{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:41:12Z","timestamp":1777704072353,"version":"3.51.4"},"reference-count":30,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2018,7,30]],"date-time":"2018-07-30T00:00:00Z","timestamp":1532908800000},"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":[[2018,8,26]]},"abstract":"<jats:p>\n                    The aim of this paper is to introduce and study the concepts of fuzzifying semipre-\n                    <jats:italic>\u03b8<\/jats:italic>\n                    -neighborhood system of a point, fuzzifying semipre-\n                    <jats:italic>\u03b8<\/jats:italic>\n                    -closure of a set, fuzzifying semipre-\n                    <jats:italic>\u03b8<\/jats:italic>\n                    -interior of a set, fuzzifying semipre-\n                    <jats:italic>\u03b8<\/jats:italic>\n                    -open sets and fuzzifying semipre-\n                    <jats:italic>\u03b8<\/jats:italic>\n                    -closed sets in fuzzifying topological spaces, and investigate some of their basic properties. Also, we present two types of functions in a fuzzifying topological spaces called fuzzifying strong\n                    <jats:italic>\u03b2<\/jats:italic>\n                    -irresolute and fuzzifying weak\n                    <jats:italic>\u03b2<\/jats:italic>\n                    -irresolute functions. The interrelations of these functions with the parallel existing allied concepts are established. Further, several characterizations of these functions along with different conditions for their existence are obtained.\n                  <\/jats:p>","DOI":"10.3233\/jifs-172094","type":"journal-article","created":{"date-parts":[[2018,7,31]],"date-time":"2018-07-31T18:14:18Z","timestamp":1533060858000},"page":"2137-2148","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Strong\n                    <i>\u03b2<\/i>\n                    -irresoluteness and weak\n                    <i>\u03b2<\/i>\n                    -irresoluteness based on continuous valued logic"],"prefix":"10.1177","volume":"35","author":[{"given":"Ahmed Mostafa","family":"Khalil","sequence":"first","affiliation":[{"name":"College of Mathematics and Information Science, Shaanxi Normal University, Xi\u2019an, P.R. 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China"}]},{"given":"Fei","family":"You","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Yulin University, Yulin, China"}]},{"given":"Sheng-Quan","family":"Ma","sequence":"additional","affiliation":[{"name":"College of Information Science and Technology, Hainan Normal University, Haikou"}]}],"member":"179","published-online":{"date-parts":[[2018,7,30]]},"reference":[{"key":"e_1_3_3_2_2","first-page":"77","article-title":"\u03b2 -Open sets and \u03b2 -continuous mapping","volume":"12","author":"Abd El-Monsef M.E.","year":"1982","unstructured":"Abd El-MonsefM.E., El-DeebS.N. and MahmoudR.A., \u03b2 -Open sets and \u03b2 -continuous mapping, Bull Fac Sci Assiut Univ 12 (1982), 77\u201390.","journal-title":"Bull Fac Sci Assiut Univ"},{"key":"e_1_3_3_3_2","first-page":"24","article-title":"i-preopen sets","volume":"38","author":"Andrijevi\u0107 D.","year":"1986","unstructured":"Andrijevi\u0107D., i-preopen sets, Mat Vesnik 38 (1986), 24\u201332.","journal-title":"Mat Vesnik"},{"key":"e_1_3_3_4_2","first-page":"285","article-title":"El-Monsef, \u03b2 -Irresolute and \u03b2 -topological invariant","volume":"27","author":"Mahmoud R.A.","year":"1990","unstructured":"MahmoudR.A. and AbdM.E., El-Monsef, \u03b2 -Irresolute and \u03b2 -topological invariant, Proc Pakistan Acad Sci 27 (1990), 285\u2013296.","journal-title":"Proc Pakistan Acad Sci"},{"key":"e_1_3_3_5_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1024687630089"},{"key":"e_1_3_3_6_2","first-page":"235","article-title":"\u03b2 -Closure and \u03b2 -interior","volume":"10","author":"Abd El-Monsef M.E.","year":"1986","unstructured":"Abd El-MonsefM.E., MahmoudR.A. and LashinE.R., \u03b2 -Closure and \u03b2 -interior, J Fac Ed Ain Shams Univ 10 (1986), 235\u2013245.","journal-title":"J Fac Ed Ain Shams Univ"},{"key":"e_1_3_3_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(68)90057-7"},{"key":"e_1_3_3_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"e_1_3_3_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(94)90264-X"},{"issue":"3","key":"e_1_3_3_10_2","first-page":"707","article-title":"On fuzzy SP-continuity and \u03b2 s(\u03b2\n                  *s)-closedness","volume":"7","author":"Zahran A.M.","year":"1999","unstructured":"ZahranA.M., On fuzzy SP-continuity and \u03b2 s(\u03b2*s)-closedness, J Fuzzy Math 7(3) (1999), 707\u2013721.","journal-title":"J Fuzzy Math"},{"key":"e_1_3_3_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(91)90100-5"},{"issue":"3","key":"e_1_3_3_12_2","first-page":"547","article-title":"\u03b2 -continuity and D(c, \u03b2)-continuity in fuzzifying topology","volume":"7","author":"El-Hakeim A.","year":"1999","unstructured":"El-HakeimA., ZeyadaF.M. and SayedO.R., \u03b2 -continuity and D(c, \u03b2)-continuity in fuzzifying topology, J Fuzzy Math 7(3) (1999), 547\u2013558.","journal-title":"J Fuzzy Math"},{"key":"e_1_3_3_13_2","first-page":"297","article-title":"Fuzzy \u03b2 -irresolute functions and fuzzy \u03b2 -compact spaces in fuzzifying topology*","volume":"30","author":"Sayed O.R.","year":"2006","unstructured":"SayedO.R. and Abd-AllahM.A., Fuzzy \u03b2 -irresolute functions and fuzzy \u03b2 -compact spaces in fuzzifying topology*, Iran J Sci & Tech, Trans A 30 (2006), 297\u2013314.","journal-title":"Iran J Sci & Tech, Trans A"},{"issue":"1","key":"e_1_3_3_14_2","first-page":"1","article-title":"\u03b2 -Separation axioms based on \u0141ukasiewicz logic","volume":"1","author":"Sayed O.R.","year":"2012","unstructured":"SayedO.R., \u03b2 -Separation axioms based on \u0141ukasiewicz logic, Eng Sci Letters 1(1) (2012), 1\u201324.","journal-title":"Eng Sci Letters"},{"key":"e_1_3_3_15_2","doi-asserted-by":"publisher","DOI":"10.4236\/am.2012.39146"},{"key":"e_1_3_3_16_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-141522"},{"key":"e_1_3_3_17_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-161714"},{"key":"e_1_3_3_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(92)90181-3"},{"key":"e_1_3_3_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(93)90132-2"},{"key":"e_1_3_3_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(93)90215-4"},{"key":"e_1_3_3_21_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-2012-0588"},{"key":"e_1_3_3_22_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-141515"},{"key":"e_1_3_3_23_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-17845"},{"key":"e_1_3_3_24_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01001956"},{"key":"e_1_3_3_25_2","article-title":"Application of point set topology in the description of topological relations, 77\u2013 82. 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