almost <jats:inline-formula>\n                     <h:math xmlns:h=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\">\n                        <h:mi>\u2113<\/h:mi>\n                     <\/h:math>\n                  <\/jats:inline-formula>-continuous, weakly <jats:inline-formula>\n                     <j:math xmlns:j=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\">\n                        <j:mi>\u2113<\/j:mi>\n                     <\/j:math>\n                  <\/jats:inline-formula>-continuous, and almost weakly <jats:inline-formula>\n                     <l:math xmlns:l=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\">\n                        <l:mi>\u2113<\/l:mi>\n                     <\/l:math>\n                  <\/jats:inline-formula>-continuous multifunctions are introduced. Some properties and characterizations of these multifunctions along with their mutual relationships are discussed with the help of examples.<\/jats:p>","DOI":"10.1155\/2022\/8954163","type":"journal-article","created":{"date-parts":[[2022,6,13]],"date-time":"2022-06-13T21:20:06Z","timestamp":1655155206000},"page":"1-10","source":"Crossref","is-referenced-by-count":1,"title":["A New Notion of Fuzzy Local Function and Some Applications"],"prefix":"10.1155","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2921-3224","authenticated-orcid":true,"given":"I. M.","family":"Taha","sequence":"first","affiliation":[{"name":"Department Basic Sciences, Higher Institute of Engineering and Technology, Menoufia, Egypt"},{"name":"Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt"}]},{"given":"S. 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