{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:47:18Z","timestamp":1777704438417,"version":"3.51.4"},"reference-count":20,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2018,8,22]],"date-time":"2018-08-22T00:00:00Z","timestamp":1534896000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2018,10,27]]},"abstract":"<jats:p>\n                    In this paper, (2,\n                    <jats:italic>M<\/jats:italic>\n                    )-double fuzzifying topology as a generalized (2,\n                    <jats:italic>M<\/jats:italic>\n                    )-fuzzifying topology introduced by H\u00f6hle [\n                    <jats:xref ref-type=\"bibr\">7<\/jats:xref>\n                    ] is introduced. The relations between (2,\n                    <jats:italic>M<\/jats:italic>\n                    )-double fuzzy topology and (2,\n                    <jats:italic>M<\/jats:italic>\n                    )-double fuzzifying topology are studied. Also, we provided the definition of (2,\n                    <jats:italic>M<\/jats:italic>\n                    )-double fuzzifying preproximity structure. Not only that we studied the properties of these new notions, but we have also generated (2,\n                    <jats:italic>M<\/jats:italic>\n                    )-double fuzzifying topology from (2,\n                    <jats:italic>M<\/jats:italic>\n                    )-double fuzzifying preproximity. Finally, we introduced (2,\n                    <jats:italic>M<\/jats:italic>\n                    )-double fuzzifying preproximially continuous mapping which it used in more properties.\n                  <\/jats:p>","DOI":"10.3233\/jifs-17691","type":"journal-article","created":{"date-parts":[[2018,8,24]],"date-time":"2018-08-24T13:54:03Z","timestamp":1535118843000},"page":"4643-4655","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["(2,\n                    <i>M<\/i>\n                    )- Double fuzzifying topological spaces and (2,\n                    <i>M<\/i>\n                    )-double fuzzifying preproximity spaces"],"prefix":"10.1177","volume":"35","author":[{"given":"A.A.","family":"Abd El-latif","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Arts at Belqarn, Sabt Al-Alaya, University of Bisha, Kingdom of Saudi Arabia"},{"name":"High Institute of Computer King Marriott, Alexandria, Egypt"}]},{"given":"Mohammed M.","family":"Khalaf","sequence":"additional","affiliation":[{"name":"High Institute of Engineering and Technology King Marriott, Alexandria, Egypt"}]}],"member":"179","published-online":{"date-parts":[[2018,8,22]]},"reference":[{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(84)90221-X"},{"key":"e_1_3_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(87)90154-0"},{"key":"e_1_3_1_5_2","first-page":"341","article-title":"Infinitesimal spaces","volume":"76","author":"Efremovic V.A.","year":"1951","unstructured":"EfremovicV.A., Infinitesimal spaces, Doklady Akademii Nauk, SSSR 76 (1951), 341\u2013343. 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